towards self-pumped difference frequency generation in

Towards Self-Pumped Difference Frequency Generation in

Bragg Reflection Waveguide Lasers

by

Nima Zareian

A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy

Graduate Department of Electrical and Computer EngineeringUniversity of Toronto

c© Copyright 2016 by Nima Zareian

Abstract

Towards Self-Pumped Difference Frequency Generation in Bragg Reflection Waveguide

Lasers

Nima Zareian

Doctor of Philosophy

Graduate Department of Electrical and Computer Engineering

University of Toronto

2016

Bragg reflection waveguide lasers are demonstrated in the GaAs/AlGaAs material sys-

tem for phase-matched frequency conversion through second order nonlinearities. Bragg

waveguide design considerations such as modal propagation loss and far-field are studied.

Effect of etch depth on propagation loss of 2D ridge Bragg lasers is assessed both theo-

retically and experimentally, and the underlying physics is examined. The results allow

for design of functional Bragg lasers with minimal propagation loss. Far-field properties

of Bragg lasers are also systematically investigated providing an analytical framework for

the design of single-lobed far-field operation of devices for improved in- and out- coupling

to integrated devices.

An ebeam lithography process is developed for the fabrication of various laser con-

figurations including ring and DFB lasers in a single-sided Bragg laser structure. This

is the first time that the full fabrication of diode lasers based on ebeam lithography is

developed in the TNFC cleanroom in University of Toronto. The fabricated lasers are

tested for various characteristics such as laser performance, modal analysis, and nonlinear

conversion. The mode selection mechanism in the single-sided structure is studied and

based on the results an improved double-sided Bragg laser wafer design structure is pro-

posed. The new wafer design is confirmed to emit only at the Bragg mode, which shows

the efficacy of the applied methodology. A comprehensive study of difference frequency

ii

generation (DFG) is presented in double-sided ridge Bragg lasers. We report internal

normalized nonlinear conversion efficiency of 1.84%/W/cm2 in the structure, as a first

time demonstration of DFG in active semiconductor devices. Tuning of phase-matching

wavelength through thermal effects as well as current injection is documented. This

study provides a clear roadmap to inform future device designs to realize self-pumped

DFG, and to predict their performance when electrically injected. When fully optimized,

milliwatt level output powers can be generated through nonlinear conversion using this

platform, which is useful for various applications such as on-chip sensing.

Lastly, given that the current platform can allow for self-pumped nonlinear generation,

an analysis of modulation properties of such semiconductor optical parametric oscillators

was carried out and presented. To facilitate the analysis of dynamic properties, a novel

model based on diode laser rate equations and nonlinear conversion is developed.

iii

Acknowledgements

It is a great pleasure for me to acknowledge those who gave me the opportunity to

go through this journey in the course of this work. First and foremost, I would like to

thank my supervisor, Professor Amr Helmy, for his trust, support, and encouragement

during the course of this thesis. This work could not have reached a successful conclusion

without his guidance and advice.

I had the opportunity to benefit from the help of many talented graduate students and

post-doctoral fellows. I would particularly like to mention Payam Abolghasem, Dongpeng

Kang, and Dylan Logan. My graduate studies would not have been as enjoyable if it was

not for help and presences of many of my colleagues, Rajiv Prinja, Charles Lin, Steve

Rutledge, and Gregory Iu among many others. Some of the numerical simulations of the

devices in this work were carried out using a home-made MatLab mode solver by Dr.

Payam Abolghasem. Some of the microfabrication processes employed in this thesis were

also based on the work carried out by Dr. Bhavin Bijlani. I would like to acknowledge

their work in this regard.

Many thanks to Dr. Henry Lee, Mr. Yimin Zhou, and Dr. Alexander Tsukernik

for their help and support for keeping the TNFC cleanroom equipment up and running

and providing training and insight. Also I would like to thank Mr. Etienne Grondin and

other University of Sherbrooke CRN2 staff who helped us with the the contact deposition.

Wafer growth and fabrication of the devices would have not been possible without the

financial and material support from the Canadian Microelectronics Corporation (CMC).

I am additionally thankful to Professor Li Qian for providing access to their femto-second

tunable laser to carry out some of the experiments in this thesis.

I owe the deepest gratitude to my parents who have always supported me throughout

my academic journey. Last but certainly not least, I would like to thank my wife, Samira,

for her support, help, and encouragement throughout the course of this work. She was

always there for me with love and care.

iv

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.1.1 Second-order nonlinear processes . . . . . . . . . . . . . . . . . . 9

1.1.2 Monolithic integration in the Bragg waveguide platform . . . . . . 14

1.2 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 Bragg lasers: design considerations 18

2.1 Design methodology of the vertical structure . . . . . . . . . . . . . . . . 19

2.1.1 Formulation and definitions . . . . . . . . . . . . . . . . . . . . . 19

2.1.2 Phase-matched Bragg laser design in compound semiconductors . 23

2.2 Two-dimensional confinement properties . . . . . . . . . . . . . . . . . . 28

2.2.1 Bragg waveguide 1D modal characteristics . . . . . . . . . . . . . 29

2.2.2 Confinement of guided modes in ridge Bragg waveguides . . . . . 31

2.3 Far-field diffraction pattern . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3.1 Gaussian approximation of the field profile . . . . . . . . . . . . . 37

2.3.2 Quarter-Wave Bragg waveguide design criteria . . . . . . . . . . 41

2.3.3 Other configurations: Single-sided Bragg waveguide . . . . . . . . 44

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3 Fabrication process using electron beam lithography 48

3.1 Summary of the fabrication process . . . . . . . . . . . . . . . . . . . . . 49

v

3.2 Defining the mesa structure . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.3 Electrical isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.4 Contact deposition and liftoff . . . . . . . . . . . . . . . . . . . . . . . . 59

3.4.1 Ebeam process for defining the liftoff pattern . . . . . . . . . . . . 60

3.4.2 Metal contact deposition and liftoff . . . . . . . . . . . . . . . . . 60

3.4.3 Contact characterization . . . . . . . . . . . . . . . . . . . . . . . 63

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4 Single-sided Bragg laser design 68

4.1 Wafer design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2 Fabry-Perot lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.1 Laser performance . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.2 Nonlinear performance . . . . . . . . . . . . . . . . . . . . . . . . 83

4.3 DFB lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.3.1 Bragg reflector design considerations . . . . . . . . . . . . . . . . 86

4.3.2 Fabrication challenges and performance . . . . . . . . . . . . . . 89

4.4 Ring lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.4.1 Cavity and coupler design considerations . . . . . . . . . . . . . 95

4.4.2 Fabrication challenges and laser performance . . . . . . . . . . . 99

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5 Double-sided Bragg laser design 107

5.1 Wafer design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.2 Laser fabrication and performance . . . . . . . . . . . . . . . . . . . . . . 113

5.3 Nonlinear device performance . . . . . . . . . . . . . . . . . . . . . . . . 118

5.3.1 Tuning the phase-matching wavelength . . . . . . . . . . . . . . . 124

5.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

vi

6 Semiconductor Optical Parametric Oscillators 130

6.1 Formalism: rate equations in active, nonlinear media . . . . . . . . . . . 132

6.2 Steady-state analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

6.2.1 Stability conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 136

6.2.2 Numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . 138

6.3 Dynamic analysis and large signal response . . . . . . . . . . . . . . . . . 142

6.3.1 Rise time and build-up time: definition and closed-form approxi-

mation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.3.2 Dynamic behavior for an initial condition of zero bias . . . . . . . 144

6.3.3 Dynamic behavior for device biased above OPO threshold . . . . 149

6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7 Conclusions 154

7.1 Summary of contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 157

7.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

A Epitaxial design of the grown wafers 162

A.1 Wafer 1: single sided Bragg laser . . . . . . . . . . . . . . . . . . . . . . 162

A.2 Wafer 2: double sided Bragg laser . . . . . . . . . . . . . . . . . . . . . . 162

B Detailed step-by-step fabrication process 166

C Other developed ebeam processes 175

C.1 ma-N 2410 resist recipe: mesa structures . . . . . . . . . . . . . . . . . . 175

C.2 ZEP resist recipe: mesa structures . . . . . . . . . . . . . . . . . . . . . . 177

C.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

D Verification of 2D mode solver 180

vii

E Full derivation of the SOPO model 182

E.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

E.2 Chirp terms in the SOPO model . . . . . . . . . . . . . . . . . . . . . . 186

Bibliography 188

viii

List of Figures

1.1 An overview of wavelength ranges attainable in the tunable mid-IR sources

currently available. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Index profile (top) and schematic of a sample 1D Bragg waveguide (bot-

tom). Mode profile of the TM Bragg mode (blue) and TM TIR mode (red)

are plotted at a wavelength of 980nm. . . . . . . . . . . . . . . . . . . . . 6

1.3 Schematics of a) a double-sided ridge Bragg reflection waveguide and b) a

single-sided ridge Bragg reflection waveguide. . . . . . . . . . . . . . . . . 7

1.4 Three-wave mixing photon interaction diagrams. . . . . . . . . . . . . . . 11

1.5 An overview of various phase matching techniques common in semicon-

ductors. a) Index and mode profile of a waveguide designed for BPM [1]

c©2005 IEEE, b) A schematic of a domain disordered QPM device [2]

c©2011 IEEE, c) Comparison of generated power through exact phase-

matching (A), QPM (B), and an unphase-matched process (C) [3] c©1992

IEEE, c) Index and mode profile of a waveguide designed for MPM [4]. . 12

1.6 Schematic of a representative a) doubly resonant SOPO and b) self-pumped

DFG laser. In the former the end facets of the diode laser are high re-

flection coated (HR) at pump, signal and idler wavelengths, while in the

later, high-reflection coating is only required at the pump wavelength. . . 15

1.7 Schematic of a ring laser integrated with a nonlinear waveguide for fre-

quency conversion outside the laser cavity. . . . . . . . . . . . . . . . . . 16

ix

2.1 Schematic of a general multilayer waveguide structure. The propagation

direction is taken along the z-axis. . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Refractive index profile and mode profile of example 1 at 775nm (red),

and 1550nm (blue) wavelengths. Dashed lines plotted on the index profiles

depict the refractive indices. . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Effective index mismatch for design example 1. The algorithm determined

value for phase-matched neff is is 3.204 as shown with the dashed lines.

The resulting core thickness is 327.7nm. . . . . . . . . . . . . . . . . . . 26

2.4 Refractive index profile and mode profile of example 2 at 980 (red), 1550

(blue), and 2665nm (black) wavelengths. Dashed lines plotted on the index

profiles depict the refractive indices. . . . . . . . . . . . . . . . . . . . . . 26

2.5 Normalized nonlinear conversion efficiency for example 2 plotted for a

range of core thickness, tc. A locally optimum thickness of 562nm is de-

termined in the range investigated. . . . . . . . . . . . . . . . . . . . . . 27

2.6 a) Index and mode profile of a generic Bragg waveguide, and b) 1D effective

index of the slab region versus etch depth in the x direction. The 1D

effective index of the ridge section is shown as a dashed line. The star

markers show the interfaces of the periods, and the square markers show

the interface of core and the top and bottom first bi-layers. The inset

shows the results for the first two periods with a higher magnification. . . 30

2.7 (color online) Schematic of a generic ridge Bragg reflection waveguide plot-

ted together with a sample mode intensity profile. . . . . . . . . . . . . . 31

2.8 Bragg waveguide modal propagation loss of the 2D ridge waveguide plotted

versus etch depth in the x direction. . . . . . . . . . . . . . . . . . . . . 33

x

2.9 Two-dimensional mode profile of the test structure at etch depths a)

3.524µm and b) 3.657µm. At 3.524µm etch depth where the loss is close

to its maximum, the mode is completely de-localized, whereas at 3.657µm

etch depth where loss is nearly minimal, the mode is confined well beneath

the ridge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.10 a) A measured far-field profile of a sample Bragg laser [5], and b) a

schematic of the far-field measurement setup. LD: laser diode; PD: photo-

diode. The intensity profile is measured through a slit for various angles. 36

2.11 Near field of the three design examples as given in Table 2.1; exact (solid)

and approximate (dotted). . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.12 Far field of the three design examples as given in Table 2.1; exact (solid)

and approximate (dotted). . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.13 Ψ1 (solid) and Ψ2 (dashed) expressed in (2.21) for the design examples

studied in Table. 2.1. Both terms are normalized to the maximum of Ψ1. 42

2.14 a) Index profile and near field, and b) far field profile of example 2 in sec-

tion 2.1.2. The solid curves show the values calculated through Transfer

Matrix Method, and the dashed-dotted curve shows the Gaussian approxi-

mation results. The dashed line in the index profile represents the effective

index of the Bragg mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1 Major stages in fabrication of semiconductor diode lasers. . . . . . . . . . 49

3.2 Summary of stage 1 of the fabrication process: defining the mesa structures. 50

3.3 Summary of stage 2 of the fabrication process: electrical isolation and

defining the via openings. . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.4 Summary of stage 3 of the fabrication process: Deposition of the electrical

contacts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.5 EBPG 5000+ electron-beam nanolithography system by Vistec Lithogra-

phy Ltd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

xi

3.6 a) Microscope image of 2µm wide waveguides patterned on AlGaAs, using

the diluted Fox15 resist. The exposure dose was 450µc/cm2. b) An SEM

micrograph of the cross section of the same sample after 120s etch. . . . 55

3.7 a) top view optical microscope image and b) cross sectional SEM micro-

graphs of samples planarized with HSQ, after annealing. . . . . . . . . . 58

3.8 a) top and b) cross-sectional SEM micrographs of vias patterned on Al-

GaAs waveguides covered with 340nm silica after 100s silica etch and resist

removal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.9 a) A microscope image of separate contact pads after developing the resist.

b) An close-up SEM micrograph of the separation region between two

contact pad regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.10 Edwards Auto 306 ebeam evaporator and a diagram of evaporation process. 61

3.11 Optical and SEM micrographs of a sample after the metal liftoff. . . . . . 64

3.12 a) A circular contact resistance test structure. The golden regions repre-

sent metallic contacts. Gap spacing, d, and radius, L, are shown in the

figure. b) Total resistance for the circular TLM test structure before and

after data correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.1 a) Calculated normalized nonlinear coupling efficiency, η, as a function of

(tm,top; tc,top) for single-sided Bragg waveguide. A maximum efficiency of

5.2505 × 10−6%/W/cm2 is obtained at (tm,top; tc,top) = (341; 237)nm for

a 2mm long test waveguide. b) Ratio of optical confinement factor of the

Bragg mode to the zeroth-order TIR mode for the same range of thicknesses. 73

4.2 Refractive index profile and mode profile of the structure at 980 (red),

1500 (green), and 2826nm (blue) wavelengths. The black dashed lines in

the index profiles represent the effective indices in the according wavelength. 74

xii

4.3 a) Simulated energy band diagram of the unbiased device and b) calculated

tuning curve for the designed structure. Ev, Ec, and Ef represent the

valence and conduction band levels, and Fermi level, respectively. . . . . 75

4.4 a) A schematic of the designed ridge structure, and b) a scanning electron

micrograph of a fabricated single-sided Bragg laser device before the metal

deposition. The via opening for current transport is clearly seen in the SEM. 76

4.5 Experimental setup for laser characterization. M, mirror; MF flip-out

mirror; PD, silicon photodetector; BRL, the laser bar; obj, objective lens. 76

4.6 a) Continuous wave LIV curves for a sample laser operated at 17C, and b)

normalized optical spectrum of the laser output for the laser under test,

operated CW at 17C with 50mA (solid), 100mA (dotted), and 200mA

(dashed) injected currents. . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.7 Temperature dependence of a) threshold current density and b) slope ef-

ficiency. The solid lines are the theoretical fits to the data. . . . . . . . 79

4.8 Collected under-threshold spectrum at 35mA injected current. The inset

shows the no-gain region of the spectra where the method in [6] was used

to extract the initial loss estimate. The squares show the maxima and

minimum used for the calculation. . . . . . . . . . . . . . . . . . . . . . 80

4.9 a) Fourier transform of the spectrum at 35mA. The slope of these peaks

on the semilog scale is related to the gain/loss. b) A plot of the calculated

gain/loss values at the measured currents. The circles are the measured

values and solid lines are the theoretical fits to the loss data. . . . . . . . 80

4.10 Near-field of the laser under test at 17C and 50mA current. a) Calculated,

and b) measured 1D NF profile, c) calculated, and d) measured 2D NF

profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.11 Sample spectrum of a laser with a peak at 948nm at 100mA and 20C. . 82

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4.12 Measured a) 1D and b) 2D near-field profile of the laser under test at

100mA current, plotted together with the calculated c) 2D and d) 1D

near-field profile for the TE01 mode. e) Simulated 2D modal loss for the

two dominant modes. The losses are plotted in logarithmic scale to better

compare the loss for the two modes. . . . . . . . . . . . . . . . . . . . . . 83

4.13 a) Schematics of the self-pumped DFG setup. FC, fiber collimator; FPC,

fiber polarization controller; SMF: single mode fiber; 10x obj, 10x objec-

tive lens; BRL, the laser bar; IR-obj, mid-IR objective lens; M, mirror;

MF flip-out mirror; Ge-PD, Germanium photodetector; OSA, optical spec-

trum analyzer; 3xLPF, 3 long-pass filters; PbS, lead sulphide detector. b)

Measured mid-IR power plotted as a function of signal wavelength. The

diode laser is kept on at a constant current of 200mA and the signal power

is kept constant at 82mW, TM. . . . . . . . . . . . . . . . . . . . . . . . 84

4.14 Schematics of a) laterally coupled and b) laterally corrugated surface grat-

ings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.15 A flowchart of the DFB laser design procedure. . . . . . . . . . . . . . . 89

4.16 a) Side view and b) cross sectional SEMs of a sample seventh-order grating. 90

4.17 a) A schematic of the device with non-ideal etch. . . . . . . . . . . . . . 92

4.18 Coupling coefficient of a seventh-order grating versus. a) etch depth when

ungrooved width is tg2 = 0.6µm, and b) ungrooved region width when the

total etch depth is 1.87µm. . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.19 a) A sample LI curve for a DFB device with ungrooved and grooved widths

of 0.6µm and 2µm, respectively. b) Output spectra of the device at 90A

CW injection current. c) Near-field emission profile of the DFB laser

when operated at 90mA. The scale is estimated based on image size on

the camera and the optics used. . . . . . . . . . . . . . . . . . . . . . . 93

xiv

4.20 A sample plot of calculated bar-coupling versus coupler length for two

straight 2µm wide waveguides separated by 2µm. The etch depth is as-

sumed to be 1.97µm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.21 A sketch of the uni-directional device. The blue region shows the contact

pads and the red represents the waveguides. The clockwise and counter-

clockwise directions are marked on the figure. . . . . . . . . . . . . . . . 100

4.22 An optical mirograph of a fabricated ring laser. . . . . . . . . . . . . . . 100

4.23 a) Cross sectional and b) side view SEM micrographs of damaged samples

after metal deposition. The planarization HSQ has incurred large cracks,

undercut near the cracks, and chipping out in multiple places. . . . . . . 101

4.24 Continuous-wave LI characteristics for a sample ring laser with 320µm

coupler length. Bus waveguide bias is a) 0mA, b) 40mA, and c) 100mA.

The blue curve shows straight facet output (clockwise mode) and black

illustrates the curved facet output (counter clockwise mode). . . . . . . . 102

4.25 Pulsed LI characteristics for a sample ring laser with 320µm coupler length.

Bus waveguide bias is a) 0mA, b) 40mA, and c) 100mA. The blue curve

shows straight facet output (clockwise mode) and black illustrates the

curved facet output (counter clockwise mode). The pulses are 1µs long

with 20µs delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.26 Measured near-field profile from the ring laser with 320µm coupler length

where bus waveguide is biased at a) 0mA and b) 100mA CW. The ring is

biased at 600mA, pulsed, in both cases. The scales are estimated based

on the optics used and image size on camera. . . . . . . . . . . . . . . . . 104

xv

5.1 a) Calculated normalized nonlinear coupling efficiency, η, for SHG as a

function of (tc; xm) for double-sided Bragg laser. A maximum efficiency of

6.07×10−4%/W/cm2 is obtained at (tc; xm) = (240nm; 0.2) for a 2mm long

test waveguide. Aluminum concentration was kept above 0.2 to minimize

bandgap effects and core thickness was limited to 240nm to for confinement

factor optimization purposes. b) Ratio of optical confinement factor of

Bragg mode to that of all the available TIR modes for the optimized

structure. The lowest ratio is 35.3. . . . . . . . . . . . . . . . . . . . . . 110

5.2 Refractive index profile and mode profile of the structure at 775 (red),

and 1550 (blue for TM and green for TE) wavelengths. The dashed lines

together with the index profiles represent the effective indices in the ac-

cording wavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.3 a) Some of the tested doping profiles, and b) simulated LIV characteristics

of the laser for the corresponding doping profiles. . . . . . . . . . . . . . 112

5.4 a) Simulated energy band diagram of the unbiased laser for the selected

doping profile; Ev, Ec, and Ef represent the valence and conduction band

levels, and Fermi level, respectively. b) Calculated tuning curve for the

designed structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.5 a) A schematic of the designed ridge structure, and b) a scanning electron

micrograph of a fabricated double-sided Bragg laser device before the metal

deposition. The via opening for current transport is clearly seen in the SEM.114

5.6 a) CW LIV curves for a sample laser operated at 20C, and b) normalized

optical spectrum of the laser under test, operated CW at 20C at 40mA

(solid) and 100mA (dashed) injected currents. c) Normalized optical spec-

trum of the laser under test at 100mA at various stage temperatures. . . 115

xvi

5.7 Near field of the laser under test at 20C and 100mA current. a) Calcu-

lated, and b) measured cross-sectional NF profile, c) calculated, and d)

measured 2D NF profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

5.8 Near field profile of a laser emitting in the TIR mode. a) Calculated, and

b) measured cross-sectional NF profile, c) calculated, and d) measured 2D

NF profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

5.9 a) A sample plot of 1/ηD vs. length and the fitted parameters, and b)

Theoretically simulated Bragg mode (solid) and TIR mode (dashed) loss,

plotted together with the measured losses for Bragg (circles) and TIR

(squares). The TIR mode is only confined at etch depths above 2.27µm

where modal loss simulation was possible. . . . . . . . . . . . . . . . . . 117

5.10 Theoretically simulated Bragg mode (solid) and TIR mode (dashed) a)

confinement factor, and b) threshold gain. . . . . . . . . . . . . . . . . . 118

5.11 Schematic of SHG experimental setup. A tunable source emitting at 1535-

1565nm wavelength is injected into the sample after amplification, beam

shaping, and polarization control. SMF: single mode fiber; FPC: fiber

polarization controller; FC: fiber collimator; LPF: 1450nm long-pass filter;

PBS: polarization beam splitter; S: beam sampler; M: mirror; MF: flip-

mount mirror; BRL: Bragg reflection waveguide laser; Ge-PD: Germanium

photodetector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.12 Power spectral density of the femto-second laser a) before and b) after

amplification through the EDFA. The laser and the EDFA were biased at

110mA and 60mA, respectively. . . . . . . . . . . . . . . . . . . . . . . . 120

5.13 Power spectral density of the generated second harmonic for a) type-I and

b) type-II configurations. The femto-second laser and EDFA were biased

at 110mA and 60mA, respectively. . . . . . . . . . . . . . . . . . . . . . . 120

xvii

5.14 Schematic of DFG experimental setup. Two tunable sources emitting

around 816nm and 1550nm wavelength are injected into the sample af-

ter beam shaping and polarization control. SMF: single mode fiber; BPF:

tunable band-pass filter; FPC: fiber polarization controller; FC: fiber col-

limator; PBS: polarization beam splitter; BS: beam splitter; S: beam sam-

pler; M: mirror; MF: flip-mount mirror; BRL: Bragg reflection waveguide

laser; Ge-PD: Germanium photodetector. . . . . . . . . . . . . . . . . . 121

5.15 a) A sample spectrum of the generated idler for pump/signal wavelength

of 816.3/1550nm. b) Idler power plotted against pump wavelength for

a constant signal wavelength of 1550nm. The circles are the measured

data and the solid line shows a Lorentzian fit. c) Idler power plotted as a

function of signal power for a constant pump power of 90mW. The circles

are the measured data and the solid line is a linear fit. d) Measured DFG

tuning curve. All measurements carried out at room temperature (25C). 122

5.16 a) Idler power plotted against pump wavelength and stage temperature.

The temperature step was 10C. b) Idler power plotted against pump

wavelength and injected current at a constant stage temperature of 20C.

The injected current step size was 10mA. Idler power is normalized to its

maximum at each given temperature/current. c) The raw and corrected

phase-matching point as a function of injected current, extracted from the

previous figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.1 Schematic of a representative doubly resonant SOPO where the end facets

of the diode laser are high reflection coated (HR) at pump, signal and idler

wavelengths. A scheme of a typical Bragg reflection waveguide SOPO is

shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

xviii

6.2 a) Steady-state internal power of the pump, signal and idler and b) adia-

batic frequency chirp of the simulated SOPO plotted as functions of the

injected current. The lines and circles represent the calculated and sim-

ulated data, respectively. The steady-state regions of operation are sepa-

rated with vertical dashed-lines, and are distinct from the change in the

slope of the graphs. c©2005 IEEE [113] . . . . . . . . . . . . . . . . . . 140

6.3 Wavelength tuning curve of the simulated SOPO showing the variation of

signal and idler wavelengths as functions of the pump wavelength. A shift

in the pump wavelength by +2nm, results in a signal and idler wavelength

tuning by 18nm and −38nm, respectively. . . . . . . . . . . . . . . . . . 142

6.4 The build-up time and rise time shown for a step response, assuming the

turn-on time to be at t = 0s. Here P1 = Pmin + 0.1∆P and P2 =

Pmin+ 0.9∆P where ∆P = Pmax− Pmin. . . . . . . . . . . . . . . . 143

6.5 a) Internal pump power, and b) frequency dynamics of the un-phase-

matched laser for current steps of 2Ith, 4Ith, and 6Ith. The inset shows the

injected current as a function of time. . . . . . . . . . . . . . . . . . . . 145

6.6 a) Internal power, and b) frequency dynamics of the un-phase-matched

laser for currents changing from 2IOPO,th to 10IOPO,th in steps of IOPO,th.

The inset shows the injected current as a function of time. . . . . . . . . 146

6.7 a) Internal power, and b) frequency dynamics of the SOPO under-study

for current steps of 2IOPO,th to 10IOPO,th in steps of IOPO,th. The inset

shows the injected current as a function of time. . . . . . . . . . . . . . 147

6.8 Dependence of signal and idler power a) build-up times and b) 10%-90%

rise times on injected current simulated for the example SOPO. The initial

current is 0 mA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

xix

6.9 Dependence of signal and idler power a) build-up times and b) 10%-90%

rise times on injected current simulated for the example SOPO. Solid

and dashed curves show the response to initial currents of 1.1IOPO,th and

2IOPO,th, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

C.1 a) Microscope image of an evanescent coupler patterned on silica/AlGaAs,

using the ma-N 2410 resist. The exposure dose was 30µc/cm2. b) An SEM

micrograph of an etched ridge prepared using ma-N 2410 resist. The etch

time was 146s in the III-V etcher. . . . . . . . . . . . . . . . . . . . . . 177

C.2 a) Microscope image of a 2µm wide waveguide patterned on silica/AlGaAs,

using the ZEP-520A resist. The exposure dose was 120µc/cm2 for the

10µm vicinity of the sample and 240µc/cm2 for the rest of the exposed

area. The resist remaining at the unexposed area can be seen at the top

and bottom. b) An SEM micrograph of the cross section of an etched

sample prepared using ZEP-520A resist. The etch time was 110s in the

III-V etcher. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

D.1 a) The calculated effective index as a function of mesh size for the sample

chosen here. b) Two-dimensional mode profile of the sample structure

simulated with a mesh size of 50nm. . . . . . . . . . . . . . . . . . . . . 181

xx

List of Tables

1.1 Overview of available tunable mid-IR sources. Note that for wideband

tuning of semiconductor mid-IR lasers outlined in the first three rows, an

external cavity configuration is required which increases their form-factor

and alignment complexity. . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Design parameters for examples D1 to D3. All three examples operate at

the free space wavelength of λ = 775nm. . . . . . . . . . . . . . . . . . . 39

3.1 Detailed mesa structure development recipe for Fox15:MIBK (1:1). . . . 54

3.2 EBL exposure parameters for the various feature sizes of the mesa struc-

tures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3 EBL exposure parameters for the various feature sizes of the mesa struc-

tures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.4 Detailed ZEP-520A recipe for via openings in the electrical isolation. . . 58

3.5 Detailed liftoff pattern development recipe for ZEP-520A. . . . . . . . . 60

3.6 EBL exposure parameters for the two exposed areas in the 10µm (high

resolution) and above 10µm (low resolution) vicinity of the contact gap. 60

3.7 Summary of the RTA recipe for contact alloying. . . . . . . . . . . . . . 63

4.1 The optimized single-sided Bragg laser structure. . . . . . . . . . . . . . 73

4.2 Detailed GaAs plasma etch recipe. . . . . . . . . . . . . . . . . . . . . . 91

5.1 The optimized double-sided Bragg laser structure. . . . . . . . . . . . . . 110

xxi

6.1 Design parameters for the test structure. . . . . . . . . . . . . . . . . . 140

A.1 Detailed epitaxial structure of the single-sided design. . . . . . . . . . . . 163

A.2 Detailed epitaxial structure of the double-sided design. . . . . . . . . . . 164

C.1 Detailed ma-N 2410 recipe for defining mesa structures. . . . . . . . . . . 176

C.2 Detailed mesa structure development recipe for ZEP-520A. . . . . . . . 178

C.3 EBL exposure parameters for the two exposed areas in the 10µm (high

resolution) and 10-40µm (low resolution) vicinity of the mesa structures. 178

xxii

List of Acronyms

BOE: Buffered oxide etchant

BPM: Birefringence phase-matching

BRW: Bragg reflection waveguide

BRL: Bragg reflection waveguide laser

CW: Continuous wave

DBR: Distributed Bragg reflector

DFB: Distributed feedback

DFG: Difference frequency generation

DS-BRL: Double-sided Bragg reflection waveguide laser

EDFA: Erbium doped fiber amplifier

FF: Far field

FSR: Free spectra range

FWHM: Full-width at half-maximum

HSQ: Hydrogen silsequioxane

IOPO: Intracavity optical parametric oscillator

IR: Infrared

LIV: Light-power intensity-voltage characteristics

MOCVD: Metal-organic chemical vapor deposition

MMI: Multi-mode interference

MPM: Modal phase-matching

NF: Near field

OPO: Optical parametric oscillation

PBS: Polarizing beam splitter

PPLN: periodically poled LiNBO3

xxiii

PSD: Power spectral density

QCL: Quantum cascade laser

QPM: Quasi phase-matching

RTA: Rapid thermal annealer

SEM: Scanning electron microscopy

SH: Second harmonic

SHG: Second harmonic generation

SS-BRL: Single-sided Bragg reflection waveguide laser

TBR: Transverse Bragg reflector

TIR: Total internal reflection

TLM: Transmission line method

TNFC: Toronto nanofabrication center

xxiv

Chapter 1

Introduction

Lasers have influenced nearly every aspect of human life since their introduction over five

decades ago. From fiber-optic communications to laser machining, medical treatments,

and CD and DVD technologies, lasers have been used in various applications all over

the world. Gas, solid-state, fiber, and semiconductor lasers are some of most dominant

coherent sources of light. However, such sources are limited by their material physical

properties. The near- and mid-infrared emission region is of interest due to the spectral

fingerprint of various materials in this region. Compact, widely tunable coherent mid-IR

light sources have been under study for various applications such as chemical monitoring,

medical diagnostics, and gas sensing in this spectral region known as the fingerprint

region. Many gases and organics such as carbon monoxide and glucose exhibit absorption

features in the short-wave end of the mid-IR spectrum, 2-3µm. However, there are

currently limited room temperature sources available in this spectral band. A summary

of some of the mid-IR generation methods used to date is presented in table 1.1 and

Fig. 1.1.

Recently, interssubband [7–9] and interband [10–13] semiconductor lasers were inves-

tigated to provide engineered bandstructures for emission in the near-IR and terahertz

regime. Of the two, the former is more widely investigated. Intersubband semiconduc-

1

Chapter 1. Introduction 2

tor lasers, also known as Quantum cascade lasers (QCLs) emitting in the mid-IR region

are usually based on GaInAs/AlAs/InP or GaInAs/AlAsSb/InP material system. Un-

like conventional lasers in which emission occurs due to recombination of electron-hole

pairs across the bandgap, photon emission in QCL occurs due to transition of carriers

between subbands in the same band. As such, the emission wavelength is very depen-

dent on the structure and can be engineered to various wavelengths. QCLs have been

proposed for short mid-IR [9] up to terahertz [8] radiation, with powers up to watt level,

and tunabilities up to 500cm−1. However, room-temperature operation of these lasers at

the 2-3µm range has been limited so far due to inter-valley scattering and high strain

material growth issues [7].

Mid-IR lasing has also been demonstrated through interband transitions. Interband

cascade lasers (ICLs) can be implemented using antimonides or lead salts [10, 11, 14].

Such devices combine the band engineering capabilities of QCLs with cascaded multiple

interband transitions, essentially eliminating nonradiative-relaxation path responsible for

relatively high thresholds in the QCL. Room temperature antimonide-based ICLs can be

implemented from 3-5.7µm [14]. In addition to cascaded lasers, regular quantum well

antimonide-based lasers have been under investigation for mid-IR generation specifically

in the 2-3µm regime [13]. InGaAsSb/GaSb VCSELs have been shown to provide tuning

up to 150nm in this wavelength regime [15]. Even though all the semiconductor sources

reported above are capable of providing watt-level powers in the mid-IR regime, tun-

ing the lasing wavelength for more than a few hundred nanometers from a single chip

is dependent on the gain bandwidth. Even with wide gain bandwidths attainable with

chirped QCLs, external cavity configurations are usually required to provide the wide-

band tuning from a single chip. Including an external cavity will increase the alignment

complexities and limit hand-held applications of such sources.

In addition to the lasing mechanism, nonlinear frequency conversion mechanisms such

as nonlinear optical parametric processes and difference-frequency generation (DFG) are


Table 1.1: Overview of available tunable mid-IR sources. Note that for wideband tun-ing of semiconductor mid-IR lasers outlined in the first three rows, an external cavityconfiguration is required which increases their form-factor and alignment complexity.

Technology Tunability limitation Form-factor Alignment PowerQC lasers Gain bandwidth limited Compact None Hi

Sb based ICLs Gain bandwidth limited Compact None HiSb based QW lasers Gain bandwidth limited Compact None HiConventional DFG Transparency/source limited Large Complex HiConventional OPO Crystal transparency limited Large Complex HiSelf-pumped DFG Transparency/source limited Compact Moderate LowSelf-pumped SOPO Crystal transparency limited Compact None Low

Figure 1.1: An overview of wavelength ranges attainable in the tunable mid-IR sourcescurrently available.

potential alternatives for providing tunable coherent sources in mid-IR. In nonlinear con-

version, essentially the range of generated wavelengths is limited by the pump sources

and the nonlinear crystals. There has been multiple reports of DFG sources in the mid-IR

regime [16, 17]. As an example, a tuning range of 3-3.9µm was achieved with periodi-

cally poled LiNBO3 (PPLN) and a combination of 1030-1100nm pump and 1530-1570nm

signal wavelengths [17]. Optical parametric oscillators (OPOs), on the other hand, only

require a pump wavelength where the signal and idler wavelengths will be generated from

parametric down-conversion of the pump photons. There has been numerous reports of

externally pumped [18, 19] and intracavity OPOs [20] for very wideband (up to a few

microns) tuning in the mid-IR region. IOPOs offer distinct advantages over other OPO

configurations, especially due to the lower threshold pump power needed in the CW

mode of operation. In the case of IOPOs, nonlinear parametric generation takes place in

the same cavity where the lasing takes place. This leads to a larger pump power avail-


able inside the laser cavity and consequently to lower threshold levels compared with

conventional OPOs. A notable limitation of these systems is instability due to relax-

ation oscillations [21] and operating the pump laser in the Q-switched pulsed mode is

one of the solutions to overcome this stability issue [22, 23]. Sources based on nonlin-

ear frequency conversion are commonly implemented in either table-top or fiber based

configurations. This limits their application to portable applications due to stringent

alignment complexities and large form-factors.

While devices based on nonlinear frequency conversion utilize bulk optical elements or

fibers, recent developments in the field of integrated photonics usher in a new era of inte-

grated electrically injected semiconductor optical parametric oscillators (SOPOs). These

devices can provide numerous advantages due to their robustness, low power consump-

tion, compact form-factor, and being alignment free [24]. Integrated devices based on

nonlinear frequency conversion usually provide much lower powers compared to table-top

nonlinear sources and mid-IR semiconductor lasers. Even though the potential of achiev-

ing milliwatt-level power by utilizing integrated nonlinear devices may not be sufficient

for free space spectroscopy, it is more than enough for on-chip spectroscopy, for example

in capillary based systems [25]. While realizing self-pumped SOPOs requires stringent

optimization and very high quality factor cavities [26], realization of self-pumped DFG

is less technology dependent. Moreover, in a self-pumped DFG process, generation of

one of the wavelengths through lasing will reduce the complexity of alignment, as only

one wavelength will need to be coupled into the device. As such, self-pumped DFG is an

important step in realizing self-pumped SOPOs.

Nonlinear dielectrics such as periodically poled Lithium Niobate (PPLN) are widely

used for integrated nonlinear frequency conversion [27]. However, the limited trans-

parency window of PPLN, up to 5µm, and complexities for integration with electrically

injected semiconductor sources limits the use of this material system. III-V semiconduc-

tors such as indium phosphide and gallium arsenide have also been proposed for nonlinear


conversion [2,24,28]. Among these, GaAs/AlGaAs material system is specifically suitable

for monolithic integration and nonlinear conversion for mid-IR generation in the 2-3µm

band due to the bandgap/emission wavelength available to the GaAs/AlGaAs material

system. The GaAs-based semiconductor devices benefit from mature fabrication process

and excellent nonlinear properties including high damage threshold, large nonlinear co-

efficient, and transparency in the 1-17µm regime. Recently, a GaAs/AlGaAs platform

conducive to realizing monolithic parametric generation and nonlinear conversion has

been developed, namely Bragg reflection waveguides (BRWs) or in short Bragg waveg-

uides [29,30]. Such a solution will provide a universal integrated solution not only to the

2-3µm mid-IR regime, but to the whole transparency window of GaAs.

Bragg waveguides, in their simplest form, are 1D photonic crystals with a line defect.

Figure 1.2 shows a schematic of a sample Bragg waveguide together with its refractive

index profile. Such waveguides are capable of guiding modes by two distinct guiding

mechanisms: guiding based on total internal reflection (TIR) and Bragg reflection. The

Bragg mode usually has an effective index lower than that of the refractive index of the

waveguide layers and is confined within the core through the photonic bandgap effect.

The TIR mode, on the other hand, usually possesses an effective index higher than the

cladding layers. As such, this mode is confined in the high index layers of the Bragg

structure and exponentially decays in the lower index layers. Figure 1.2(b) illustrates a

schematic of a 1D Bragg waveguide together with the Bragg and TIR mode profiles.

In practical applications, usually the light is confined in two directions rather than

one. Ridge waveguides are one of the most common configurations for 2D confinement

of light in integrated optics. Figure 1.3 shows a schematic of two common types of ridge

Bragg waveguides, namely double-sided, and single-sided Bragg ridge waveguides. In

such structures, the defined ridge profile confines the light in the lateral (y) direction

through the regular TIR phenomenon. In the vertical direction, however, the light can

be confined through the Bragg effect or total internal reflection similar to the 1D Bragg


−2 −1 0 1 22.8

33.23.43.6

x [µm]

inde

x pr

ofile

−2 −1 0 1 2−1

0

1

x [µm]

field

pro

file

[a.u

]

Figure 1.2: Index profile (top) and schematic of a sample 1D Bragg waveguide (bottom).Mode profile of the TM Bragg mode (blue) and TM TIR mode (red) are plotted at awavelength of 980nm.

waveguide case. Throughout this thesis, Bragg waveguide has been used both for 1D slab

Bragg structures and 2D ridge Bragg waveguides. Given the well-studied effect of ridge

confinement, many of the design and optimization considerations in this thesis only focus

on 1D analysis of the Bragg structure in the vertical direction. As such, unless specifically

mentioned, Bragg waveguide analysis is considered to take place in the vertical direction.

Coexistence of the two distinct guiding mechanisms, i.e. Bragg reflection and total

internal reflection, in Bragg waveguides allows for modal phase matching for nonlinear

frequency conversion. In such applications, the Bragg mode is used to guide the higher

frequency, while the lower frequency signals are guided through total internal reflection

phenomena. Through such an approach, Bragg waveguide implementation in nonlinear

optical applications which utilize χ(2) nonlinearities has led to record conversion efficien-

cies in both double-sided [29, 31] and single-sided [32, 33] ridge Bragg waveguides. Effi-


Figure 1.3: Schematics of a) a double-sided ridge Bragg reflection waveguide and b) asingle-sided ridge Bragg reflection waveguide.

cient second harmonic generation [29, 31], sum frequency generation [34], and difference

frequency generation [30] have been recently demonstrated. For example, normalized

conversion efficiencies of up to 1.14 × 104 W−1cm−2 were reported for type II second

harmonic generation [29]. These unique nonlinear properties have proven Bragg waveg-

uides very interesting for quantum communications as well. Recently, GaAs/AlGaAs

Bragg waveguides were implemented for generation of photon pairs through spontaneous

parametric down-conversion (SPDC) [35, 36]. As can be seen, this nonlinear conver-

sion method is so versatile that can be used for applications in near-IR [31] and mid-IR

generation [33], as well as quantum communications [36]. Essentially, with proper struc-

tural design, given the right input wavelength, almost any wavelength can be generated

through various nonlinear conversation mechanisms.

Bragg reflection waveguide lasers (BRLs) or Bragg lasers, have also been under inves-

tigation in double-sided [37] and single-sided [38] arrangements. In such devices, lasing

takes place in the vertical Bragg mode of the structure. Recently, parametric fluorescence

was reported in GaAs/InGaAs Bragg lasers [39] and self-pumped SPDC was observed in

GaAs/AlGaAs Bragg lasers [40]. However, many nonlinear properties of devices remained

unexamined, as the focus was mainly on laser design and photon pair generation. Self-

pumped DFG offers a simple solution to providing widely tunable coherent light. In this

thesis, we will focus on the design and implementation of Bragg lasers for self-pumped


DFG. We will also provide the experimental background for future work in realization of

practical self-pumped SOPOs through study of nonlinear conversion properties of Bragg

lasers in the DFG process.

The Bragg lasers previously developed in the group [5,37] suffered from high thresh-

old currents and very high temperatures, which can offer a wafer growth shortcoming.

The reported threshold current densities were above 230A/cm2 [37] and junction tem-

peratures well above 70oC [41]. Moreover, the phase-matched Bragg lasers were found to

be unable to operate under continuous wave (CW) condition and were only tested in the

pulsed regime [42]. In addition to these shortcomings, the 3-4µm etch depth needed for

proper confinement of the mode under the ridge structure made it extremely challeng-

ing to integrate photonic devices such as short-period gratings and directional couplers

in the Bragg laser platform. To accommodate better electrical properties and better

modal confinement, two solutions are considered in this thesis: single-sided (SS-BRL),

and double-sided Bragg lasers (DS-BRL) with reduced upper transverse Bragg reflec-

tor (TBR) thickness. Initially, the single-sided design is proposed which offers thinner

upper cladding layers with less interfaces compared to the regular double-sided design.

This can potentially lead to less heat accumulation and deterioration of laser quality.

To improve mode selection characteristics, however, double-sided Bragg lasers were re-

considered but with thinner than regular top Bragg reflection region. To improve the

electrical characteristics, the doping profile of the designed structure is optimized through

a commercial laser analysis package. The thin cladding layer of both designs lends itself

to implementation of integrated devices in the Bragg laser platform.

Given the upper thin cladding region, ridge waveguides can be formed on the pro-

posed designs by etch depths as low as 2µm. The shallow etch facilitates realization

of etched periodic structures and directional couplers as the integrated optical circuit

building blocks. Semiconductor ring lasers and lasers based on distributed Bragg reflec-

tors such as distributed feedback (DFB) and distributed Bragg reflector (DBR) lasers


have shown tremendous promise for monolithic integration of light sources with other

passive and active devices [43, 44]. DFBs and DBRs offer accurate control of emission

wavelength which can be extremely beneficial for aligning the phase-matching and lasing

wavelengths. Moreover, providing a mode-hop free single lasing wavelength will be essen-

tial for optimal performance and tuning of SOPOs. As such, device designs incorporating

ring resonators and Bragg reflectors will be explored to provide a framework for future

device implementations.

Aside from the improvements in the Bragg laser properties, quantitative design tools

and insight is needed for enabling functional SOPOs, akin to the optimization of the

IOPO cavity that took place prior to the implementation of efficient table-top IO-

POs. Some SOPO design trade-offs including the OPO threshold power were studied

recently [26]. We developed a comprehensive time-domain model for SOPO analysis to

provide more insight into the power and chirp dynamics. Theoretical studies on the

design considerations will be presented towards the end of this thesis.

1.1 Background

1.1.1 Second-order nonlinear processes

The field of nonlinear optics flourished right after coherent sources of light, i.e. lasers

became available in the 1960s. Light propagation in the matter generates a polariza-

tion vector through the medium which at high enough intensities can be nonlinearly

related with the electric field. If the phase velocity of the generated nonlinear polariza-

tion vector equals the sum of phase of individual harmonics which initiate the nonlinear

interaction, the oscillating polarization momentum of the dipoles will constructively com-

bine to form a coherent nonlinear polarization vector. This condition is usually referred

to as phase-matching. In compound semiconductors and various dielectrics, the second-

order nonlinear susceptibility χ2 is utilized for three-wave mixing frequency conversion.


Energy and momentum conservation conditions essentially represent the frequency and

phase matching conditions, respectively:

ω1 − ω2 − ω3 = 0 (1.1)

~k1 + ~k2 + ~k3 = 0. (1.2)

In the case of collinear nonlinear conversion in waveguides, the wavevectors ~kj , j ∈ 1, 2, 3

can be replaced by βj, the modal wavenumbers:

∆β = β1 − β2 − β3 = 0. (1.3)

In the general case presented here, the three waves are labeled as 1, 2 and 3. Typically,

there are different three-wave mixing conversion processes possible as depicted in Fig. 1.4.

Sum-frequency generation (SFG), is the process of combining two photons at ω1 and ω2

to generate the higher frequency ω3 photon; second-harmonic generation (SHG) is the

degenerate case where ω1 = ω2 creating a photon at second harmonic, ω3 = 2ω1; lastly,

difference-frequency generation (DFG) is the process where a high frequency photon,

ω1, splits into two lower energy photons, ω2 and ω3. Optical parametric amplification

and oscillation are processes similar to DFG with regards to the energy and momentum

conditions. In these two processes, the high frequency photon is usually called pump,

represented by ωp, and the two other photons are termed signal and idler, expressed

by ωs and ωi rather than ω2 and ω3, respectively. Lastly, parametric fluorescence is a

quantum effect in which an optical parametric oscillator emits light in the signal and

idler wavelengths when the pump power is below the OPO threshold level. In such a

process, the emitted power is usually very small as it stems from the vacuum noise of the

system.

In rectangular guided wave GaAs/AlGaAs structures used for nonlinear conversion,

light is typically guided in the [110] direction. Given the propagation direction, there


Figure 1.4: Three-wave mixing photon interaction diagrams.

are normally two configurations of phase matching possible in these waveguides, namely

type-I and type-II phase matching. In type I DFG, pump is TM polarized along the [001]

direction, and the two other wavelengths are TE polarized along the [110] direction. In

type-II phase matching, pump is TE polarized, and one of signal and idler is TE polarized

and the other one is TM polarized. The same definitions are valid for other three-wave

mixing processes.

Conventionally, phase-matching condition has been implemented through the use of

a birefringent crystal as the nonlinear medium. However, due to the isotropic nature

of many materials used in integrated optics, this can not be achieved trivially in many

cases. Compound semiconductors, specifically AlGaAs is mainly attractive for nonlinear

optics applications in the infrared (IR) and mid-infrared range due to its large second-

order nonlinear coefficient (d≈100 pm/V in the near-IR), in addition to its broad IR

transparency range, and well developed epitaxial growth and fabrication technologies.

However, due to absence of birefringence in AlGaAs, other phase matching schemes have

been proposed. These techniques include form-birefringence phase matching (BPM) [1,

28], quasi phase matching (QPM) [2,45], and modal phase matching (MPM) [30,46–48].

Schematics of waveguides phase-matched through each method are presented in Fig. 1.5.

These methods will be reviewed in more details in the following.


(a) (b)

(c) (d)

Figure 1.5: An overview of various phase matching techniques common in semiconduc-tors. a) Index and mode profile of a waveguide designed for BPM [1] c©2005 IEEE, b)A schematic of a domain disordered QPM device [2] c©2011 IEEE, c) Comparison ofgenerated power through exact phase-matching (A), QPM (B), and an unphase-matchedprocess (C) [3] c©1992 IEEE, c) Index and mode profile of a waveguide designed forMPM [4].

It is well known that periodic dielectric structures whose periodicity happens to be

much smaller than the wavelength of propagating light, behave as if they were uniaxial

birefringent media. This phenomenon is usually referred to as form-birefringence. Alu-

minum oxidation processes were used for birefringence phase matching (BPM) through

breaking the isotropy of bulk GaAs by inserting thin oxidized AlAs (AlOx) layers in

GaAs [1, 28]. Fig. 1.5(a) shows the index and field profile of an AlGaAs/AlOx waveg-

uide previously used for birefringence phase-matching. Despite the successes of form-

birefringence phase matching in various nonlinear interactions, the necessity of incor-


porating insulating AlOx layers not only limits the operating window of birefringence

phase-matching devices but also eliminates the possibility of integration of such devices

as electrically-injected self-pumped nonlinear sources of light.

Quasi phase matching is another approach involving a periodic modulation in a non-

linear medium. This method is not, however, based on a complete phase matching, but

rather comprises a compensation of the phase difference through periodic change in lin-

ear or nonlinear susceptibility of the media. Quasi phase-matching is widely used in

dielectrics, for example in periodically poled Lithium Niobate, both in bulk [49] and in-

tegrated [27] settings. In III-V semiconductors, quasi phase-matching was implemented

through various techniques such as domain-disordering [2] and domain-reversal [45]. De-

spite the large nonlinear conversion efficiencies achieved in such methods, fabrication

difficulties and large losses limit the application of this technique in III-V material sys-

tem.

Modal dispersion in waveguides can be utilized to allow exact phase matching between

the intended wavelengths. The third order mode of an M-waveguide was previously used

to achieve modal phase-matching [46, 47]. Lasers emitting in the third-order mode were

also recently realized for SHG [50] and proposed for entangled photon pair generation [51].

However, the aluminum-rich layers in the proposed M-waveguides are prone to oxidation

issues. Moreover, exploiting the higher-order modes in these pieces of work can lead to

higher leakage losses and difficulties in lasing in the intended mode.

A variant of modal phase-matching was recently proposed in our group using Bragg

reflection waveguides [31, 52] and tested in various three-wave mixing processes [29, 30,

34, 35]. In this case, the modal dispersion of the fundamental Bragg mode allows exact

phase matching with the fundamental TIR modes. Moreover, due to the use of transverse

Bragg reflectors to guide the light in Bragg mode, modal confinement can be achieved

through structural design rather than using aluminum-rich layers as low index claddings

such as what used in M-waveguide. These unique characteristics make Bragg reflection


waveguides a promising platform for the development of all-semiconductor parametric

devices.

1.1.2 Monolithic integration in the Bragg waveguide platform

A photonic integrated circuit is a device that integrates multiple photonic functions onto

a single chip through either monolithic or hybrid integration. Monolithic integration

offers various benefits including reduced cost, simplicity of design, physical robustness,

and bonding free fabrication.

Monolithic integration of nonlinear conversion and lasing devices into a single chip has

been under study in the past few decades. Intracavity optical parametric oscillators have

been suggested as means to such a goal [24]. Recently, electrically injected parametric

fluorescence was reported in intracavity OPOs in the Bragg laser platform [39]. In such an

intracavity design, pump is generated through lasing in the Bragg mode, and the signal

and idler are generated through parametric conversion in the same cavity. A schematic

of an integrated intracavity OPO is presented in Fig. 1.6(a). This thesis will explore the

various characteristics of parametric light generated in such an intracavity configuration.

Self-pumped nonlinear parametric generation imposes many restrictions on the device

design such as the cavity quality factor, parametric gain, and use of multi-wavelength

high-reflection coatings which may complicate the device fabrication and design. Self-

pumped DFG can be realized with less design constraints, providing an alternative easy-

to-align tunable source. In this case, while pump is still generated inside the laser cavity,

the signal light is pumped into the device so as to generate the idler through nonlinear

interaction with the pump wavelength. Fig. 1.6(b) illustrates a schematic of an electrically

injected self-pumped DFG device. Generation of pump inside the device eliminates the

need for pump alignment for pump, and the device can be realized without the need

for high-reflection coatings at the facets. These advantages prove self-pumped DFG a

good candidate for three-wave mixing for IR generation. While there has been reports


(a) (b)

Figure 1.6: Schematic of a representative a) doubly resonant SOPO and b) self-pumpedDFG laser. In the former the end facets of the diode laser are high reflection coated (HR)at pump, signal and idler wavelengths, while in the later, high-reflection coating is onlyrequired at the pump wavelength.

of self-pumped parametric fluorescence [39], and self-pumped spontaneous parametric

down-conversion [40] in Bragg laser devices, electrically injected self-pumped DFG has

never been reported in semiconductor devices to the best of our knowledge.

In addition to integrating the nonlinearities into the source, even more devices can

be integrated onto the same single chip in order to exploit the light generated through

the nonlinear process. Semiconductor ring lasers [43] do not require cleaved facets for

optical feedback and thus are suited for monolithic integration. Such lasers can be easily

integrated with other active and passive devices to form robust integrated circuits. The

OPO threshold for the present Bragg lasers was predicted to be above 4W in a doubly-

resonant OPO configuration [26]. These powers can be achieved through mode-locking

of the lasers; however, such mode-locking techniques are not available in the current

platform. Ring cavities have been previously used for mode-locking of lasers [53,54]. As

such, realization of semiconductor ring lasers on the Bragg laser platform can also be a

very attractive step in the integration of active, nonlinear devices. Fig. 1.7 illustrates

a schematic of a ring laser on a single-sided Bragg laser wafer which is used for off-

cavity nonlinear conversion. An important feature in the design of ring resonators and

semiconductor ring lasers is the coupling scheme. Evanescent couplers [43, 53, 55] are

one of the most widely used methods for out-coupling of the ring laser output power.

The spacing between the evanescently coupled waveguides is usually less than a few


Figure 1.7: Schematic of a ring laser integrated with a nonlinear waveguide for frequencyconversion outside the laser cavity.

micrometers. As such, formation of deeply etched evanescent couplers in double-sided

Bragg lasers [37] can be challenging, given the currently available fabrication equipment

in the University of Toronto cleanroom. Due to their thin upper cladding [32], single-

sided Bragg lasers can be an alternative platform to alleviate the deep etch constraint for

formation of ring lasers. Alternatively, double-sided Bragg lasers with thin top reflectors

can be subject to use in ring structures as well.

In addition to allowing for monolithic integration, DBR and DFB lasers offer very

attractive mode selectivity and wavelength tuning properties due to the frequency sen-

sitivity of the Bragg reflectors [44, 56]. Wavelength of a DBR laser can be easily tuned

through variation of the temperature or current injection into the grating section. In-

corporating such a scheme in the Bragg laser platform for nonlinear conversion provides

an extra degree of freedom in the experiment and allows for tuning of the parametrically

generated wavelengths. Conventionally, gratings in DBR and DFB lasers are grown by

interrupting the growth above the active region, etching the grating, and then growing

the upper cladding [56]. Other methods have been proposed to eliminate the technically

demanding multi-step growth such as multi-step etched laterally coupled gratings [57]

and laterally corrugated gratings [58]. Laterally coupled gratings need a two-step etch

process which will add to the complexities of the device multiple-step fabrication process.

One of the simplest grating formations available are laterally corrugated gratings which

can be fabricated in a single etch step.


1.2 Thesis overview

This thesis aims to design, fabricate, and characterize efficient Bragg reflection waveguide

lasers which are phase matched for second-order nonlinear processes. The objective

is to demonstrate self-pumped difference frequency generation in the Bragg waveguide

platform in various laser configurations to facilitate monolithic integration with other

integrated optical devices. In particular, realizing DFG in Fabry-Perot and DBR lasers

is of interest for further integration. Furthermore, the design tools needed to analyze

the device characteristics such as the far-field and temporal behavior is developed and

presented.

This dissertation is organized as follows. The general Bragg reflection waveguide

design procedure for realization of efficient phase-matched devices is presented in Chapter

2. This chapter also presents the details of a wafer design which is used for fabrication

of the devices discussed in the future chapters. Chapter 3 presents a summary of the

fabrication process, and the electron-beam lithographic processes which were developed

throughout this work to realize the presented devices. Design and characterization of a

single-sided Bragg laser which was designed for non-degenerate DFG will be reviewed in

Chapter 4. Further, implementation and characterization of various laser configurations

such as Fabry-Perot, ring lasers, and DFB lasers implemented on this wafer is outlined in

the same chapter. These test results include output power-input current curves, thermal

analysis, loss measurements, and some preliminary nonlinear measurements. Based on

modal properties of the non-degenerate single-sided Bragg laser, a double-sided Bragg

laser was designed for near-degeneracy DFG which will be reviewed in Chapter 5. The

laser characteristics as well as DFG nonlinear performance will be outlined in the same

chapter. The theoretical framework of SOPOs is examined in Chapter 6 as a guideline for

future generations of devices which will allow for nonlinea optical parametric generation.

Lastly, a summary of the contributions and possible future directions in this area are

outlined in chapter 7.

Chapter 2

Bragg lasers: design considerations

In contrast to conventional waveguides in which waveguiding relies on total internal

reflection, Bragg waveguides utilize the stop-band of transverse Bragg reflectors to provide

Bragg reflection, and hence confinement of the guided waves. Within the same structure,

light can also be confined in the high index layers through total internal reflection hence

allowing for propagation of conventional TIR modes as well. This coexistence of two

types of modes allows for modal phase-matching for second-order nonlinear frequency

conversion in Bragg waveguides. For this class of nonlinear waveguides, Bragg reflection

waveguide lasers, or Bragg lasers, serve as the platform that facilitates self-pumped DFG,

where the pump is generated inside the laser cavity and only one external source is needed

to generate a third wavelength.

In order to design practical Bragg waveguides and Bragg lasers for phase-matching,

suitable theoretical tools and design methodology is required. To this end, not only the

laser performance needs to be optimized, but also the linear and nonlinear properties of

the three interacting waves as well as their nonlinear overlap coefficients [26].

This chapter describes the conventions of designing planar Bragg waveguides and

Bragg lasers, and their modal properties. Initially, the general phase-matched planar

Bragg laser design methodology is reviewed. Section 2.2 explains two-dimensional con-

18

Chapter 2. Bragg lasers: design considerations 19

finement considerations for ridge Bragg waveguides. This novel approach will be used to

monitor and the Bragg laser etch depth for improved performance, in future chapters.

Lastly, section 2.3 provides analytical formulae for Bragg waveguide and Bragg laser

far-field calculation. Not only the far-field formulation presented can help design Bragg

waveguides with favored single-lobed far-field profiles, but also it can provide insight into

the design procedure and far-field characteristics.

2.1 Design methodology of the vertical structure

Detailed analysis of modal properties of planar Bragg waveguides with quarter-wave

Bragg reflectors was previously discussed in [59]. Furthermore, the design methodology

for phase-matched matching-layer enhanced Bragg waveguides [60] and multi-layered

single-stack Bragg waveguides [32] were studied recently. Bragg laser design methodology

has also been studied as well [26]. The present section provides a methodology for

designing planar phase-matched Bragg laser structures with a general profile. After a

short summary of Bragg waveguide modal analysis, the remainder of this section will

focus on designing the phase-matched vertical structure.

2.1.1 Formulation and definitions

A planar multi-layer dielectric waveguide is schematically illustrated in Fig. 2.1. For the

propagating mode with effective mode index of neff, the x component of wavenumber

within a given layer with refractive index nj, takes on discrete values as

kj = k0

√

n2j − n2

eff (2.1)

where k0 is the wavevector in free space and j is the layer number.

In a quarter-wave stack, each layer accumulates π/2 phase at the Bragg wavelength.

Operating at the quarter-wave condition is attractive for several reasons. For example,


Figure 2.1: Schematic of a general multilayer waveguide structure. The propagationdirection is taken along the z-axis.

at this operating point, the highest reflection coefficient from Bragg mirrors is tenable

and leads to maximum exponential decay for the guided mode in the periodic claddings,

which guarantees maximum confinement in the core. Additionally, for quarter-wave

Bragg reflection waveguides there exist simple analytical expressions for calculating the

modal dispersion properties. Given a known modal effective index, the thickness of bi-

layers of the quarter-wave Bragg reflector, t1 and t2, can be easily calculated through

k1t1 = k2t2 = π/2. (2.2)

Provided the effective index of the Bragg mode, number of periods, and refractive index

of bi-layers, the Bragg reflector stack can be easily constructed. The attributes of the rest

of waveguide layer such as the core thickness should be determined through assumption

and the resonance condition.

Assuming a thickness tj for any arbitrary layer, the transverse resonance condition is

given by [61],

2kjtj + φl + φr = 2mπ. (2.3)

Here m is the mode order, and φl and φr are the phase shifts acquired when the wave is

incident upon the top and bottom boundaries of the current layer, respectively. These


phase shifts are essentially the phase of the complex reflection coefficient from the left

and right interfaces. The reflection coefficient can be easily calculated through transfer

matrix method. Also, we usually focus on the lowest order even Bragg mode for nonlinear

conversion purposes. Adoption of the lowest order mode allows for smaller loss and

better vertical confinement while operation in the even modes provides the best nonlinear

conversion to the TIR modes which are as well lowest order even modes.

Based on the above equations, Bragg waveguides and Bragg lasers with any general

profile can be designed. Aside from the initial Bragg waveguide design, nonlinear proper-

ties of the Bragg waveguide should be examined and the structure should be modified for

optimal performance. Normalized nonlinear conversion efficiency, η, is a key parameter in

quantitative study and optimization of the nonlinear conversion process. In a nonlinear

material with length L, η is defined as Pi

PsPpL2 for a DFG process, where Pσ, σ ∈ i, s, p is

the power available for idler, signal, or pump, respectively. Similar expressions are valid

for other three-wave mixing processes. Such a constant can be calculated experimen-

tally through direct measurement of the above powers, or theoretically through coupled

mode theory. In a guided-wave structure such as the present one, normalized conversion

efficiency can be formulated as follows for a DFG process [42],

η =Pi

PsPpL2= κ2λ2i e

−αiL. (2.4)

Here, the amount of loss in the signal and idler wavelengths is assumed to be equal

(αs = αi), λi defines the difference frequency wavelength, and κ is defined as below.

κ =

√

√

√

√

deff28π2

nsninpǫ0cA(2)eff

, (2.5a)

deff =

∫∫ +∞−∞ EsEiEpd(x)dxdy∫∫ +∞−∞ EsEiEpdxdy

, (2.5b)


A(2)eff =

∫∫ +∞−∞ E2

sdxdy∫∫ +∞−∞ E2

i dxdy∫∫ +∞−∞ E2

pdxdy(

∫∫ +∞−∞ EsEiEpdxdy

)2 . (2.5c)

In the above equations, deff is the structural effective nonlinear constant, which is a

weighted average of the local effective nonlinear constant, d(x) throughout the structure.

Also, A(2)eff represents the effective nonlinear area which determines the modal overlap of

the three interacting waves in the three-wave mixing process. The same set of equations

can be used to determine the effective nonlinear efficiency both in 1D and 2D problems.

Through such calculations, the conversion performance in nonlinear waveguides can

be assessed and the waveguide structure can be optimized. However, nonlinear conversion

efficiency does not take into account any of the laser parameters. The final major step

in designing efficient phase-matched Bragg lasers is to optimize the laser properties and

ensure lasing takes place in the correct mode.

A semi-classical methodology has been previously proposed for analyzing and op-

timizing the Bragg laser nonlinear conversion efficiency together with the laser perfor-

mance [26]. It was explained that the major parameter that needs to be analyzed for such

optimization is the optical confinement factor. Optical confinement factor is inversely

related to the laser threshold current which dictates the laser performance. Optical con-

finement factor, Γ, is the proportion of energy which is effectively present in the gain

region:

Γ =

∫∫

active|Ep|2dxdy

∫∫∞−∞ |Ep|2dxdy

. (2.6)

This factor implies that only a fraction of the electromagnetic energy which is confined

in the active region experiences amplification. The threshold gain therefore, is inversely

dependent on the confinement factor, as well as being dependent on waveguide and mirror

losses, αp and αm:

γth =1

Γ(αp + αm). (2.7)

Equation (2.7) shows that in a multi-moded waveguide, modes which exhibit the


lowest loss and highest confinement factor will reach the lasing threshold at a lower gain.

As such, when designing diode lasers, the structure should be optimized to provide the

highest optical confinement factor to the desired vertical mode. In the design process

of Bragg lasers, we try to maintain a minimum ratio of 20 between the confinement

factor of the lowest order Bragg mode in which lasing takes place, and all the TIR modes

available in the structure. The next subsection provides a more detailed step-by-step

design procedure together with a few design examples. We will investigate the effect of

Bragg waveguide modal losses in another section in this chapter.

2.1.2 Phase-matched Bragg laser design in compound semi-

conductors

Designing phase-matched vertical 1D Bragg lasers can be sub-divided into two tasks:

finding the phase matching point, and optimizing the designed structure for optimal

nonlinear interactions while maintaining a large enough confinement factor. The design

of phase-matched Bragg waveguides can be carried out as follows:

1. For the given nonlinear interaction, determine the type and polarization of the

optical modes involved in the frequency mixing process.

2. Choose the materials used in the design. As we were using AlGaAs material system

in this thesis, the aluminum concentrations of core, bi-layers of the Bragg reflectors,

matching layers, quantum wells, and barriers have to be decided upon. Based on

the aluminum concentrations and the chosen wavelengths, the refractive indices,

nc, n1, n2, nm, nq, and nb can be calculated from index models such as that of [62].

3. Determine the effective index range of the Bragg mode. Ultimate minimum and

maximum values would be the minimum index at the idler frequency, and the

maximum index at the pump wavelength.


4. Decide on a layer unknown thickness other than the Bragg reflector bi-layers to

construct the structure. If the intended Bragg waveguide is a simple quarter-wave

Bragg waveguide with a single core layer, the unknown has to be the core thickness,

tc. For Bragg waveguides with multiple layer cores, the thickness of all but one of

the layers has to be pre-determined, where the unknown layer thickness will be

calculated through the solver.

5. For every chosen effective index in a loop, calculate thickness of the Bragg reflector

bi-layers, t1 and t2, and thickness of the unknown layer, based on equations 2.2 and

2.3.

6. Given the number of bi-layers in the Bragg reflectors, construct the structure and

solve for total internal reflection modes at the relevant wavelengths.

7. Check if the effective indices of the TIR and Bragg modes satisfies the exact phase

matching condition (1.3).

8. Repeat steps 4-7 to sweep the value of Bragg waveguide effective index until the

phase matching condition is satisfied.

Using the methodology presented above, a phase matched Bragg waveguide can be

generated for any given material of choice, assuming there is a solution available. For

example, Figs. 2.2 and 2.4 depict two different phase-matched examples designed through

the above process. Example 1 depicts a simple quarter-wave double-sided Bragg waveg-

uide phase matched for type-I SHG at 1550nm, and 775nm. The initial aluminum concen-

trations are taken to be x1 = 0.20, x2 = 0.60, and xc = 0.40 for the bi-layers and core. For

a type-I SHG process, the phase matching condition gets simplified to neff,ω = neff,2ω.

This is clearly shown in Fig. 2.3 which depicts an algorithm generated plot of effective

index at fundamental and second harmonic wavelengths. The selected effective index is

used as a basis for calculating the rest of waveguide parameters including t1, t2, and tc.


−2 0 22.8

33.23.43.6

Fundamental, TE0(ω)

x [µm]Ref

ract

ive

inde

x [a

.u.]

−2 0 22.8

33.23.43.6

Second harmonic,TM0(2ω) Bragg

x [µm]Ref

ract

ive

inde

x [a

.u.]

−3 −2 −1 0 1 2 3−1

0

1

x [µm]

field

pro

file

[a.u

]

Figure 2.2: Refractive index profile and mode profile of example 1 at 775nm (red),and 1550nm (blue) wavelengths. Dashed lines plotted on the index profiles depict therefractive indices.

As illustrated in Fig. 2.2, the refractive indices are calculated based on the aluminum

concentrations at all wavelengths, the layer thicknesses calculated, and the effective index

is shown as a dashed line at each diagram.

The second example studied here is a matching-layer enhanced, quarter-wave single-

sided Bragg waveguide designed for type-II phase-matched DFG. The waveguide param-

eters from top to bottom, where chosen to be xclad = 0.75, xm,top = xm,bot = 0, xc = 0.24,

x1 = 0.35, and x2 = 0. Thickness of the core, tc, and top matching layer, tm,top, was also

pre-determined to be 600nm and 200nm, respectively. The transverse resonance condition

determines the thickness of the lower matching layer, tm,bot. Once more, the methodology

presented above was used to construct the structure for DFG phase matching at 980nm,

1550nm, and 2665nm and the final structure is presented in Fig. 2.4 together with the

mode profiles. This example was studied to represent the capacity of this methodology

in designing phase-matched Bragg waveguides with any general profile.

Along with the structural design, the Bragg laser should be optimized for nonlinear

conversion and lasing characteristics. For optimization of nonlinear conversion, one or

more of the pre-determined parameters in step 2 above can be modified. For example, core

thickness, can be swept to determine the thickness required to maintain a local optimum


3 3.05 3.1 3.15 3.2 3.253.2

3.202

3.204

3.206

3.208

3.21

3.212

3.214

neff,2ω

n eff,ω

Figure 2.3: Effective index mismatch for design example 1. The algorithm determinedvalue for phase-matched neff is is 3.204 as shown with the dashed lines. The resultingcore thickness is 327.7nm.

−2 0 2

3

3.5

x [µm]Ref

ract

ive

inde

x [a

.u.] Pump, TE

0 Bragg

−2 0 2

3

3.5

x [µm]Ref

ract

ive

inde

x [a

.u.] Signal, TM

0

−2 0 2

3

3.5

x [µm]Ref

ract

ive

inde

x [a

.u.] Idler, TE

0

−2 −1 0 1 2 3−1

0

1

x [µm]

Fie

ld p

rofil

e [a

.u.]

Figure 2.4: Refractive index profile and mode profile of example 2 at 980 (red), 1550(blue), and 2665nm (black) wavelengths. Dashed lines plotted on the index profilesdepict the refractive indices.


350 400 450 500 550 600 6500

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

−9

tc (nm)

η (%

/W/c

m2 )

Figure 2.5: Normalized nonlinear conversion efficiency for example 2 plotted for a rangeof core thickness, tc. A locally optimum thickness of 562nm is determined in the rangeinvestigated.

for nonlinear conversion efficiency. This is illustrated in Fig. 2.5. Unless the sweep

space is the whole range that the parameter can take, this method only provide local

rather than global maxima. Carrying out a global optimization of nonlinear conversion

efficiency requires modification of many parameters through a vast parameter space.

Such complex optimization problems can be tackled through intricate techniques such as

genetic algorithms and simulated annealing [63]. Implementation of such techniques is

not within the scope of this thesis, and as such, we only focused on improving the device

performance by finding local optimum nonlinear conversion efficiencies. In the process of

laser design, confinement factor should also be examined for all the TIR modes available

in the structure to assure large enough confinement factor for the Bragg mode for strong

modal discrimination. The overall optimization process can be summarized as follows:

1. Sweep any chosen pre-determined waveguide parameter such as aluminum con-

centrations or thicknesses and calculate nonlinear conversion efficiency from equa-

tion (2.4). For any given choice of waveguide parameters, use the Bragg waveguide

design process above to construct and investigate a phase-matched structure.


2. Determine the optimum parameters which yields maximum efficiency for the pro-

cess under study.

3. Calculate the TIR mode profile in the pump wavelength for the optimized structure

and determine the optical confinement factor for all the modes using equation (2.6).

4. If the ratio of Bragg mode confinement factor and any other TIR mode confinement

factor, ΓBRW/ΓTIR, is less than 20, choose another waveguide parameter from step

2, which provides the optimum efficiency while maintaining ΓBRW/ΓTIR ≥ 20.

Figure 2.5 shows an optimization graph for example 2 based on the core thickness.

As the core thickness changes, so does the mode profile, hence the effective nonlinear

area/nonlinear constant change according to equation (2.5). The figure shows that in the

range of core thicknesses investigated, 562nm was chosen as it provides the maximum

nonlinear conversion efficiency within that range. The presented guidelines will be used

in chapters 4 and 5 to design single-sided and double-sided Bragg lasers for efficient phase

matching.

2.2 Two-dimensional confinement properties

A vertically defined Bragg reflection waveguide can be etched to form a laterally defined

ridge to confine the light in both vertical and lateral directions. In such a structure, the

vertical and lateral confinement occur through photonic bandgap and total internal reflec-

tion effects, respectively. Ridge Bragg reflection waveguides are reported previously for

confinement of light in passive [29,30] and active [5,37] configurations. However, experi-

ments reveal very large sensitivity of modal properties on the ridge Bragg waveguide etch

depth level. There has never been a systematic report on ridge waveguide characteristics

based on the ridge etch depth. As such we investigated the confinement characteristics

of ridge Bragg waveguides to provide insight into the physics of this phenomenon. Unlike


numerical techniques such as FDTD, effective index method [64] usually takes very little

time to calculate waveguide properties and provides better insight into the modal charac-

teristics. We analyzed the confinement properties through both a commercially available

2D mode solver [65] and effective mode theory to provide accurate 2D loss calculations

and examine the underlying physics.

2.2.1 Bragg waveguide 1D modal characteristics

In a 1D Bragg reflection waveguide with semi-infinite Bragg reflectors, Bloch-Floquet

formalism, can predict dispersion equations for the fundamental TE and TM propagating

Bragg modes [59]. In the practical situation of a finite Bragg reflector, the Bloch theorem

can still be approximately applied, given a large enough decayed in the filed profile. As

the field decay is determined by the Bloch wavenumber, the condition reduces to

ρ = ξm << 1. (2.8)

Here ξ is the imaginary part of the Bloch wavenumber and m represents the number

of periods. Therefore if the number of periods is large enough, two identical Bragg

waveguides with different number of periods will act similarly with respect to modal

properties. In other words, the effective index of a finite Bragg waveguide will not vary if

the first few bi-layers of the top Bragg reflector are etched/removed, given condition 2.8

is valid.

As a numeric example, a quarter-wave Bragg waveguide with the following parameters

is considered: index and thickness of Bragg reflector bi-layers was set to n1 = 3.379,

n2 = 3.095, t1 = 165.9nm, and t2 = 418.2nm, index and thickness of core was taken to

be nc = 3.147 and tc = 600nm, number of bi-layers in Bragg reflectors was taken to be 6,

and the simulation wavelength was set to λ = 980nm. The substrate is assumed to have

the same refractive index as that of layer 2, and the environment is assumed to be air. At


(a)

0 1 2 3 4 52.96

2.98

3

3.02

3.04

3.06

etch (µm)

Sla

b ef

fect

ive

inde

x

0 0.5 1

(b)

Figure 2.6: a) Index and mode profile of a generic Bragg waveguide, and b) 1D effectiveindex of the slab region versus etch depth in the x direction. The 1D effective index ofthe ridge section is shown as a dashed line. The star markers show the interfaces of theperiods, and the square markers show the interface of core and the top and bottom firstbi-layers. The inset shows the results for the first two periods with a higher magnification.

the number of periods considered here, ρ = 0.002 which satisfies condition 2.8. Effective

index of the TE polarized 1D slab mode closest in modal index to a Bragg mode was

calculated through transfer matrix method when the top Bragg reflector is etched to a

range of etch depths - in the x direction as denoted in Fig. 2.6(a).

Figure 2.6(b) illustrates the outcome, together with the effective index of the original

slab waveguide plotted as a dashed line. The non-monotonous changes in the effective

index in Fig. 2.6(b) allow for the etched slab Bragg waveguide and original Bragg waveg-

uide effective indices to be equal at multiple etch depths. We previously explained that

the modal effective index of an etched waveguide can be unchanged if the etch stops at

the interface of two bi-layers and condition 2.8 is valid. The above simulation shows that

this phenomenon can also occur at certain etch depths even if the condition does not

hold. Note that in the simulation, effective index of the etched and original slab waveg-

uides become equal at etch depths which correspond to location of mode profile zeros. A

ray optics method can explain that the effective index of an infinite and a semi-infinite

Bragg waveguide are generally equal, as explained in the appendix. The effect of such

characteristics on the mode confinement in 2D guided modes will be discussed in detail


Figure 2.7: (color online) Schematic of a generic ridge Bragg reflection waveguide plottedtogether with a sample mode intensity profile.

in the next section.

2.2.2 Confinement of guided modes in ridge Bragg waveguides

Figure 2.7 shows a typical ridge patterned on a lateral Bragg waveguide structure. The

optical mode of such a structure is vertically confined through photonic Bandgap effects,

while in the lateral direction, y, total internal reflection confines the mode. This section

studies the confinement properties of such modes in ridge Bragg waveguides through the

investigation of 1D and 2D modal properties.

Effective index of a 1D Bragg mode is normally lower than the index of all the other

waveguide layers. It is clear that in ridge Bragg waveguides the 2D confinement properties

of the Bragg mode will be completely different from the conventional fundamental total

internal reflection (TIR) mode. For the fundamental TIR mode, the effective index is the

highest available mode index in the ridge and the etched slab regions, which prohibits

coupling of the mode to other higher order and surface slab modes. On the other hand,

the Bragg mode effective index is lower than many slab modes in the etched section which

compete for draining the mode power outside the ridge area.

Effective index theory [64] can be used to analyze the 2D ridge mode properties


through calculation of the 1D effective index of the etched and unetched sections of the

ridge structure. In addition to analysis of conventional total internal reflection modes,

effective index method has previously been used to analyze modal properties of Bloch

modes similar to the present case [66]. We will consider a wafer structure similar to the

Bragg waveguide structure discussed in the previous example. For a 2D ridge waveguide

etched on this substrate, the 1D effective index of the etched and unetched regions are

illustrated in Fig. 2.6(b). As discussed in section 2.2.1, effective index of the etched and

unetched 1D waveguides become equal at certain etch depths. Effective index theory

predicts a lack of lateral confinement at such etch depths where the mode becomes a

slab mode. Moreover, at some areas where the 1D effective index of the etched region is

larger than that of the unetched ridge section, the structure only allows for a leaky mode

in the lateral direction to exist.

Figure 2.8 illustrates the calculated propagation loss for the 2µm-wide ridge. The

calculated loss from effective mode theory can be compared to the simulation results

from a fully vectorial commercial mode solver [65] to better illustrate the accuracy of the

predictions. Also, the mode profile is plotted at two different etch depths in Fig. 2.9. The

calculated loss values may not be strictly accurate as the de-localized mode is absorbed by

perfectly matched layers, leading to excess calculated loss values. However, the etch depth

corresponding to these peaks can accurately determine the points at which confinement is

lost. In the commercial mode solver simulations, the boundary conditions and simulation

mesh size were chosen so as to confirm consistency of the simulations. Appendix D

provides some details on evaluation of the chosen parameters. Also note that loss is

not plotted for etch depths lower than 2.7µm, as in such etch depths Bragg mode is

not localized to allow for calculation of the mode index or modal loss. As can be seen,

the modal loss culminates at certain etch depths, denoting decreased confinement in

those points. The figure shows a very good correspondence between the effective mode

theory and commercial mode solver simulations. Effective index theory approximates the


0 1 2 3 4 5−1000

0

1000

2000

3000

4000

5000

Etch depth (µm)

BR

W m

ode

loss

(dB

/cm

)

Effective mode theory2D solver

No 2D modalconfinementin this region; loss was not calculated.

Figure 2.8: Bragg waveguide modal propagation loss of the 2D ridge waveguide plottedversus etch depth in the x direction.

maximum leakage positions with less than 2% deviation from the 2D loss calculations.

The above calculations were based on the Bragg mode of a ridge Bragg waveguide.

However, a similar argument holds for any other Bragg mode in more complicated Bragg

waveguides, and even all higher order TIR modes. For every vertical ridge wafer design,

similar calculations could be carried out to determine suitable etch depths for fabrica-

tion of low-loss ridge Bragg reflection waveguides. Also, in Bragg waveguides, a major

implication of such effects is that with any modification in either index profile or wave-

length, the etch depth low loss window of operation will slightly move. As such, the stage

temperature, injection current, and lasing wavelength will eventually change the modal

propagation loss of ridge Bragg lasers.

Curved waveguides are an essential part of current integrated photonic circuits which

have been the subject to intensive research. Analysis of bent waveguides usually includes

a conformal mapping that transforms the curved optical waveguides into straight inho-

mogeneous structures which only support leaky modes. The loss characteristics of such

conformally mapped ridge waveguides can be analyzed for various etch depths using the

effective index method or 2D mode solvers similar to what presented here for regular ridge


y(µm)

x(µm

)

Mode intensity profile, 3.524µm etch depth

−5 0 5

−4

−3

−2

−1

0

1

2

3

4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(a)

y(µm)

x(µm

)


−5 0 5

−4

−3

−2

−1

0

1

2

3

4

0

0.2

0.4

0.6

0.8

(b)

Figure 2.9: Two-dimensional mode profile of the test structure at etch depths a) 3.524µmand b) 3.657µm. At 3.524µm etch depth where the loss is close to its maximum, the modeis completely de-localized, whereas at 3.657µm etch depth where loss is nearly minimal,the mode is confined well beneath the ridge.

waveguides. Such analysis will be presented in chapter 4 for determining an optimized

etch depth for realizing low loss ring resonators and lasers.

2.3 Far-field diffraction pattern

In integrated devices incorporating Bragg waveguides, analysis of the radiation pattern of

the guided modes is essential for obtaining a thorough understanding of the strengths and

limitations of these structures in interfacing with other components in any optical system.

If these devices are to be used in an integrated monolithic setting, a key parameter

in analyzing the optical radiation is the far-field (FF). To the best of our knowledge,

no previous work has been carried out on systematic analysis of the far-field patterns

of modes in Bragg waveguides. The performance and figures of merit associated with

applications utilizing Bragg waveguides such as frequency conversion and edge-emitting

Bragg-based lasers depend on a suitable far-field profile for these structures, which is the

motivation of this work.

Lasers based on single- and double-sided Bragg waveguides have been proposed the-


oretically [67] and were demonstrated recently [37, 68]. In earlier theoretical [67] and

experimental [5] studies, the dual-lobed nature of the far field of the fundamental mode

of some Bragg waveguide configurations has been identified as an impediment for effi-

cient device to device coupling of light. This is because of its incompatibility with other

guided-wave structures and optical fibers, where Gaussian-like profiles of fundamental

TIR modes are more common. For example, Fig. 2.10 shows measured far-field profile of

a Bragg laser together with the optical setup usually utilized to measure the far-field. It

is clear that the divergent, dual-lobed nature of far-field profile in the vertical direction,

where waveguiding is based on Bragg reflection, will limit the efficacy of device-to-device

coupling in certain applications; this requires use of complex optical elements for optimal

collection of the generated/guided light and adds to cost and complexity of the final

solution.

One of the goals of this thesis was to integrate nonlinear Bragg lasers with other

devices. However, while that task is being pursued, we need to couple the light in and

out of the devices using free-space optical elements such as objective lenses. The complex

far-field profile of Bragg waveguides and Bragg lasers leads to complexities in coupling the

light into and out of those devices and necessitates the use of high numerical aperture

lenses for a yet sub-optimal coupling. As such, it is imperative to study the far-field

profile through analytical and numerical approaches to improve the far-field profile for

better device-to-device coupling.

For 2D ridge structures, the lateral far-field profile can be easily approximated due

to the single-lobed shape of the near-field profile in that direction. As such, here, we

will only focus on characteristics of the Bragg mode in 1D vertical Bragg structures.

This section systematically investigates the far-field properties of the lowest order even

Bragg mode in 1D Bragg waveguides. Such a study will shed light on various far-field

regions of operation of Bragg waveguides, which have not been systematically studied

before in the literature. In addition, this work will develop an approximate formulation


(a) (b)

Figure 2.10: a) A measured far-field profile of a sample Bragg laser [5], and b) a schematicof the far-field measurement setup. LD: laser diode; PD: photo-diode. The intensityprofile is measured through a slit for various angles.

to describe the far-field of Bragg mode in Bragg waveguides using a closed-form analytical

formulation and defines its domain of validity. Our analysis is based on the introduction

of an approximation, that exploits the Gaussian expansion of an optical mode profile,

which in turn leads to an analytical formulation for the far-field of the fundamental Bragg

mode. This analytic formulation for the far-field pattern provides insight into the design

and optimization process of this type of waveguides.

Field distribution in Bragg waveguides can be easily calculated using the transfer

matrix method. Here, we use ψ(x) to denote the transverse profile of the tangential elec-

tric/magnetic field for TE/TM polarizations. Using the Rayleigh-Sommerfeld diffraction

integral with a minimum possible number of approximations leads to the diffraction for-

mula [69, 70]

Ψ(θ) = cos(θ)

∫ +∞

−∞ψ(x) exp [−ik0x sin(θ)] dx (2.9)

where θ is the observation angle from the direction of wave propagation and the term

cos(θ) provides a good approximation to the inclination factor [69].

Numerical integration can be used to calculate the far-field diffraction pattern and

predict the far-field properties. However, the advantage of having the insight of design-

ing the device using analytical closed form expressions is not available when using such


integration techniques. Consequently, the presented explanation does not provide insight

in the design and optimization process of Bragg waveguides. A more intuitive under-

standing will significantly assist in the optimization of Bragg waveguide structures for

numerous applications. This is indeed possible if a prediction of the far-field pattern of

the fundamental mode of the Bragg waveguides can be obtained via an analytical ap-

proach. We shall demonstrate the availability of analytic approximation for the far-field

intensity of the fundamental Bragg mode in the next section based on a methodology sim-

ilar to [71,72]. Initially, the focus is on conventional double-sided Bragg waveguides, but

more general cases such as single-sided Bragg waveguide will be studied in a subsection

at the end of this section.

2.3.1 Gaussian approximation of the field profile

In a quarter-wave Bragg waveguide with sufficiently large number of unit-cells in Bragg

reflectors, for the fundamental even mode, the field value at the interface of the core

and the Bragg reflectors vanishes. In this sense, the Bragg mirrors resemble perfect

conducting boundaries and the central portion of the field profile can be expressed as a

cosine function with a half-period of tc, the core thickness. Such a field profile, as can be

seen in Fig. 2.11, consists of a central portion in the core and periodically interchanging

out-of-phase and in-phase portions inside the Bragg reflectors. Ratio of the first out-of-

phase lateral peak to the central peak can be obtained by simply using the continuity of

tangential components of electric and magnetic fields at the interface between the core

and the first layer of the periodic cladding as

ρc =

(

n1

nc

)2fkck1. (2.10)

Once more, nc and n1 are the refractive indices of core and first Bragg reflector layer

adjacent to the core, respectively. Also kc and k1 are the transverse wavenumbers asso-


ciated with the two layers. Due to the imaginary nature of the Bloch wavenumber in a

Bragg waveguide, the fields in the Bragg reflector decay swiftly in an oscillatory manner.

The absolute value of the ratio of the adjacent peaks in the Bragg stack can be calculated

as

ρTBR =

(

n1

n2

)2fk2k1. (2.11)

In our analysis, each in/out-of phase part of the oscillating Bragg mode profile is

replaced with a Gaussian approximation, ψw(x), defined as

ψw(x) = exp(− x2

w2). (2.12)

with the according width, sign, and amplitude. It is well-known that a cosine function

with a half-period t is best fit to the Gaussian function, ψw(x), when [71]

w

t=

1

π. (2.13)

As such, we approximate the field distribution of the core layer with a Gaussian function

of width wc = tc/π. Similarly, the rest of the field distribution inside each unit-cell is

approximated by a Gaussian function with w = Λ/π as well. Using (2.10) and (2.11),

and assuming the amplitude of each Gaussian function equal to the maximum value for

each section, one can approximate the entire field profile as

ψ(x) = ψtc/π(x)− ρc

N−1∑

m=0

(−ρTBR)m ψΛ/π(x±∆m), (2.14)

where N is the number of unit-cells of Bragg reflectors and

∆m =tc + (2m+ 1)Λ

2. (2.15)

Expression (2.14) offers an analytical form for the near-field approximation of the Bragg


Table 2.1: Design parameters for examples D1 to D3. All three examples operate at thefree space wavelength of λ = 775nm.

Design example D1 D2 D3

nc 3.1714 3.1714 3.1714n1 3.5305 3.5305 3.5305n2 3.1771 3.1771 3.1771tc (nm) 140 700 3000t1 (nm) 61.1 117.6 124.4t2 (nm) 69.8 331.1 845.6neff 1.5482 3.1227 3.1688

mode. We can now proceed to calculate the far-field using the diffraction integral.

The contribution of the Gaussian function in (2.12) to the diffraction integral of (2.9)

is given as

Ψw(θ) = cos(θ)ξw(θ), (2.16)

ξw(θ) =w√2exp

[

− [k0 sin(θ)w]2] . (2.17)

Using (2.14) and (2.17), an approximate diffraction pattern for the waveguide is obtained

as

I(θ) ∝ |Ψ(θ)|2 = cos2(θ)[

ξtc/π + ρcξΛ/πG(θ)]2

(2.18)

where

G(θ) = −2N−1∑

m=0

(−ρTBR)m cos [k0 sin(θ)∆m] . (2.19)

In case of a semi-infinite structure or a Bragg waveguide with an insignificant leakage

loss, (2.19) can be further simplified as

G(θ) ≈ −2cos(

k0 sin(θ)tc+Λ2

)

+ ρTBR cos(

k0 sin(θ)tc−Λ2

)

1 + ρ2TBR + 2ρTBR cos (k0 sin(θ)Λ). (2.20)


Figure 2.11: Near field of the three design examples as given in Table 2.1; exact (solid)and approximate (dotted).

We examined the validity of the proposed model by applying it to three examples

introduced in Table 2.1. The resulting near and far fields are illustrated in Figs. 2.11

and 2.12 respectively. The approximate near-field is calculated using (2.14) and is plotted

together with the exact solution in Fig. 2.11. Similarly, in Fig. 2.12 the exact far fields

are obtained using expression (2.9), whereas the approximation conveys the results of

the model presented in (2.18). The two presented figures illustrate a good agreement

between the exact and approximate near-field and far-field in all the examples, which in

turn demonstrates the accuracy of the proposed model.

In general, analytical approaches impart a useful intuition about the influence of the

various waveguide parameters on the FF. In the approximation discussed here, detailed

analysis of the far-field behavior can be achieved by examining the equations derived

here. Such analysis was presented in [73] and can be used to facilitate the design and

optimization procedures for Bragg waveguides and Bragg lasers.


Figure 2.12: Far field of the three design examples as given in Table 2.1; exact (solid)and approximate (dotted).

2.3.2 Quarter-Wave Bragg waveguide design criteria

Manipulation and tailoring the far-field diffraction of an optical device is an essential

design consideration for many photonic devices. In most practical applications, a single-

lobed, low-divergence beam is desired for enhancing power coupling between optical

elements. In what follows, we will investigate a condition leading to a Bragg mode

far-field to be a single lobe centered around θ = 0.

Equation (2.18) can be reformulated as

Ψ(θ) = ξtc/π cos(θ) + ρcξΛ/πG(θ) cos(θ) = Ψ1(θ) + Ψ2(θ). (2.21)

This expression is composed of two terms: the first term accounts for the far-field of

the field profile within the core layer, and the second term is associated with the far

field resulting from the rest of the near field distribution. Examining these two terms

separately elucidates the significant role which the first term plays in contributing to a

single lobe in the FF.

The contribution of each of the two terms discussed above is illustrated in Fig. 2.13


Figure 2.13: Ψ1 (solid) and Ψ2 (dashed) expressed in (2.21) for the design examplesstudied in Table. 2.1. Both terms are normalized to the maximum of Ψ1.

for the design examples introduced in Table 2.1. For design example D1, the second

term, Ψ2, encounters one single extremum at θ = 0. Therefore, although the two terms

act to partially cancel each other out, the resulting far-field is a single lobe. This takes

place when the effective index is well below the stack refractive indices, which usually

significantly increases the leakage losses of the waveguide when using finite Bragg stacks

and is hence seldom used in practical structures. However, the behavior is different for

D2. As illustrated in Fig. 2.13, the second term has more than one extremum. Although

the two lateral maxima have small values compared to the value at θ = 0, the overall

far-field pattern is double-lobed as a result of the destructive superposition of the two

terms at the center. In the last example, D3, Ψ1 is much larger than Ψ2 due to the large

ratio of the peaks in (2.10), therefore leading to one single lobe in the superposition of

the two terms.

The effect of Ψ2 on the total far field can be quantitatively accounted for by examining

the overall far field in the central region, Ψ(0). From (2.21) and (2.20), this value can be


expressed as,

Ψ(0) ≈ 1− 2ρc

1 + ρTBR

= 1− 2

(

n2

nc

)2fkc

k1n2f2 + k2n

2f1

. (2.22)

It can be clearly seen that Ψ1 acts to partially cancel out Ψ2 at the far-field center as

discussed previously. Hence, disregarding the special cases in which Ψ2 has only one

extremum, it is deduced that the far-field profile will be closer to a single-lobed pattern

for smaller second terms. As such, the condition of having a single lobe for the far-field

reduces to the examination of the wavenumbers and refractive indices in different layers

of Bragg waveguides, and can be expressed as

2

(

n2

nc

)2fkc

k1n2f2 + k2n

2f1

<< 1. (2.23)

A well confined single-lobed far-field is essential for appropriate communication with

other optical components. However single-lobed D1-like structures are of no practical

use due to the lossy nature of the Bragg mode. Hence, the only possibility to achieve a

favorable far-field profile is the structures which fulfill the above condition. In example

D3, on the contrary, where the mode is well confined in the core, the left hand side

of (2.23) reduces to 0.1441, which is sufficiently small to comply with the condition

in (2.23). Such an equation is meant to provide a condition for single-lobed FF, and does

not set any limitations on the spatial divergence. In order to improve the usefulness of

this condition, an additional constraint can be introduced to limit the tolerable far-field

width for a given application. Due to our interest in well confined low-loss modes, it is

possible to disregard the cos(θ) term to further simplify the expression of the far-field

in (2.18). After some manipulation, the full width at half maximum (FWHM) of the

total far-field can be approximated as,

FWHM ≈ 2 sin−1

(

π

k0tc

√

ln 2

2

)

. (2.24)


The constraints (2.23) and (2.24) provide a set of basic tools for designing double-

sided Bragg waveguides with suitable, single-lobed and low divergence far-field profiles.

However, not only the mentioned conditions can be used to achieve such far-field prop-

erties, but also the Gaussian model presented in (2.18) itself can be adopted to further

manipulate the far field in more complex settings.

2.3.3 Other configurations: Single-sided Bragg waveguide

In the previous subsection, Gaussian approximation was focused on the far-field analysis

of double-sided quarter-wave Bragg waveguides. A similar approach can be used to

approximate the far-field of any other field profile with analytically known near-field

characteristic and Gaussian-like lobes. Such modes may include, but are not limited to:

higher order Bragg modes, asymmetric Bragg modes, and ARROW modes. However,

the near-field characteristics presented here should be changed accordingly for any of

the above-mentioned analysis. As the present thesis proposes single-sided Bragg lasers

for integration applications, such structures were examined to demonstrate the ability

of the current Gaussian approximation to model the far-field of other Bragg waveguide

structures.

In order to model complex Bragg structures such as single-sided Bragg waveguides,

there should be some changes made to the method described in the previous sections,

to fit the new multi-layered core structure. For example, if the structure designed in

example 2 in section 2.1.2 is to be analyzed, there will be matching layers on top and

bottom of the core layer. Hence, the absolute ratio of peak in the peak and adjacent

matching layers will read as,

ρcm =

(

nm

nc

)2fkckm

(2.25)

where nm and km represent the refractive index and transverse wavenumber in the match-

ing layers. Moreover, as the refractive index of the first layer is lower than the second


2.83

3.23.43.6

Ref

ract

ive

inde

x [a

.u.] Pump, TE

0 Bragg

−2 −1 0 1 2 3−1

0

1

x [µm]

Fie

ld p

rofil

e [a

.u.]

(a)

−50 0 500

0.2

0.4

0.6

0.8

1

far−

field

inte

nsity

(A

.U.)

θ (degrees)

(b)

Figure 2.14: a) Index profile and near field, and b) far field profile of example 2 in sec-tion 2.1.2. The solid curves show the values calculated through Transfer Matrix Method,and the dashed-dotted curve shows the Gaussian approximation results. The dashed linein the index profile represents the effective index of the Bragg mode.

layer in the Bragg reflector, equation (2.11) should be changed to:

ρTBR,SS =

(

n2

n1

)2fk1k2, (2.26)

and finally the mode profile can be estimated as the following:

ψ(x) =− ρcmψtm,top/π(x+tc + tm,top

2) + ψtc/π(x)− ρcm

N−1∑

m=0

(−ρTBR,SS)m ψΛ/π(x−∆m),

(2.27a)

∆m =tc + tm,bot − t2 + (2m+ 1)Λ

2. (2.27b)

Here tm,top and tm,bot define thickness of the top and bottom matching layers, respectively.

In the above solution there were two major changes compared to (2.14): the contribution

of the top and bottom matching layers have been added to the near-field profile; and

only the contribution of the bottom Bragg stack to near-field is taken into account as

there is no top Bragg stack in the structure.

Fig. 2.14(a) illustrates the approximated near-field profile as well as the exact mode

profile calculated through Transfer Matrix Method. The figure shows a good agreement


between the two mode profiles showing less than 8% deviation in the peak values in

the two normalized near-field profiles. Similar to the previous cases, the far-field profile

associated with the above near-field profile can be calculated through the diffraction

integral. Through this, the diffraction pattern for this structure reads as:

I(θ) ∝ |Ψ(θ)|2 = cos2(θ)[ξtc/π + ρcm[ξtm,top/π exp (−ik0 sin(θ)[tc + tm,top]/2) + ξΛ/πGSS(θ)]]2.

(2.28a)

GSS(θ) =N−1∑

m=0

(−ρTBR,SS)m exp (ik0 sin(θ)∆m) , (2.28b)

where ∆m is defined in (2.27). A plot of this model is illustrated in Fig. 2.14(b) together

with the diffraction integral of the exact mode profile. The figure shows a close agreement

between the Gaussian approximation and values directly calculated from the diffraction

integral of the exact mode profile. This example shows accuracy and versatility of the

proposed analytical approximation as a universal tool for estimating and optimizing far-

field profile of any generic Bragg mode.

2.4 Summary

This chapter focused on theoretical investigation of various design aspects of Bragg

waveguides and Bragg lasers for designing practical devices for integration. Initially,

a methodology for design of one-dimensional phase-matched Bragg waveguides/Bragg

lasers was reviewed along with a few different numerical examples. Some of the design

considerations outline here such as monitoring confinement factor of guided modes will

have major impact on the wafer designs outlined in chapters 4 and 5. Two-dimensional

confinement properties of Bragg waveguides were studied as well, through both numerical

and semi-analytical methods. Effective index theory was employed to provide insight into


the physics of modal loss properties of ridge Bragg waveguides. It was shown that the

modal lateral optical confinement is lost at certain ridge etch depths, and the effect was

ascertained to the equality of effective index of the ridge and the slab modes. This novel

study will be extremely important in determining the suitable etch depth for functional

ridge Bragg lasers implemented in the future chapters.

Lastly, far-field properties of Bragg waveguides were investigated and design guide-

lines were suggested for single-lobed far-field operation of Bragg waveguides. A Gaussian

approximation of the fundamental Bragg mode near-field profile was proposed. By apply-

ing such an approximation, an analytical formula for calculation of the far-field diffraction

pattern of a Bragg mode can be derived for a simple and effective far-field pattern calcula-

tions. Using the proposed close-form formulation, a design criteria for Bragg waveguides

with tightly focused single-lobed far-field was provided. Even though the method was

initially derived for quarter-wave Bragg waveguides, it was shown that it can be used for

any general Bragg waveguide structure, albeit with slightly larger errors. This far-field

study provides an analytical tools that inform the design and enables the optimization

of Bragg waveguides and Bragg lasers with improved far-field profile and for better in-

and out-coupling from the devices.

Chapter 3

Fabrication process using electron

beam lithography

The initial aim of this research was to implement various elements including ring cavities

and surface gratings to enhance the functionality of the Bragg waveguide platform. These

components require sub-micron feature size and/or strict constraints on the feature sizes.

Both of these characteristics are offered by electron beam lithography. Photolithography-

based processes for microfabrication of ridge waveguides and diode lasers were available

within the group, thanks to previous work carried out by other group members. However,

when this research started, there were no robust ebeam lithographic processes developed

for fabrication of diode lasers within TNFC. Hence, one of the tasks on the processing

front for this research was recipe development for ebeam lithographic microfabrication

and modification of the steps in between based on the new lithography requirements.

This chapter presents an outline of the fabrication process, as well as the details of

different ebeam processes developed. In addition to the lithography process, we worked

on other fabrication steps, such as improvement of the GaAs plasma etch quality and

process development for n-type and p-type contact deposition for GaAs. There were

not processes for the laser diode contacts available within TNFC at the start of this

48

Chapter 3. Fabrication process using electron beam lithography 49

Figure 3.1: Major stages in fabrication of semiconductor diode lasers.

work. The developed processes will be reviewed in this chapter where a separate chapter,

Appendix B, is dedicated to the details of the final process in a step-by-step format.

3.1 Summary of the fabrication process

The many steps to fabricating diode lasers can typically be broken into three major

stages as illustrated in Fig. 3.1. Each stage is composed of many steps, which should be

carefully carried out to lead to good device performance at the final stage. Figures 3.2,

3.3, and 3.4 show detailed flowchart descriptions of the steps required during each stage.

In stage 1, the mesa structures such as the ridge waveguides and etched marker

patterns are defined into the substrate by plasma etching of the AlGaAs substrate. De-

pending on the resist used, and its resistivity to III-V plasma etching processes, there

may be a need for a hard mask. Usually, polymer-based ebeam resists need to be used

in conjunction with a silica hard mask for III-V material plasma etch. Given its good

resistivity to plasma etch and resolutions it provides, Hydrogen silsesquioxane (HSQ)

was used for this process. The use of this resist eliminates the need for a separate silica

hard mask.

In stage 2 of the fabrication process, the surface is electrically and optically isolated


Figure 3.2: Summary of stage 1 of the fabrication process: defining the mesa structures.

using a layer of silica, and planarized using HSQ. To let the current pass through the

active region of the laser, a via opening is patterned above the ridge. Inaccurate imple-

mentation of this stage can lead to vias etched on the waveguide sidewalls, or even not

within the waveguide region; this can eventually lead to oxidation of the cladding and

render the diode lasers unusable. Finally, in stage 3, suitable n-type and p-type contacts

are deposited and the sample is thinned to allow for cleaving sufficiently short laser bars

while avoiding damaging the laser facets.

Resist exposure in the above-mentioned steps can be carried out through either pho-

tolithography or electron-beam lithography. In the ebeam lithography procedure, the

electron beam sensitive material - the resist - is exposed by an electron beam accurately

controlled by the electron gun and the piezo-controlled stage. The areas which are ex-

posed/not exposed by the beam will be washed away during the development phase, if

the resist used is a positive/negative-tone resist. Ebeam lithography is well-suited for

applications which need very high resolutions, in the nm regime. Moreover, unlike pho-


Figure 3.3: Summary of stage 2 of the fabrication process: electrical isolation and definingthe via openings.

tolithography, ebeam lithography provides flexibility due to its lack of need to a physical

mask, leading to applications in low-volume production of semiconductor components

and research and development. University of Toronto is host to an EBPG 5000+ ebeam

lithography system (Fig. 3.5). This tool allowed us to explore various device structures

which needed either resolutions not achievable through photolithography or flexibility in

the mask design.

In order to do the two latter stages in Fig. 3.1, a rigorous alignment procedure is

needed. In photolithography, the alignment was carried out by careful manual aligning

of the structures monitored using the optical microscope. In ebeam lithography, however,

the alignment is automatic, and metal or etched markers are needed to do the exposure.

We used 20 × 20µm etched markers for aligning the patterns in the different levels of

laser fabrication process. These etched markers are patterned on the sample at the first

stage along with the waveguides.


Figure 3.4: Summary of stage 3 of the fabrication process: Deposition of the electricalcontacts.

Figure 3.5: EBPG 5000+ electron-beam nanolithography system by Vistec LithographyLtd.


The ebeam lithography processing of the device has to be carried out in the same three

stages as the fabrication process: defining the mesa structures including the waveguides

and etched markers, defining the via openings, and defining the contact mask. The details

of the overall fabrication process including a step-by-step recipe is presented in a separate

chapter as Appendix B to this thesis. Due to the high precision and good etch quality

needed for functional devices, there were a few different recipes and resists proposed

to decide on an optimum and rebuts ebeam recipe. Appendix C outlines the recipes

developed for each lithographic stage, and the final developed recipes are presented below.

3.2 Defining the mesa structure

The waveguides and etch markers should be first patterned using ebeam lithography, and

then plasma etched using the Minilock compound semiconductor etcher in the Bahen

cleanroom. These steps are summarized in this section. Based on the ebeam resists

available in the TNFC cleanroom, we had to propose a few different processes before

we decided on the most versatile and least expensive process for defining the features

etched in the AlGaAs wafer. The ebeam resists which were examined included ma-N

2410, ZEP-510A, and Hydrogen silsesquioxane (HSQ). While negative tone resists are

more suited for patterning small form factor features such as waveguides, positive resists

can be better used in patterning trenches.

HSQ is a negative tone electron-beam resist suitable for high resolution lithography.

The resist is available in the market in various concentrations. In our experiments, we

used Dow Corning’s Fox15 diluted with MIBK in a 1:1 ratio. Due to the changes in its

physical and chemical properties after exposure and curing, HSQ can replace the silica

hard mask for plasma etching of GaAs. This lack of need to deposit an additional layer

of silica on the GaAs surface and silica plasma etching leads to a great reduction in the

complexity of the whole fabrication process. The ebeam resist was spin coated on the


Table 3.1: Detailed mesa structure development recipe for Fox15:MIBK (1:1).Spin coat Soft bake Development time Rinse time Hard bake

3000RPM 160oC 180s in CD-26 30s in 160oC(584accl) (120s) DI water (300s)

substrate using spinners with precise rotation speed and acceleration control. A faster

spin speed results in a thinner resist film. In this case, based on the final etch depth

requirements, a spin speed of 3000 RPM, rotation per minute, was selected to provide

a 200nm thick layer of resist. After spinning, the sample was soft-baked at 160C to

evaporate the resist solvents and leave a solid film on the substrate. After this, the

sample was loaded into the EBL tool for exposure.

The development time of HSQ is heavily dependent on the size of exposed features.

For example, throughout our experiments, we found out that while a 2µm waveguide

exposed at 450muC/cm2 would be fully developed after 120s of development time, 20µm

square markers exposed at the same dose will be over exposed even after 300s of devel-

opment time. As such, a rigorous lithographic recipe had to be developed to allow for

full development of all the different features exposed at systematically chosen doses. In

our experiments, we had a few different waveguide widths and device configurations: 1-

2µm wide waveguides; 2- 4µm wide waveguides; 3- 2µm wide waveguides evanescently

coupled with a 2µm air gap; 4- 2µm wide waveguides evanescently coupled with a 2µm air

gap; and 5- surface gratings of 898nm period. Table 3.1 shows the details of the process

developed for HSQ including the parameters chosen for each configuration. As shown in

the table, after the exposure, samples are immersed in developer so that the non-exposed

areas are washed away, or developed. Fig. 3.6(a) shows an optical micrograph of the

developed resist patterns for 2µm wide waveguides.

After defining the waveguides and markers, the samples should be hard baked for

5 minutes at 180C and then etched in the compound semiconductor plasma etcher

available in TNFC cleanroom. The gases used are chlorine, BCl3 and Argon, and the


Table 3.2: EBL exposure parameters for the various feature sizes of the mesa structures.

Feature size Beam current Exposure dose Resolution

2µm 5nA 450µC/cm2 25nm4µm 5nA 400µC/cm2 25nm

4µm coupler 5nA 300µC/cm2 25nmSurface grating 5nA 400µC/cm2 5nm20µm marker 5nA 300µC/cm2 25nm

(a) (b)

Figure 3.6: a) Microscope image of 2µm wide waveguides patterned on AlGaAs, usingthe diluted Fox15 resist. The exposure dose was 450µc/cm2. b) An SEM micrograph ofthe cross section of the same sample after 120s etch.

detailed etch recipe is presented elsewhere [42]. To avoid heating the samples and affecting

etch rate and quality, a 100s cool-down step was introduced into the etch process for every

50s etch time. During the cool-down step, the samples remained in the etcher chamber,

but the plasma and gases were turned off. Figure 3.6(b) shows a cross sectional SEM of

a sample after 120s AlGaAs etch.

After the AlGaAs plasma etch, the resist has to be removed to allow for carrying out

the rest of the steps. At this point, due to the multiple heating processes and the plasma

etch, HSQ has turned into crystallized silica. Hence, to remove the resist we utilized

the silica plasma etcher in the TNFC cleanroom the Phantom etcher. The etch process

uses CHF3 as the active gas and Helium [42]. Note that in contrast to previous recipes

developed in the group [42], in the current recipe the use of buffered-oxide-etchant, BOE,


is avoided as it could damage the high aluminum concentration cladding layer in some

of wafers under study [74].

Mesa etching and/or implant processes are usually used to isolate GaAs structures

electrically, and to limit current diffusion when electrically injected [75]. Proton implan-

tation is specifically more important in gain guided diode lasers where current diffusion

can be exceedingly high. As there were no proton implantation systems in the TNFC

cleanroom, injected current of diode lasers had to be only confined through mesa etch of

ridges. This can potentially have adverse effects on device electrical performance. Due

to plasma etch rate inaccuracies, the etch depth cannot be controlled accurately and

can range from 0.9-1µm/min with the current plasma etch recipe. Aside from carrier

diffusion, there are two effects which define the optimal etch depth for mesa structures:

etch profile cannot be deeper that the location of active region to avoid formation of

surface states and carrier surface recombination; Moreover, as discussed in section 2.2, to

provide functional confinement in the Bragg mode the etch is limited to certain depths.

As such, reduction of carrier diffusion can be accomplished through accurately designed

and controlled mesa etch. The designs considered here, were normally etched up to less

than a few hundred nanometers above the active region which should largely diminish

the effect of current diffusion.

3.3 Electrical isolation

Since reaction of AlGaAs with the ambient, especially oxygen, can modify the chemical

and hence electronic and optical properties of the devices, it is essential to limit exposure

of the etched ridges to the ambient. Silicon oxide and silicon nitride are widely employed

to isolate AlGaAs integrated devices such as diode lasers. After the AlGaAs etch and

resist removal, a 400nm silica layer is deposited on the samples for electrical isolation

using a pre-existing plasma enhanced chemical vapor deposition (PECVD) recipe [42].


Table 3.3: EBL exposure parameters for the various feature sizes of the mesa structures.

Feature size Beam current Exposure dose Resolution

2µm 5nA 450µC/cm2 25nm4µm 5nA 400µC/cm2 25nm

4µm coupler 5nA 300µC/cm2 25nmSurface grating 5nA 400µC/cm2 5nm20µm marker 5nA 300µC/cm2 25nm

While in a planar sample the contact metal can be deposited in an evaporator with

simple stationary holders, non-planar etched samples need to be treated in evapora-

tors with rotary holders which is not available in the TNFC cleanroom at University of

Toronto. As such, after deposition of silica, the samples were planarized with a layer of

HSQ so as to reduce surface damage to the samples, as well as improvement of contact

quality. A 500nm layer of undiluted Fox15 was spin coated on the samples at 1500rpm,

which is the lowest rotation speed which does not lead to bubble formation on the sam-

ple surface. The bake time and temperature had to be tuned to 100C and 5 minutes

through various experiments to avoid formation of cracks on sample surface. Finally,

at the end of the planarization process HSQ has to be cured at 390-450C to cross-link

the resist. Rapid thermal annealer (RTA) was used for curing the sample at various

temperatures. It was noticed that the temperature ramp up time should be long enough

to avoid temperature induced cracking of the resist. The final RTA recipe is detailed in

table 3.3, and optical and SEM micrographs of samples after the cure are presented in

figure 3.7. As seen in the figure, some cracks have formed on the sample surface after

the cure and there is room for improvement to the planarization recipe.

Formation of via openings on top of the lasers is essential for electrical injection.

Through these etched via openings, the metal contacts will be able to pass the current

through the silica layer to the active region of the individual lasers. Patterning such an

opening in the structure can be best achieved through use of positive resists due to the

minimal exposure area only in the via section.


(a) (b)

Figure 3.7: a) top view optical microscope image and b) cross sectional SEM micrographsof samples planarized with HSQ, after annealing.

Table 3.4: Detailed ZEP-520A recipe for via openings in the electrical isolation.Spin coat Soft Beam Exposure Resolution Development Rinse Hardspeed bake current dose time time bake

2×2000RPM 180C 5nA 280µC/cm2 10nm 70s in 30s in (9:1) 100C584accl (180s) ZED-N50 MIBK:IPA (300s)

ZEP-520A is a widely used positive tone ebeam resist used in this application. The

maximum resist thickness achievable with ZEP is around 500nm. Given the surface

morphology of the samples, a thicker layer of resist is needed to mask the waveguide top.

As such, two layers of resist were spin coated on the passivated samples at 2000RPM to

provide a 1µm layer of resist on flat areas of the sample surface. The samples were soft

baked at 180C for 3 minutes after each single spinning to avoid formation of cracks on

the resist surface. As a rule of thumb, less cracks would form on the resist surface at

higher soft bake temperatures.

Details of the lithography process are given in table 3.4 and microscope and SEM

micrographs of a sample treated with the recipe is presented in Fig. 3.8. After defining

the via openings using the ZEP-520 resist, silica was etched using a previously developed

plasma etch recipe in the Phantom etcher in the TNFC cleanroom. Also, the remaining

resist was removed with a 10 minute dip in ZDMAC resist remover. After inspection


(a) (b)

Figure 3.8: a) top and b) cross-sectional SEM micrographs of vias patterned on AlGaAswaveguides covered with 340nm silica after 100s silica etch and resist removal.

with optical microscope, it was noticed that some of the resist may stay on the sample,

likely due to its high temperature sensitivity. In such cases, the samples were oxygen

ashed in the plasma asher in the Bahen TNFC cleanroom for 2 minutes. The power was

set to 100W and oxygen pressure was 0.3mTorr.

3.4 Contact deposition and liftoff

After the the via preparation, contacts should be patterned on the laser samples as the

last major step in the diode laser fabrication process. To define the contact pattern, a

layer of resist is usually formed on the sample surface in areas which are not supposed

to have contact layers. After the resist formation, metal contacts are deposited on the

sample surface and then the resist is removed from the surface. Through this process, the

metal contact layer will be ”lifted off” from the sample surface, leading to a pre-designed

pattern for the remaining metal contact.


Table 3.5: Detailed liftoff pattern development recipe for ZEP-520A.Spin coat Soft bake Development time Rinse time

2×2000RPM 180oC 70s in 30s in (9:1)(584accl) (180s) ZED-N50 MIBK:IPA

Table 3.6: EBL exposure parameters for the two exposed areas in the 10µm (high reso-lution) and above 10µm (low resolution) vicinity of the contact gap.

Exposure area Beam current Exposure dose Resolution

High resolution 5nA 160µC/cm2 10nmLow resolution 25nA 360µC/cm2 100nm

3.4.1 Ebeam process for defining the liftoff pattern

Due to its ease of removal, ZEP is a favorable ebeam resist for liftoff processes. Once

more, two spin coated layers of ZEP-520A were used to provide a thick (1µm) layer of

resist to facilitate the liftoff process. Using a low resolution beam in the ebeam exposure

process can reduce the write time significantly beside using higher beam currents. In the

case of simple liftoff patterns with well-separated (> 10µm) contact sections, a resolution

as low as 100nm can be used. However, in the case of closely spaced contact pads such

as two contact pads in a multi-section laser, a low resolution pattern can lead to over

exposure of the gap area in between the two contact pads. Consequently, a hybrid

exposure process was used to allow for exposing the areas at the vicinity of the couplers

with a high resolution, while exposing the rest of the structure with a lower resolution

to reduce the write time. The dose of the two patterns were stepped in a dose test to

find the suitable doses for the two resolutions exposed at the same time. The details of

the final process are given in table 3.5 and microscope and SEM micrographs of samples

treated with the recipe are presented in Fig. 3.9.

3.4.2 Metal contact deposition and liftoff

At the beginning of this research, there were no metal deposition processes available

within the University of Toronto TNFC cleanroom for GaAs/AlGaAs semiconductor


(a) (b)

Figure 3.9: a) A microscope image of separate contact pads after developing the resist. b)An close-up SEM micrograph of the separation region between two contact pad regions.

(a) (b)

Figure 3.10: Edwards Auto 306 ebeam evaporator and a diagram of evaporation process.

devices. As stated earlier, metal deposition on non-planar samples is typically carried

out using evaporators with rotary holders so as to assure metal deposition on all surfaces.

As such, metal deposition on the group’s laser samples was traditionally carried out in

another facility (University of Sherbrooke) where electron-beam evaporators with rotary

holders are available. This process is both costly and time consuming as it requires

communication with another cleanroom facility, shipment of the samples, and relying on

the time and facility constraints of the other facility for deposition.


In order to eliminate this problem and we had to develop a metal contact deposition

recipe for GaAs/AlGaAs material system for the first time in University of Toronto. We

utilized the electron-beam evaporator available in the TNFC cleanroom, where samples

were planarized as discussed in the previous section to improve deposition on the side

walls. Further, we developed separate processes for deposition and thermal annealing

of metal contacts on p- and n-type doped GaAs surfaces using the ebeam evaporator in

TNFC cleanroom. Electrical characteristics of the deposited contacts were investigated

to assure high-quality of the deposited contacts. A summary of the electrical charac-

terization will be outlined in the next subsection. After defining the contact pattern as

explained above, p-type metal contacts were deposited on the samples using the Edwards

auto 306 ebeam evaporator. These include 8nm of titanium and 200nm of gold. Tita-

nium is mainly used to improve adhesion of the top gold layer to the bottom GaAs/SiO2

layers. Titanium and gold sources are initially loaded into the chamber in two separate

graphite crucibles and the chamber is pumped down to reach an initial pressure below

2× 10−6mbar. Generally the deposition rate was kept around 0.2-0.7nm/s which usually

required currents up to 50 and 150mA for titanium and gold, respectively.

After unloading the samples, the p-type metal was lifted off by soaking the sample in

ZDMAC resist remover heated to 60C for 20 minutes. The sample is then inspected with

the optical microscope while still soaked in ZDMAC; if shreds of metal still remain on

the liftoff regions, sample is sonified for up to 20s in the ultrasonic bath. Note that due

to the fragile nature of the multi-layered sample, especially the planarization HSQ layer,

sonification for longer times may lead to surface damage to the sample. After ensuring

that the liftoff process is fully carried out, the samples are cleaned with acetone, IPA,

and blow dried with nitrogen gun.

Depending on final size of the cleaved lasers, the samples should be thinned down

to 150-300µm thickness. Thinning and polishing is carried out using a Boehler pol-

isher available in the TNFC cleanroom. The details about the thinning process can be


Table 3.7: Summary of the RTA recipe for contact alloying.Temperature phase Time Temperature

Ramp up 180s 0-180CConstant 30s 180CRamp up 360s 180-390CConstant 60s 390CCool down 180s -

found elsewhere [76]. Consequently, the n-type metal should be deposited on the pol-

ished/tinned side of the samples. This consists of 45nm gold, 25nm germanium, 30nm

nickel, and 120nm gold and the crucible materials are graphite, quartz, alumina, and

graphite, respectively. Due to low beam quality in the Edwards evaporator, the alumina

crucible cracked multiple times during the nickel deposition. Maximum required current

to keep the deposition rates within 0.2-0.7nm/s is 120mA for both nickel and germanium.

After the metal deposition, the samples were cured with the AnnealSys rapid thermal

annealer to alloy the deposited metals. Annealing for 0.5-3 minutes at 390-420C is

commonly used [77]. Similar to the previous RTA step, temperature and ramp up time

were chosen moderately to avoid surface damage to the sample. The developed RTA

recipe is presented in table 3.7

Optical and SEM micrographs of a sample after the liftoff are presented in figure 3.11.

As can be clearly seen, the metal is completely lifted off from the gap and the two contact

pads are disconnected from each other, forming a two-section laser. However, surface

cracks in HSQ appeared in some of the samples, probably due to our many RTA cures

and various chemical processes carried out. As such, other planarization strategies should

be studied on the side in future.

3.4.3 Contact characterization

Deposition of good ohmic contacts is an important part of fabrication of good semicon-

ductor devices. The fabrication of a good ohmic contact depends on many factors and


(a) (b)

Figure 3.11: Optical and SEM micrographs of a sample after the metal liftoff.

ohmic contacts should be tested after each run to ensure quality. Here we will outline the

basic principles of transmission line method (TLM) to characterize these contacts. Our

measurements will be presented and compared to what expected from similar contact

qualities reported in the literature.

One of the most common approaches used for characterization of ohmic contact qual-

ity is the transfer length method (TLM) proposed by Shokley [78]. Due to some sim-

plifications in the original method, circular test structures were instead used for our

measurements. These consist of conducting circular inner regions of constant radius L,

a variable gap of width d, and a conducting outer region as shown in Fig. 3.12(a).

The total resistance between two pads of a circular TLM structure, RT , is shown to

be approximated by [79]

RT =Rsh

2πL(d+ 2LT )C (3.1)

where Rsh defines the semiconductor surface sheet resistance, Rc is defined as contact

resistance, LT is called transfer length, and C is a correction factor defined as

C =L

dln(1 +

d

L). (3.2)

The contact characteristics including sheet resistance, contact resistance, and transfer


length can be calculated by a linear fit to the “corrected” total resistance between two

pads with different gaps. This can be better illustrated in Fig. 3.12(b) where resistance

measurements from one of our TLM samples is illustrated together with the interpolated

values. The contact specific resistivity defines the contact quality and can be calculated

from contact resistance and transfer length: ρc = Rc(πL2T ). Units of specific contact

resistivity is Ωcm2 and values of the order of 10−6 Ωcm2 or smaller are typically reported

for good ohmic contacts.

The values calculated for the measurement presented in Fig. 3.12(b) were measured

to be: Rsh = 225.60 Ω/sq, LT = 12.31 µm, Rc = 8.84 Ω, ρc = 4.214e − 7 Ωcm2. These

values lie within those reported in the literature for p-type contact to GaAs and ensures

contacts grown in University of Toronto are of acceptable quality. Sheet resistance of the

uncoated semiconductor can be calculated through a separate method, namely four point

probe measurement, to confirm the accuracy of the measured values presented above. The

measurement was carried out using an automated four point probe measurement system

in TNFC cleanroom, and showed an acceptable agreement with the value measured wit

the TLM method (measured Rsh = 292 Ω/sq). The error in the TLM measurements

could be due to inaccurate measurement of gap resistance due to measurement equipment

sources of error such as probe resistance. There are also well-known approximations

in this TLM method which may cause various errors such as that presented here [79].

Nevertheless, the presented method is typically applied to approximate the ohmic contact

characteristics. There is no need for very accurate measurements to confirm that the

characteristics lie within those presented in the literature.

3.5 Summary

To enable the fabrication of ring and DFB lasers, the full diode laser fabrication process

based on ebeam lithography was established. We developed ebeam lithographic processes


(a)

−30 −20 −10 0 10 20 30 40 500

10

20

30

40

50

60

Gap (µm)

Res

ista

nce

(Ω)

Raw resistanceCorrected resistanceLinear fit

2LT

2RT

(b)

Figure 3.12: a) A circular contact resistance test structure. The golden regions representmetallic contacts. Gap spacing, d, and radius, L, are shown in the figure. b) Totalresistance for the circular TLM test structure before and after data correction.

for defining the waveguides, via openings, and contacts for features with various shapes

and sizes. While Fox15 was shown to be the most robust resist for defining mesa struc-

tures such as ridge waveguides and etched markers, specific doses were chosen for features

with various sizes to avoid overexposure due to backscattering of electrons. Current via

openings and contact masks, however, were shown to be defined well using the ZEP-520A

ebeam resist.

Moreover, the processes developed for sample planarization, oxygen ashing of the

excess resist, and metal contact deposition were reviewed in this chapter. Both pla-

narization and metal deposition are essential for high-quality metal contacts. To confirm

the quality and to optimize the process, electrical properties of the developed metal con-

tacts were measured using TLM method showing comparable values to those previously

reported in the literature. The full fabrication process was not presented in detail here

in this chapter, where only the major developed processes were outlined for brevity. The

step-by-step fabrication process is outlined in chapter B as an appendix to the thesis,

and some of the less successful developed processes which were left aside in favor of the

current fabrication process are reviewed in appendix C. The work presented in this chap-


ter provides a full functioning ebeam lithography process for fabrication of diode lasers.

All the steps are carried out on campus in the TNFC cleanroom which eliminates the

requirement for lengthy shipment of samples between various microfabrication facilities.

Chapter 4

Single-sided Bragg laser design

Integrated room temperature mid-IR coherent light sources have been under study for

various applications such as sensing [80]. Even though quantum cascade lasers can pro-

vide mid-IR emission above 3.5µm, room-temperature operation of these lasers at the

2-3µm range is currently limited due to inter-valley scattering and high strain material

growth issues [81]. Optical parametric processes and difference-frequency generation are

potential alternatives for providing tunable coherent sources at this wavelength range.

One of the approaches to DFG is the use of Bragg waveguide and Bragg laser devices in

compound semiconductors [48]. This chapter outlines the details of a Bragg laser wafer

design for self-pumped DFG providing an idler wavelength around 2.6µm.

Recently, an asymmetric Bragg waveguide design, namely single-sided Bragg waveg-

uide, was proposed for nonlinear conversion [32,33]. Single-sided Bragg waveguide lasers

offer upper cladding layers with minimal number of interfaces which can potentially lead

to lower series resistance and less thermal effects compared to double-sided Bragg lasers.

Moreover, a thinner upper cladding allows for thicker lower cladding. This is especially

important for idler generation in longer mid-IR wavelengths where the idler mode profile

FWHM and leakage to substrate increase as a function of wavelength. In such a situa-

tion, a thicker lower cladding/Bragg reflector helps reduce the idler leakage loss as much

68

Chapter 4. Single-sided Bragg laser design 69

as possible.

A single-sided Bragg laser was chosen here to provide good thermal performance and

shallow mesa etch depth requirements. With the considered design ridges can be defined

with less than 2µm etch depth, just half of what was needed in the devices previously

designed in the group. Reducing the etch depth leads to better fabrication tolerance

for high-aspect ratio structures. This allows for the study of various integrated laser

configurations. Other than the conventional Fabry-Perot cavity, DFB and ring lasers

were implemented on the same wafer and their performance was studied. In the following

sections, we will first focus on the wafer design and performance of ridge Fabry-Perot

lasers. Consequently, DFB lasers and ring lasers will be studied and the difficulties in

implementation of such devices in the current platform will be outlined.

4.1 Wafer design

A single-sided Bragg laser can be described as a 1D structure containing an active region

for providing gain, and a core with one or multiple layer(s) surrounded on the bottom side

by a transverse Bragg reflector and on top by a low index cladding. Using a multilayer

core provides extra degrees of freedom which help controlling the laser properties such

as the optical confinement factor. This can also help tailoring the spatial field profile

of the Bragg mode to better overlap with the optical modes involved in the nonlinear

conversion process. This latter property increases the conversion efficiency and has been

demonstrated to improve the second harmonic generation conversion efficiency over the

conventional single core Bragg structures. In this case, we decided to use a matching-

layer enhanced structure. In this case, the two layers sandwiching the active region are

regarded as the two core layers, and the two layers adjacent to them are called upper and

lower matching layers. A low-index cladding is considered on top of the upper matching

layer for light confinement, while the light is confined from the bottom through Bragg


reflection from the bottom Bragg reflector.

Based on the guidelines presented in section 2.1, a single-sided Bragg laser was de-

signed for lasing at 980nm (pump) and parametric generation in the telecommunication

band (signal) and near-IR (idler). Based on previous data from the past designs within

the group [39, 41], the phase-matching point seems to shift from the originally designed

point so that the signal wavelength will be red-shifted, while the idler wavelength bears

a blue-shift to maintain the phase-matching condition. In the above-mentioned pieces of

work, it was shown that the signal wavelength can red-shift by as much as 200nm. This

phenomenon was ascribed to the large heat accumulation effects within the structure, as

well as the changes devised by the current injection [41].

Accordingly, the phase-matching point for the present device was set to be at the

lowest wavelength range available through the tunable CW and pulsed sources for the

S-band. However, as the signal wavelength is already blue-shifted, a red-shift in the

signal wavelength can cancel the designed blue-shift, and lead to parametric emission

in the C- or L-band. The laser was designed to emit in the Bragg mode of a Bragg

laser structure at 980nm as the DFG pump, where the 1500nm signal, and 2826nm idler

wavelengths were chosen to be conventional TIR modes. The material system used is

AlxGa1−xAs with two In0.2Ga0.8As quantum wells separated by 6nm GaAs barriers. Due

to quantum well gain characteristics, diode lasers can only emit in the TE mode. As

such, the structure was designed for type-II phase matching with TE pump and idler,

and TM signal.

It is well-known that larger Bragg reflector bi-layer index contrast leads to better

modal confinement. Moreover, it has been shown that increasing the index contrast leads

to improvement of nonlinear coupling efficiency [59]. As such, the aluminum concentra-

tion contrast between the two Bragg reflector bi-layers was taken to be the maximum

allowable. Obtaining high enough activated dopant levels in the multi-layer structure

is essential for operation of the device at a low series resistance. As per the wafer


grower’s specifications, activated doping level of the crystal abruptly drops at AlGaAs

layers with an Al concentration above 35% and only partially recovers at concentrations

above 70%. Given these two constraints, the Bragg reflector bi-layers were chosen to

be GaAs/Al0.35Ga0.65As. To reduce the TIR mode confinement factor in Bragg lasers,

usually the core is chosen to be low-index [26]. To provide the required contrast and

to support modes with a peak in the core region, the matching layer index is required

to be GaAs to provide maximum index. Refractive index of the cladding, on the other

hand, has to be the lowest among all the layers so as to provide confinement from the

top cladding through total internal reflection. However, aluminum rich layers are more

prone to oxidation and chemical changes. Provided the available Al concentration range,

Al0.75Ga0.25As was picked for the cladding layer.

Similar to what previously discussed in section 2.1, the vertical structure was designed

using a mode solver where we systematically solved for modes in the signal and idler

wavelengths for a range of pump effective indices to find the suitable structure for phase

matching at the desired wavelengths. The core Al concentration and thickness, as well as

top matching layer thickness were picked as optimization variables, while the mode solver

provides the thickness of Bragg reflector bi-layers as well as the bottom matching layer.

Initial simulations provided suitable starting points for the optimization variables which

provided considerably large nonlinear conversion efficiency. These three optimization

parameters were then swept within a range, seeking a local maximum for the normalized

nonlinear conversion efficiency at the presumed wavelengths. To gain insight into the

design trade offs involved, a sample efficiency optimization curve for the thickness of the

top matching layer, tm,top, and the upper core layer sandwiched between that and the

quantum wells, tc,top, is plotted in Fig. 4.1(a).

In order to assure lasing in the right mode, the confinement factor ratio of the zeroth-

order Bragg mode and the zeroth-order TIR mode was kept above 40 for selection of the

above-mentioned parameters. The confinement factor ratio for the same parameter range


is plotted in Fig. 4.1(b). Following the above procedure, a locally optimum 1D efficiency

of 5.2505× 10−6%/W/cm2 and ΓBRW/ΓTIR0= 62.30 is obtained at (tm,top; tc,top) = (341;

237.5)nm. Note that the conversion efficiency reported here is for the one dimensional

structure, whereas the 2D conversion efficiency will be orders of magnitude higher due

to the confinement in the lateral direction [42]. The calculated 1D nonlinear conversion

efficiency is nearly an order of magnitude lower compared to that of a passive device

recently designed for DFG in the same regime of operation [33] and nearly twice as large

as that of an older Bragg laser designed in the group [37]. The small efficiency compared

to the passive device can mainly be ascribed to the different constraints in the design of

the active structure posed by the laser performance and the grower, including limitations

on the aluminum concentration.

The current design is not necessarily a global optimum, but it is rather a locally

optimum design with specific advantages over the previous Bragg laser designs, such as

the reduced top cladding layer thickness. Advanced nonlinear optimization tools may

be used to arrive at a global optimum. To better illustrate where the current design

stands in terms of efficiency, we calculated a higher limit on the optimum nonlinear

conversion efficiency for this design. Equation (2.5) shows that the effective nonlinear

area has a major effect in nonlinear conversion efficiency. To provide an upper limit on

the conversion efficiency, we assumed that the pump and idler field profiles are exactly the

same as that of the signal to maximize the effect of A(2)eff in nonlinear conversion. Using

this assumption and the current structure, a nominal upper limit of 4.314×10−6%/W/cm2

was calculated for the nonlinear conversion efficiency. It is clear that the ideal case where

the field overlap is artificially set to its largest value only provides less than two orders of

magnitude improvement in the conversion efficiency. Given the large difference of pump

Bragg mode and signal and idler TIR modes, such a drop in the conversion efficiency is

well expected.

The ratio of confinement factor of Bragg mode to the zeroth-order TIR mode is also


Table 4.1: The optimized single-sided Bragg laser structure.xclad xm,top xc,top xb xc,bot xm,bot x1 x20.75 0 0.24 0 0.24 0 0.35 0

tclad tm,top tc,top tb tc,bot tm,bot t1 t21500nm 341nm 237nm 6nm 296nm 532nm 189nm 781nm

tc,top

(nm)

t m,to

p (nm

)

η %/W/cm2

235 240 245 250325

330

335

340

345

350

355

2.6

2.65

2.7

2.75

2.8x 10

−6

(a)

tc,top

(nm)

t m,to

p (nm

)

ΓBRL

/ΓTIR

(A.U.)

235 240 245 250325

330

335

340

345

350

355

25

30

35

40

45

(b)

Figure 4.1: a) Calculated normalized nonlinear coupling efficiency, η, as a func-tion of (tm,top; tc,top) for single-sided Bragg waveguide. A maximum efficiency of5.2505 × 10−6%/W/cm2 is obtained at (tm,top; tc,top) = (341; 237)nm for a 2mm longtest waveguide. b) Ratio of optical confinement factor of the Bragg mode to the zeroth-order TIR mode for the same range of thicknesses.

plotted in Fig. 4.1. As can be seen, the ratio is higher than 20 at the entire chosen

range and more than 64 at the optimum nonlinear conversion point. If the confinement

factor is not well studied, nonlinear conversion may be optimized without providing a

high enough confinement factor to the Bragg mode. Even though here the confinement

factor was calculated for the zeroth-order TIR mode, the performance of higher-order

TIR modes were left unexamined at the time of design. As will be outlined later, this

lead to large enough confinement factors in the first-order TIR mode that lead to lasing

in the first-order TIR mode rather than the Bragg mode in some specific etch depths.

Figure 4.2 illustrates the refractive index profile of the designed structure as well

as the mode profile of the slab structure in 980, 1500, and 2826nm wavelengths. The

designed lower transverse Bragg reflector consists of 4 periods of Al0.35Ga0.65As/GaAs


−4 −2 0 2 42.8

3

3.2

3.4

3.6

x [µm]

Ref

ract

ive

inde

x [a

.u.]

−4 −2 0 2 42.8

3

3.2

3.4

3.6

x [µm]

Ref

ract

ive

inde

x [a

.u.]

−4 −2 0 2 42.8

3

3.2

3.4

3.6

x [µm]

Ref

ract

ive

inde

x [a

.u.]

−4 −3 −2 −1 0 1 2 3 4−1

0

1

x [µm]

Fie

ld p

rofil

e [a

.u.]

Figure 4.2: Refractive index profile and mode profile of the structure at 980 (red), 1500(green), and 2826nm (blue) wavelengths. The black dashed lines in the index profilesrepresent the effective indices in the according wavelength.

with a thickness of 937/194nm. There is a bottom matching layer of 538nm GaAs,

bottom and top core layers of 296/237nm GaAs/Al0.24Ga0.76As, and a top matching layer

of 341nm GaAs materials. Two InGaAs quantum wells and three 6nm GaAs barriers are

inserted between the two core layers. The cladding is a 1500nm Al0.35Ga0.75As layer,

and a 50nm GaAs cap layer is applied on top of the structure. The full details of the

designed structure and the doping levels are presented in table A.1 in an appendix to

this thesis. The band diagram of the final device was simulated using a commercial laser

simulator [82] as shown in Fig. 4.3(a). It is clear that the simplified two-layer upper

cladding reduces the number of interfaces. As there are no major barriers for the carriers

to overcome, the series resistance of the device should be lower compared to double-sided

Bragg lasers. In addition to the above, tuning curve of the device was also calculated

based on the material and modal dispersion and is plotted in Fig. 4.3(b). The simulation

shows the large tuning range of signal and idler with a small modification in the pump

wavelength.


(a) (b)

Figure 4.3: a) Simulated energy band diagram of the unbiased device and b) calculatedtuning curve for the designed structure. Ev, Ec, and Ef represent the valence andconduction band levels, and Fermi level, respectively.

4.2 Fabry-Perot lasers

The designed wafer was grown on 2-off [001] n-type GaAs using metal-organic chemical

vapor deposition (MOCVD). Following the photolithographic processes available within

the group [42], a set of straight Fabry-Perot lasers were fabricated on the wafer. Ridge

lasers 3-4µm wide and 1.75µm deep were patterned using plasma etching. The structure

was then passivated with a 120nm layer of silicon oxide, and contact windows were etched

on top of the waveguides to enable the current flow through the deposited metal contacts.

A schematic of the device together with an SEM micrograph of a fabricated device are

shown in Fig. 4.4. Lasers were then cleaved into individual laser bars which were mounted

on a copper stage without bonding for further tests.

4.2.1 Laser performance

An overview of the laser characterization setup is depicted in Fig. 4.5. This setup is

capable of testing unpackaged diode laser chips or bars in CW or pulsed modes. The

laser was biased using a current source through coaxial gold-coated probes. The sample


(a) (b)

Figure 4.4: a) A schematic of the designed ridge structure, and b) a scanning electronmicrograph of a fabricated single-sided Bragg laser device before the metal deposition.The via opening for current transport is clearly seen in the SEM.

Figure 4.5: Experimental setup for laser characterization. M, mirror; MF flip-out mirror;PD, silicon photodetector; BRL, the laser bar; obj, objective lens.

stage is a copper piece with thermoelectrically moderated temperature. The beam was

collected using a 40x diode laser objective, and the collimated output was coupled into

either a silicon photodetector for power measurements, or a camera/beam profiler for

monitoring the near-field profile, or an Ando 6310C optical spectrum analyzer (OSA) for

spectrum and loss measurements.

The silicon detector was used in conjunction with the current controller to measure

light output-current and voltage-current characteristics of the lasers (LIV). A sample

LI curve is illustrated in Fig. 4.6. The device under test here has a width of 3µm and

length of 1.49mm. In this experiment, the laser was operated at 17C in CW condition.


(a)

980 985 990 995 10000

0.2

0.4

0.6

0.8

1

Wavelengtha (nm)

PS

D (

A.U

.)

(b)

Figure 4.6: a) Continuous wave LIV curves for a sample laser operated at 17C, and b)normalized optical spectrum of the laser output for the laser under test, operated CWat 17C with 50mA (solid), 100mA (dotted), and 200mA (dashed) injected currents.

The threshold current density of the device is 1020A/cm2. The threshold voltage was

measured to be 1.55V, well below the 2.6V measured for a double-sided Bragg laser

previously reported in the literature [5] as anticipated from the thinner, single-sided

device. The kink free LI curve implies that no additional modes start lasing throughout

the current injection range. To confirm this, the power spectral density (PSD) was

inspected above threshold at currents 50-200mA and is illustrated in Fig. 4.6(b). As can

be seen, the peak is maintained at currents up to 200mA. This provides some evidence

that mode hoping does not occur in this device.

Due to the use of low aluminum concentration core layers in the laser design, Bragg

laser lasers commonly enjoy better carrier confinement compared to conventional TIR

lasers. This leads to longer carrier leakage lifetimes and weaker sensitivity to temperature.

Sensitivity of laser diodes to temperature can be assessed by threshold characteristic

temperature, T0, and the slope characteristic temperature, T1,

Ith(T ) = Ith,0eTT0 (4.1)

η(T ) = η0e− T

T1 . (4.2)

where Ith represents the threshold current, η is the slope efficiency, and T is the temper-


ature in Kelvins.

To characterize dependency of single-sided Bragg laser devices on temperature, LI

curves of a device were measured at various temperatures in pulsed mode. The efficiency

and threshold current were plotted and T0 and T1 were extracted from the data as shown

in Fig. 4.7. The fitted values were Ith,0 = 1.7350mA, T0 = 94.518K, η0 = 7.262W/A,

T1 = 59.347K. These values are smaller than those previously reported for double-sided

Bragg lasers [5] and generally small compared to GaAs devices. For example, typical T0

values for GaAs based quantum well lasers is 250-400K for T > 270K [83]. A lower T0

may be observed in quantum well lasers due to heterobarrier carrier leakage, or other non-

radiative recombination mechanisms. These may be influenced by the structure, growth,

and doping conditions. As the doping profile, quantum well, and current confinement

mechanism of the current device are similar to that of the previous Bragg lasers studies

within the group, we ruled out the effect of doping profile and lack of proton isolation on

the small measured T0 and T1 values. Two other effects which may have been responsible

for this characteristics are the GaAs barrier layers and mode of lasing. Barrier layers used

in this design were 6nm, thinner that the previous wafer designs [5] which could have

lead to higher than normal carrier leakage. Also, as will be shown later in this chapter,

the current wafer design is very multi-moded; hence the device differential efficiency and

threshold current are very dependent on the operating conditions, as lasing may occur

at different modes when operated in different thermal conditions. Both these factors

may affect this lower characteristic resistance and will be accounted for in the next wafer

designs.

Modal loss of lasers can be measured through spectral measurement of under threshold

emission through various methods [6, 84–86]. We used the method reported in [6] to

determine a loss approximation to be used as an initial guess in a second calculation

based on [85]. The spectrum of the diode laser was measured in CW mode with the OSA

at the highest available resolution, 20nm, using a single mode fiber brought close to the


280 290 300 310 32034

36

38

40

42

44

46

48

50T

hres

hold

cur

rent

(m

A)

Temperature (oK)

(a)

280 290 300 310 320

0.04

0.045

0.05

0.055

0.06

0.065

Inje

ctio

n ef

ficie

ncy

(W/A

)

Temperature (oK)

(b)

Figure 4.7: Temperature dependence of a) threshold current density and b) slope effi-ciency. The solid lines are the theoretical fits to the data.

laser output facet. The measurement was carried out at several currents below threshold

covering the whole gain spectrum. A sample spectrum measurement and a close-up of

the no-gain region are shown in Fig. 4.8.

Loss was initially calculated to be 10.014 /cm based on the spectrum close to 1020nm

wavelength where gain is nearly zero. To calculate this value, mirror losses were calculated

based on simulated mirror reflectivities, and the Fabry-Perot loss formula [6, 84]

α = ln(

√r + l√r − 1

)/L− αm, (4.3)

was used where r is the peak to valley ratio of the measured Fabry-Perot resonances.

Consequently, through a separate measurement, the gain at each current was calculated

through the ratio of adjacent peaks in the Fourier transformed spectrum. Using the loss

value calculated above as a starting point, a more accurate value for loss, α, transparency

current, I0, and transparency gain, G0, were calculated through a fit to the gain-current

relation,

G = G0ln(I

I0)− α− αm. (4.4)

A sample Fourier transform of the spectrum, and the fitted data are shown in Fig. 4.9.

The final calculated values were G0 = 13.27 /cm, I0 = 16.123mA, α = 8.412 /cm. The


970 980 990 1000 1010 10200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

−6

λ (nm)

PS

D (

A.U

.)

1019.8 1019.9 10202.5

3

3.5

4

4.5x 10

−8

Figure 4.8: Collected under-threshold spectrum at 35mA injected current. The insetshows the no-gain region of the spectra where the method in [6] was used to extract theinitial loss estimate. The squares show the maxima and minimum used for the calculation.

0 200 400 600 800 100010

−7

10−6

10−5

10−4

10−3

10−2

Optical path length (A.U.)

Inte

nsity

(A

.U.)

(a)

25 30 35 40−200

−100

0

100

200

300

Injected current (mA)

Lase

r ga

in/lo

ss (

/m)

(b)

Figure 4.9: a) Fourier transform of the spectrum at 35mA. The slope of these peaks onthe semilog scale is related to the gain/loss. b) A plot of the calculated gain/loss valuesat the measured currents. The circles are the measured values and solid lines are thetheoretical fits to the loss data.

measured modal loss is slightly smaller than that previously reported for double-sided

Bragg waveguides [31]. A lower scattering loss was expected from the current devices,

as they require shallower etch depths, and as such, smaller scattering from the sidewalls.

This was the first measurement of Bragg mode propagation loss in single-sided Bragg

structures at the time experiment was carried out.


Figure 4.10: Near-field of the laser under test at 17C and 50mA current. a) Calculated,and b) measured 1D NF profile, c) calculated, and d) measured 2D NF profile.

To confirm that lasing takes place for the designed vertical Bragg mode, near-field

(NF) of the same laser diode was measured as shown in Fig. 4.10. The calculated theoret-

ical predictions are also given in the same figure to demonstrate the good correspondence

of the results. A fully vectorial commercial mode solver was used for calculation of the

near-field profile of the ridge Bragg waveguide [65]. Further peaks are evident in the

experimental results even though less pronounced, due to diffraction effects in the optics.

The near-field preserves the shape that is characteristic of Bragg modes, and keeps that

shape throughout the entire range of bias currents which reaches six times the threshold

current.

Vertical modal discrimination and losses

While the studied laser operated in a single spectral mode, there were many lasers which

operated in multiple modes. Some of these effects were ascribed to the multiple longitu-

dinal modes available in the cavity. However, some of the lasers emitted at wavelengths

far from the quantum-well designed gain peak. For example, a sample spectrum is shown

in Fig. 4.11 where the device emission wavelength is centered at 948nm. The laser dimen-

sions were 3.5µm width, 0.490mm length, and 2µm etch depth. Inspecting the near-fields

of the lasers with a beam profiler revealed that lasers with a spectral component at the


940 950 960 970 980 990 10000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

PS

D (

AU

)

Figure 4.11: Sample spectrum of a laser with a peak at 948nm at 100mA and 20C.

lower end of the gain spectrum, i.e. 920-960nm, lase in either mixed TIR/Bragg modes or

TIR modes in the vertical direction. A sample near filed of a laser emitting in the vertical

TIR mode is presented in Fig. 4.12(a-d). The field profile of the TIR TE01 mode is also

plotted together with the measured near filed profile to better show the resemblance.

It was mentioned earlier that the current laser was designed to provide large enough

confinement factor ratio between the vertical Bragg mode and zeroth-order TIR mode,

hence not allowing for lasing in the latter. The ratio of Bragg to zeroth-order TIR

mode 1D confinement factor was calculated to be ΓBRW/ΓTIR0= 62.30 for the design

in table 4.1. However, confinement factor of other higher-order TIR modes were left

unexamined. Optical confinement factor of the Bragg and first-order TIR modes were

calculated through 1D modal analysis to be ΓBRW = 0.0209 and ΓTIR1= 0.0017, respec-

tively, leading to ΓBRW/ΓTIR1= 12.29. Even though the 1D Bragg waveguide modal

confinement factor is still an order of magnitude larger than the first-order TIR mode,

the 2D Bragg waveguide modal losses can be larger than those of the first-order vertical

TIR mode (TE01) depending on the ridge etch depth. Fig. 4.12(e) illustrates the modal

loss as a function of etch depth for both modes. As illustrated in the figure, modal

loss of the TE01 TIR mode is generally smaller than that of the Bragg mode, except

for the 1.95-2.05µm etch depth range. Consequently, the laser may lase in either mode

depending on the given etch depth.

The available samples were etched at two etch depths. Two of the samples were etched


1.6 1.7 1.8 1.9 2 2.110

−6

10−4

10−2

100

102

104

Etch depth (µm)

Loss

(dB

/cm

)

BRW modeTE

01 TIR mode

(e)

Figure 4.12: Measured a) 1D and b) 2D near-field profile of the laser under test at 100mAcurrent, plotted together with the calculated c) 2D and d) 1D near-field profile for theTE01 mode. e) Simulated 2D modal loss for the two dominant modes. The losses areplotted in logarithmic scale to better compare the loss for the two modes.

to 1.95µm and one was etched to 1.53µm. The near-field analysis showed that while all

the devices from the shallower etched sample were lasing in a TIR mode, some of the

deeper etched devices emitted in the Bragg mode or a mixture of TIR and Bragg modes.

This is in agreement with the theoretical predictions from Fig. 4.12(e). Even though

the etch depths investigated were not diverse enough to provide a full map of the device

performance, this study provides the theoretical and experimental background for future

designs with better modal discrimination characteristics. The presented experimental

results confirm the theoretically investigated effect of etch depth on Bragg waveguide

modal loss in section 2.2. In the next chapter, the effect will be investigated in more

detail in a new wafer designed based on the information gathered in this run.

4.2.2 Nonlinear performance

In addition to the laser characterizations, self-pumped DFG was investigated for the

lasers. Even though the current wafer design provides sub-optimal mode selection char-

acteristics, we studied nonlinear conversion in the form of self-pumped DFG in the single-

sided Bragg laser Fabry-Perot lasers. A type-II DFG measurement was set-up where the

Bragg laser was operated in CW mode and a CW tunable C-band laser, Agilent HP


(a)

1535 1540 1545 1550 1555 156035

40

45

50

55

Idle

r po

wer

(pw

)

Signal wavelength (nm)

(b)

Figure 4.13: a) Schematics of the self-pumped DFG setup. FC, fiber collimator; FPC,fiber polarization controller; SMF: single mode fiber; 10x obj, 10x objective lens; BRL,the laser bar; IR-obj, mid-IR objective lens; M, mirror; MF flip-out mirror; Ge-PD,Germanium photodetector; OSA, optical spectrum analyzer; 3xLPF, 3 long-pass filters;PbS, lead sulphide detector. b) Measured mid-IR power plotted as a function of signalwavelength. The diode laser is kept on at a constant current of 200mA and the signalpower is kept constant at 82mW, TM.

8168F, was used as the signal. The C-band tunable laser was amplified through an

erbium-doped fiber amplifier (EDFA), Amonics AEDFA-33-B-FA and end-fire coupled

into the ridge waveguide using a single-mode lensed fiber. To avoid measuring the back-

ground emission from the pump, signal was chopped at 90Hz. This was carried out by

coupling the signal out through a fiber collimator, chopping with a free-space mechanical

chopper, and then coupling back into another single-mode fiber using a 10x anti-reflection

coated diode laser objective. The polarization was controlled using a fiber-polarization

controller, and the TM polarized signal was coupled into the Bragg laser using a single

mode lensed fiber. An anti-reflection coated mid-IR objective lens was used to collimate

the output light from the Bragg laser and three long-wavelength-pass filters, two with

1650nm, and one with 2000nm cut-off wavelengths were used to block the signal and

pump, while passing through the 2-3µm idler. A lead-sulphide detector, PbS-020-TE2-

H, was used to measure the idler power in conjunction with a Stanford research SR830

lock-in amplifier. A schematic of the setup is shown in Fig. 4.13(a).


The device current was set to 200mA and the signal power was set to 160mW in the

TM polarization. The signal wavelength was swept from 1535-1560nm, the EDFA gain

bandwidth, and the idler power was recorded as shown in Fig. 4.13(b). Even though a

background power of 45pW average can be measured, no clear phase-matched idler peak

power was detected. Other tests were also carried out including a temperature sweep

and a current sweep, as well as parametric fluorescence spectral measurements, but none

of the experiments showed signs of phase-matched power.

Some of the main impediments in the path to a successful self-pumped DFG in the

current wafer are outlined here. As the lasing wavelength cannot be tuned independently

and to a wide range, doing a DFG experiment with two external sources can not only help

alleviate the laser tuning problem, but also can reduce uncertainties with the location of

phase-matching wavelength. The actual phase-matching wavelength of the device may

as well be outside the signal wavelength range available to us. As shown in Fig. 4.3

scanning the pump wavelength by a few nanometers leads to moving the phase-matched

signal/idler wavelength by tens of nanometers. As such, having access to a fine tunable

external source will allow for a more thorough investigation of DFG in the current device.

Moreover, as discussed previously, modal selection mechanism in the current device does

not work in favor of the Bragg mode. As such, the device may easily be lasing at other

lateral modes, making measurement of self-pumped DFG merely impossible in the current

setting. Also, given the inaccuracy in the position of DFG phase-matched wavelength, the

idler wavelength may be even outside the detection range of the lead-sulphide detector.

Moreover, as the exact focal point of the idler wavelength is unknown to us, the idler

wavelength may not be focused on the small area (1mm) detector active area. Lastly, the

water molecules in air have an absorption line near the 2.8µm window where the device

is supposed to operate. The wafer design can be modified to allow for idler emission at

lower wavelengths to avoid water absorption.

A new device design, near-degeneracy with signal and idler wavelengths around the


C-L band, will allow us to better investigate DFG with better modal discrimination

mechanisms and well-known idler properties to address many shortcomings of the current

experiment. Such a design will be discussed in the next chapter. Nevertheless, we

worked with the current wafer design to investigate manipulation of the lasing wavelength

through integration of surface gratings on the ridge waveguides to form DFB lasers, as

well as realizing ring lasers. The next two sections provide brief reviews of the attempts

towards new integrated optical elements in the Bragg laser platform.

4.3 DFB lasers

Both ring cavities and longitudinal Bragg gratings are essential components in integrated

optics as they eliminate the need for cleaved facets. Monolithic integration of laser sources

with nonlinear components in compound semiconductors can be realized through ring

lasers or grating based lasers such as DFB or DBR lasers. We initially focused on design

and fabrication of DFB and DBR lasers on the single-sided Bragg laser platform. The

design, fabrication, and preliminary results will be outlined in this section.

4.3.1 Bragg reflector design considerations

DFB lasers are essential components in today’s telecommunication industry due to the

wavelength selection mechanism offered by the distributed gratings and their low phase

noise. Integration of DFB structures on Bragg laser platform will provide single mode

lasing in the designed wavelength within the gain bandwidth. Moreover, DFB and DBR

lasers provide solutions for integration of diode lasers with other devices, for example for

external cavity nonlinear conversion. A brief summary of coupled mode theory theory

for calculation of DFB coupling coefficient is presented in this section. Coupled mode

theory has been used extensively for modeling various optical elements such as directional

couplers and Bragg gratings. The details of the method are presented elsewhere [87] and


will not be repeated here.

The DFB laser is to be designed to lase in 980nm, in the vertical Bragg mode. Initially,

mode profile of the fundamental Bragg mode of the unperturbed ridge waveguide was

calculated in a commercial-grade 2D eigenmode solver [65]. The coupling coefficient, κg,

can be calculated by integrating the mode profile over the perturbed regions,

κg =k202β

∫∫

∆ǫm(x, y)U2(x, y)dxdy

∫∫

U2(x, y)dxdy. (4.5)

Here, k0 is the wavenumber in free space, β is the wavenumber, and ∆ǫm is defined as

the mth Fourier component of the permittivity perturbation profile, ∆ǫ:

∆ǫ(x, y, z) =∑

l 6=0

∆ǫl(x, y) exp(i2π

Λlz). (4.6)

Reflection coefficient of a grating of length L can be expressed as [87]:

rg = |rg| exp iφ =iκgsin(qL)

qcos(qL)− i∆βsin(qL). (4.7)

In this expression, q = ±[(∆β)2 − κ2]1/2, and ∆β = β − β0 = β −mπ/Λ where Λ is the

grating period. In DFB and DBR lasers, grating period is chosen to satisfy the Bragg

condition [87]

Λ =mλB2neff

, (4.8)

where λB is the Bragg wavelength and neff is the effective refractive index.

Laterally coupled gratings have been used for realizing DFB lasers [57]. These gratings

can be fabricated more accurately and with less modal perturbation compared to laterally

corrugated gratings. However, the two-step etch process required for fabrication of the

former adds up to the complexities of the already multi-step laser fabrication process.

Laterally corrugated gratings have previously been used for realization of DFB and DBR

lasers [58,88] and where chosen for our purpose due to ease of fabrication in a single step


(a) (b)

Figure 4.14: Schematics of a) laterally coupled and b) laterally corrugated surface grat-ings.

etch process.

To design laterally coupled gratings the above guidelines can be used. Figure 4.15

shows a flowchart of the design process and below is a short summary of the design steps.

• Based on the fabrication limitations find the smallest possible feature size that can

be implemented

• Choose the grating order and period based on the desired lasing wavelength, effec-

tive index, and minimum attainable feature size using (4.8)

• Choose the grating grooved region width

• Using a 2D mode solver, calculate the unperturbed waveguide mode profile

• Using equation (4.5), simulate the grating coupling coefficient for a range of un-

grooved region widths

• Simulate the grating coupling coefficient for a range of etch depths

• Choose a set of etch depths and ungrooved widths that meet the coupling coefficient

requirement

We will employ this procedure to design DFB lasers in the next subsection.


Figure 4.15: A flowchart of the DFB laser design procedure.

4.3.2 Fabrication challenges and performance

First-order gratings are generally favored over higher-order gratings as they provide

the highest feedback level. The aspect ratio of etch depth to the feature size - i.e.

period×filling factor - of a laterally coupled first-order grating, however, is more than

30. Maintaining a high-quality etch with such an aspect ratio was not possible with the

current fabrication equipment. As such, we chose a seventh-order grating for implement-

ing the DFB lasers to ease the fabrication requirements. With that design, the period

was increased to 898nm which translates to an aspect ratio of less than five. With such

higher-order gratings, however, not only the coupling coefficient drops, but also occur-

rence of partial waves reduces the grating efficiency [89]. This latter effect is not taken

into account in the coupled-mode method presented earlier.

Not only the fabrication constraints dictate the period of the surface gratings, fabri-

cation tolerances reduce the etch depth accuracy as well. With the equipment available

to us, the GaAs etch rate can change by more than 10% hence reducing the fabrica-

tion accuracy. The vertical structure was also dictated by nonlinear interaction; given

all these constraints, we were seeking sub-optimal but functioning DFB action in the

designed devices.


(a) (b)

Figure 4.16: a) Side view and b) cross sectional SEMs of a sample seventh-order grating.

One of the major issues in fabrication of gratings is the etch quality. Due to the large

aspect ratio in the surface gratings, the etch chemistry can vary largely at the deeper

sections of the grating. At such positions, the concentration of radicals can be much

lower than the rest of the sample surface leading to unwanted isotropic etch conditions.

Figure 4.16 shows SEM micrographs of the fabricated gratings. The etch was performed

in the Minilock plasma etcher in the TNFC cleanroom in University of Toronto, and the

etch parameters are summarized in table 4.2. As shown in the figure, even though the

aspect ratio is only 3.8, the lower 500nm of the grating region has encountered a slanted

shallower etch compared to the rest of the device. Such a shallow etch can decrease the

grating coupling coefficient, and consequently the back reflection, by orders of magnitude.

In the etch process, RIE power plays a major role in control of the anisotropic etch.

As such, to improve etch profile four experiments were run with RIE powers of 40, 50,

60, and 100W while other recipe conditions were kept constant. The changes in the etch

profile in these experiments proved to be insignificant; as such, a multi-variable design

of experiment procedure is needed to further improve the etch qualities which is outside

the scope of the present thesis.

To choose the DFB design parameters, we studied the coupling coefficient as a function


Table 4.2: Detailed GaAs plasma etch recipe.Pressure ICP power RIE Power BCL3 flow Cl2 flow Ar flow

5MTorr 200W 50W 8sccm 4.5sccm 5sccm

of etch depth and ungrooved region widths. The grooved region width was taken to be

2µm to limit lasing in the lowest order lateral modes. We were aiming for κgL values

ranging from 0.1-5. In order to take the effect of the incomplete etch region into account,

we simulated the coupling coefficient assuming a 250nm shallower etch depth in the

grating region. Figure 4.17 illustrates a schematic of such a device. The grating filling

factor is assumed to be 50% in all the simulations.

The coupling coefficient was simulated and plotted for a total etch depth of 1.87µm

for different ungrooved region widths. Figure 4.18(a) shows the results for both the ideal

case, and the shallow etch case, for which we assumed 250nm shallower etch compared to

the total etch depth. As expected, the narrower the ungrooved region is, the higher the

coupling coefficient will be. Also, the grating is weaker when the non-ideal etch profile is

taken into account. Given the simulation results, we planned for the maximum coupling

coefficient. An ungrooved width of 0.6µm is the minimum allowable for current injection

into the active region.

To further investigate the design parameter space, we also looked into the effect of

etch depth on the grating. Coupling coefficient was plotted as a function of total etch

depth in figure 4.18(b). In this case, we took the grooved section width to be tg1 = 2µm

and ungrooved width is tg2 = 0.6µm. As can be seen in the figure, the non-ideal etch

leads to lower coupling coefficients especially at etch depths shallower than 1.85µm where

the coupling coefficient barely reaches 1 /cm. Based on the above results, an etch depth

higher than 1.9µm should provide enough coupling coefficient for successful DFB/DBR

operation. This figure, should also be studied beside the ridge loss calculation depicted

in Fig. 4.12(e). As shown earlier, in the ridge structure etch depths above 2.06µm will

lead to larger losses in the Bragg mode compared to the first-order TIR mode. With


Figure 4.17: a) A schematic of the device with non-ideal etch.

0.6 0.7 0.8 0.9 10

5

10

15

κ (/

cm)

Ungrooved region width (µm)

Ideal etchShallow etch

(a)

1.4 1.6 1.8 20

20

40

60

80

100

120κ

(/cm

)

Etch depth (µm)

Ideal etchShallow etch

(a)

(b)

Figure 4.18: Coupling coefficient of a seventh-order grating versus. a) etch depth whenungrooved width is tg2 = 0.6µm, and b) ungrooved region width when the total etchdepth is 1.87µm.

the current etch quality and handles on the etch depth control, it is very complicated to

accomplish lasing in the Bragg mode together with large enough coupling coefficients.

Gratings with a period of 898nm, etch depths of 1.8-2µm, grooved width of 0.6-1.5µm,

and ungrooved width of 2µm were fabricated. Due to the very large etch sensitivity of

the coupling coefficient, accurate control of κg is not possible with the current plasma

etch facilities. As such, multiple samples were fabricated with a range of etch depths and

grooved region widths to reach the required coupling coefficients.

Based on the above calculations, DFB lasers were fabricated using the ebeam lithogra-

phy process detailed in chapter 3 and etch recipe in table 4.2. After thinning and contact

deposition, these samples were cleaved into individual laser bars 0.6-1.4mm long. The


0 20 40 60 80 1000

2

4

6

8


Pow

er/fa

cet (

mW

)

(a)

990 990.5 991 991.5 9920

0.2

0.4

0.6

0.8

1

Wavelength (nm)

PS

D (

A.U

.)(b) (c)

Figure 4.19: a) A sample LI curve for a DFB device with ungrooved and grooved widthsof 0.6µm and 2µm, respectively. b) Output spectra of the device at 90A CW injectioncurrent. c) Near-field emission profile of the DFB laser when operated at 90mA. Thescale is estimated based on image size on the camera and the optics used.

laser bars were tested as cleaved without anti-reflection coating for LIV characteristics.

Based on the results, the better performing lasers were bonded n-side down to copper

pieces for improved thermal conduction. The output spectra do not show characteristics

of DFB lasers, i.e. the narrow single wavelength emission. The output characteristics of a

sample DFB laser are illustrated in Fig 4.19(a,b). The emission spectrum shows multiple

spectral peaks with a free spectral range (FSR) of 120pm. This FSR is in agreement with

that of a Fabry-Perot laser on the same laser bar. This, and the fact that the device is

not emitting in a single frequency clearly shows that the device operates in the Fabry-

Perot mode. The near-field of the lasers was studied to better understand the modal

characteristics, and as depicted in Fig. 4.19(c) the lasers seem to emit in TIR/mixed

mode rather than Bragg mode.

Aside from the etch profile difficulties, lack of proper modal discrimination mecha-

nisms in the lateral structure, and reflection from the cleaved facets which prohibited

the gratings from providing the required level of feedback to the Bragg mode, there are

a few other possible reasons which can prohibit the grating based laser from performing

in the right mode. Introduction of a longitudinal grating may perturb the mode profile

so much that the Bragg mode becomes even more lossy. Note that the loss values used

in this study were based on an unperturbed ridge waveguide. Additionally, in contrast


to conventional DFBs and DBRs, our devices are very multi-moded in the vertical di-

rection. Introduction of such deep grating perturbations may couple the Bragg mode

to other surface modes and higher-order TIR modes, hence increasing the modal losses

even further. Laterally coupled surface gratings can be utilized instead of the current

gratings to overcome some of the above challenges. Even though such a choice increases

the fabrication complexity, it will allow for accurate waveguide etch depth measurement,

and consequently choice of right grating etch depth for the grating in the second step.

Moreover, the shallow grating etch depth will alleviate the partial etch problem depicted

in Fig. 4.16 as well as large modal perturbations. Exploring such a two-step etch process,

however, will be a separate project which can be studied in the future. As another less

fabrication intensive alternative to integrated light sources we concentrated on realization

of ring lasers.

4.4 Ring lasers

Semiconductor ring lasers have been under study in the past two decades [43,53,54,90,91]

due to their ease of integration with other devices as well as other interesting features.

Such features include their uni-directional bistability [43] and mode-locking potential

stemming from their large cavity size [53,54]. Implementation of ring lasers in the Bragg

laser platform can be very beneficial. Aside from the potential for integration with other

devices, ring cavities can provide field enhancement effect within the cavity, and can be

used as band reject filters. With the difficulties in fabricating DFB and DBR lasers on

the Bragg laser platform, we focused on realizing semiconductor ring lasers instead for

integration of active and nonlinear effects in a single device. If the vertical structure is

phase matched for second-order nonlinear interactions, the ring laser can be designed to

allow for parametric processes either in the ring cavity itself, or in the output waveguide.

In the former, the ring resonator can be designed to be a high-quality-factor cavity for the


pump, signal, and idler wavelengths. Designing the parametric processes to take place

in the high-Q cavity accommodates very high powers inside the resonator, and hence,

possible optical parametric oscillation inside the cavity. This work would benefit from

rings because they can be used as band reject filters, field enhancement cavities for better

nonlinear interaction, or as mirror-less oscillators.

In a laser structure, the excess carrier injection in the cavity will not only increase the

losses for the parametrically generated signals, but also it will detune the phase-matching

wavelength. Both of these unwanted effects can be avoided by designing the nonlinear

processes to take place outside the laser cavity. The present section will describe details

of the ring resonator design as well as the device performance characteristics.

4.4.1 Cavity and coupler design considerations

Ring resonators have long been under study where especially CMOS compatible micro-

ring resonators have attained a lot of interest due to their ability for high speed modula-

tion [92]. In semiconductor ring lasers, however, the small difference in material refractive

indices does not allow for small bend radii and hence large cavity sizes have to be consid-

ered so as to reduce the bend losses. Nevertheless, the cavity analysis is similar in either

case. Some of the considerations in the cavity design are outlined in this section.

Similar to a Fabry-Perot resonator, the resonance conditions in a ring cavity of total

length L reads as:

Lnefff

c= m. (4.9)

Here f is the frequency, c is the speed of light, neff is the effective index of the bent

waveguide with the ring radius of r, and m is an integer. If the resonator shape is a

simple ring the length would be equal to 2πr, and for a racetrack shaped cavity, the

length would be L = 2(πr+ l). Here r is the ring radius and l is the length of the straight


section. Lastly, assuming a group index of ng, FSR can be calculated to be:

∆f =c

Lng

. (4.10)

In large radius cavities utilized in semiconductor ring lasers, FSR will be very small,

allowing for lasing at multiple longitudinal modes. As such, the laser radius will not play a

major role in defining the lasing wavelength. The ring radius, however, is very important

in the overall cavity losses. While a larger bend radius decreases the leakage losses arising

due to bending of the waveguides, a longer cavity length can increase the total loss. As

such, there can be considered a suitable ring radius to allow for an optimum overall loss

in the cavity. Bend analysis is usually carried out through a conformal mapping of the

index profile with regards to the bend radius [93,94]. The bend loss was calculated for a

bent ridge waveguide formed on top of the Bragg laser design outlined in table A.1 using

a commercially available mode solver [65]. Even though a very large radius of 1mm was

assumed for the bend, the loss was calculated to be 110.5dB/cm using PML boundaries.

However, in structures with large losses, PML boundaries usually overestimate the loss

due to the absorptions at the boundary. As such, the commercial mode solver bend loss

calculations will not be very accurate. Bend radii larger than 1mm is not advantageous

due to the wafer and sample size constraints. Hence, 1mm bend radius was selected for

the rings, even though the bending loss will probably be very large. Considering the gain

mechanism in the present laser, even though such large losses may lead to high threshold

currents in the laser, lasing will still take place.

It is well-known that bend loss is very sensitive to the etch depth. The present wafer

design does not incorporate any etch stop layers, and considering the available plasma

etcher in the TNFC cleanroom, etching the device accurately to a certain etch depth will

not be feasible. Accordingly, the bend loss of the final devices will be very dependent on

the fabrication conditions and has to be measured after the fabrication.


An important feature in the design of ring resonators is the coupling method. Y-

junctions [90], multi-mode interference (MMI) couplers [95], and evanescent couplers [43]

have been previously utilized in defining ring resonators and ring lasers. While Y-

junctions accommodate out-coupling of generated light in semiconductor ring lasers, such

structures do not provide an input port for in-coupling of light in another wavelength.

Hence semiconductor ring lasers designed using Y-junctions are not a suitable choice for

DFG devices. MMI couplers, on the other hand, provide multiple input and output ports.

Furthermore, if designed properly, the coupling coefficient in such couplers is not sensi-

tive to the etch depth, conduce device fabrication with repeatable performance. These

interesting features make MMI couplers an interesting alternative for realizing ring lasers.

However, there are two drawbacks associated with MMI couplers in the Bragg waveguide

platform for parametric generation: designing the coupler to accommodate coupling of

all the three different wavelengths will pose too many constraints on the device design;

moreover, the multi-lobe nature of the Bragg mode and its spread over a large vertical

area decreases the localization of the mode under the ridge. Hence, the multi-mode sec-

tion of the device will have a large leakage loss associated with it. These two drawbacks,

added up to the large size of the MMI section, lead us to discard the use of such couplers

in the Bragg waveguide platform.

The most suitable coupler configuration in the present platform was evanescent field

coupler in conjunction with a racetrack cavity. Evanescent couplers have been used in

various devices due to the simplicity of their design using coupled mode theory, and their

efficient coupling properties. The major drawback of these couplers is their coupling co-

efficient sensitivity to the dimension variations which reduces the possibility of repeating

the same characteristics especially due to the variation of the etch depth. Evanescent

coupling has been treated with analytical results for straight and curved [96,97] couplers.

However, we decided to use numerical simulation methods to avoid over-simplification in

the problem. Once more, Lumerical Mode [65] was used to calculate the coupling between


the two ridge Bragg reflection waveguides. In order to allow for weak coupling between

the two waveguides, a separation of 2µm was applied, and to allow enough coupling for all

three wavelengths the resonator was implemented in a racetrack configuration. Lastly,

the calculations were only based on coupling between the straight waveguide and the

straight section of the racetrack and the coupling at the curved section was disregarded.

Fig. 4.20 shows a sample calculated coupling plot for pump, signal, and idler, calcu-

lated for a 3D design space. The bar-coupling values are calculated based on the overlap

of the field inside the waveguide with the single waveguide mode. As the waveguides are

loosely confining, field overlap can never reach zero as shown in the figure. Also note that

cross coupling is calculated by subtracting the bar-coupling values from unity. Based on

such analysis, a suitable coupling length was calculated for the device, at which most of

the pump is confined inside the ring, while most of the signal and idler are coupled out.

Note that as the bend loss of the ring is very dependent on the etch depth, and has to be

measured accurately after the ring fabrication, the ring can not be designed for critical

coupling. For the 2µm wide waveguides, 320µm was decided to be the optimum length

at which almost all the generated idler power is coupled out of the ring, while more than

50% of the signal is coupled in.

Similar to bend loss, coupling coefficient is sensitive to the etch depth. In order to take

the fabrication variations into account, three different variations of the coupler length

were designed to not only allow for optimum coupling, but also accommodate bend loss

and coupling coefficient measurements in the experiments. Lastly, another ring design

was considered with a coupler length of 100µm to allow for out-coupling the pump while

limiting the in-coupling of signal and idler. In such a design, the nonlinear conversion

can take place in the un-pumped/minimally pumped straight waveguide, while lasing

takes place in the ring cavity. This particular design will be advantageous in study of

nonlinear conversion while minimizing the unwanted effects of carrier injection in the

nonlinear material.


Figure 4.20: A sample plot of calculated bar-coupling versus coupler length for twostraight 2µm wide waveguides separated by 2µm. The etch depth is assumed to be1.97µm.

Semiconductor ring lasers can emit bi-directionally or uni-directionally [43, 55]. In

order to suppress the lasing in one of the directions and only allow for uni-directional

lasing, the symmetry of feedback from external facets was broken similar to [98]. As

shown in the schematic in Fig. 4.21, the output bus waveguide has a straight end and

a curved end which serves to diminish the back-reflected power and reduce the feedback

in the clockwise direction. The next sections will outline the fabrication challenges and

performance of the fabricated lasers including the uni-directionality.

4.4.2 Fabrication challenges and laser performance

The ring lasers were designed to have two separate contact regions. One region was the

ring cavity and the coupling region while the second was the bus waveguide. The ring

cavity is to be biased above threshold to generate the coherent light whereas the bus

waveguide is supposed to be biased above transparency only to carry the generated light

out without excess loss.


Figure 4.21: A sketch of the uni-directional device. The blue region shows the con-tact pads and the red represents the waveguides. The clockwise and counter-clockwisedirections are marked on the figure.

Figure 4.22: An optical mirograph of a fabricated ring laser.

In order to accommodate two separate contact pads, the lift-off resist layer should be

thick enough to allow a successful lift-off. As explained in chapter 3 this was realized

through a planarization process and two layers of ZEP-520A resist spin coated on the

planarized surface. However, surface damage to the planarization surface tends to di-

minish the contact quality. As outlined earleir in chapter 3, the Fox-15 HSQ resist which

was used for planarization incurred some miro-cracks during the electrical isolation pro-


(a) (b)

Figure 4.23: a) Cross sectional and b) side view SEM micrographs of damaged samplesafter metal deposition. The planarization HSQ has incurred large cracks, undercut nearthe cracks, and chipping out in multiple places.

cess. As the ebeam evaporator in TNFC cleanroom was out of order, the samples had

to be shipped to another micro-fabrication facility, University of Sherbrooke, for metal

contact deposition. When characterized, we noticed very poor electrical performance.

After morphological inspection, major cracks and chippings were noticed on the HSQ

surface. SEM micrographs of the cracked regions are presented in Fig. 4.23. Further

investigation revealed that an additional BOE treatment was carried out on the devices

in the second microfabrication facility without our consent. Based on our previous tests,

buffered oxide etchant treatment is very invasive both to HSQ and the high aluminum

concentration cladding layer of this wafer and was avoided in our process. Due to this

unforeseen problem most of the samples were rendered inoperative except for one. The

functioning sample was cleaved to separate laser bars for characterization and the bars

were indium bonded to copper for better thermal conduction.

The output bus waveguide of the designed ring lasers has a curved end and a straight

end. Theoretically, the back-reflection from the curved facet should be minimal and laser

should only lase uni-directionally in the counter clockwise mode and emit from the curved

output. To confirm this effect and to characterize the laser quality, the bonded lasers

were tested for their LIV characteristics from both outputs as illustrated in Figs. 4.25.


Figure 4.24: Continuous-wave LI characteristics for a sample ring laser with 320µmcoupler length. Bus waveguide bias is a) 0mA, b) 40mA, and c) 100mA. The blue curveshows straight facet output (clockwise mode) and black illustrates the curved facet output(counter clockwise mode).

Figure 4.25: Pulsed LI characteristics for a sample ring laser with 320µm coupler length.Bus waveguide bias is a) 0mA, b) 40mA, and c) 100mA. The blue curve shows straightfacet output (clockwise mode) and black illustrates the curved facet output (counterclockwise mode). The pulses are 1µs long with 20µs delays.

The device was first tested in the pulsed mode to avoid thermally induced effects such

as thermal rollover. As can be inferred, at all bus waveguide bias voltages light can be

measured at both directional modes. At 0 bus waveguide bias current, the laser tends

to lase in either direction with nearly similar power. This can be due to small feedback

from either facet due to carrier absorption along the bus waveguide. However, as the

bus waveguide bias current increases, the feedback from the straight facet increases and

leads to strengthening of lasing in the counter clockwise direction. This does not lead


to a complete diminish of clockwise mode, probably due to minimal reflections from the

curved facet.

It is evident from Fig. 4.25(a) that clockwise and counter clockwise modes occur

intermittently at multiple ring bias currents. This effect is occurring very rapidly here

due to the instability induced from the pulsed operation. Continuous-wave measurements

shown in Figs. 4.24 better illustrate this bi-stability effect. Once more, bi-stability is

observed at 0mA bus waveguide bias and tends to diminish at higher bus waveguide

currents. The bi-stability regions are clearly observed in Fig. 4.24(a) due to the partial

lack of optical feedback from either facet and more stable operation of laser in continuous

mode. The laser output power in the counter clockwise mode saturates above 500mA ring

bias currents, most probably due to thermal rollover. The ring laser threshold current was

measured to be 280mA, corresponding to a threshold current density of 2022mA/cm2.

We measured the near-field profile of the ring lasers using a beam profilometer, as

shown in Fig. 4.26. None of the lasers seem to emit in a pure Bragg mode, as the

central lobe is more than an order of magnitude more powerful than other lobes. We

investigated this effect through assessment of calculated modal loss for Bragg and TIR

modes. Initially, the etch depth of this sample was measured through SEM microscopy

to be 2.27µm. In the design process, Lumerical Mode was used to calculate the bending

loss for the Bragg and first-order modes which possess the highest optical confinement

factors at the measured etch depth. Bend loss was calculated for 2µm wide ridges with

1mm bends to be 1261dB/cm and 6dB/cm for the Bragg and first-order TIR modes,

respectively at the operating wavelength. It can be predicted that the TIR mode will be

selected over the Bragg mode at the current etch depth. We were aiming at a window of

1.9-2µm etch depth in our samples, where the Bragg mode bend loss is smaller than the

zeroth- and first-order TIR modes. Multiple samples were etched for various times to hit

the targeted etch depth. Unfortunately, all the chips were damaged in the metalization

process and only left this over-etched sample functioning.


(a) (b)

Figure 4.26: Measured near-field profile from the ring laser with 320µm coupler lengthwhere bus waveguide is biased at a) 0mA and b) 100mA CW. The ring is biased at600mA, pulsed, in both cases. The scales are estimated based on the optics used andimage size on camera.

Due to fabrication shortcoming, this experiment was left unfinished. Further, as these

samples did not emit in the Bragg mode, nonlinear conversion tests were not carried

out on these samples. Nevertheless, the presented results show preliminary proof-of-

concept for realization of ring lasers on the Bragg laser platform. This provides valuable

background information required for future implementation of ring lasers on the Bragg

laser platform to investigate this area further. We attribute the implementation of robust

ring lasers in this work to lack of exact control over the depth of of these structure

which requires utilization of an interferometric etch depth monitor in the plasma etching

instrument. Such a control tool is not available in the TNFC cleanroom at present.

4.5 Summary

A phase matched single-sided Bragg reflection waveguide laser was designed for difference

frequency generation at 980, 1500, and 2820nm. The methodology utilized to design the

structure was discussed. Experimental results for laser characterization were presented,

showing single mode lasing in the Bragg mode in some devices and lasing in the TIR

mode in others. Laser emission in the Bragg mode was the first demonstration of lasing


in a single-sided Bragg mode in the literature. Modal discrimination in the single-sided

Bragg laser was studied and confinement issues at certain etch depths were shown to

be causing mixed TIR/Bragg mode lasing in some of the devices. These experimental

results lay out the ground work for improvement of mode selection mechanism in the

next wafer design. This will include monitoring all the guided modes to suppress lasing

in the wrong mode, and switching back to an asymmetric Bragg structure for better

mode control. In addition, some impediments to realize DFG in the current design were

discussed and possible solutions were provided for another wafer design. Phase-matching

the structure near-degeneracy in the C-band was suggested as one of the solutions to

avoid some of the uncertainties with the current design.

Possibility of realizing integrated sources of light on this platform was studied. The

design criteria for sidewall corrugated gratings for DFB lasers, and directional couplers

for ring lasers was investigated, and DFB and ring lasers were fabricated on the single-

sided Bragg laser wafer. It was shown that similar to the Fabry-Perot lasers implemented

on this wafer, lasing can easily take place in the TIR mode instead of Bragg mode in both

ring and DFB lasers which hindered the fabricated DFB and ring lasers from working as

expected. Nevertheless, this proof-of-concept implementation of DFB and ring lasers on

the Bragg laser structure provides valuable information for future implementation of such

devices on wafers with better mode selectivity mechanisms. For example, uni-directional

lasing characteristics of the fabricated ring lasers was investigated and documented for

future implementations. With the current wafer design, accurate etch depth control

is required to accommodate modal discrimination towards lasing in the Bragg mode;

such accuracies can be extremely complex with the current fabrication equipment. The

moderate confinement factor of the first-order TIR mode compared to the Bragg mode

can aggravate modal discrimination and increase the possibility of lasing in the wrong

mode in the current wafer design. As such, in the future device designs confinement

factor of all higher-order TIR modes will be monitored to diminish accommodate lasing


in the Bragg mode with less stringent etch depth requirements.

Chapter 5

Double-sided Bragg laser design

As described earlier, the single-sided wafer design presented in the previous chapter was

limited in its operation due to sub-optimal modal selection mechanisms. In general,

symmetric structures only allow for guided even and odd modes. As the confinement

factor of odd modes in a symmetric structure are generally very small and the number

of even modes is limited, manipulation of guided modes in a symmetric double-sided

Bragg laser is far less complicated that a single-sided Bragg laser. Using this information

another wafer was designed and tested for self-pumped DFG to address the issues raised

with the previous design. A double-sided Bragg laser was considered for better control

of optical confinement factor, and hence reducing the possibility of lasing in modes other

than the Bragg mode. Also, in order to reduce uncertainties regarding the idler focus

and losses, and to avoid beam absorption due to the H2O bond absorption line around

2.8µm, the new device was revisited to be phase-matched near degeneracy close to the

telecommunication C-band and 775nm.

The top Bragg reflector was designed to include only four periods to provide prac-

tical confinement at shallow mesa etch depths as well as good thermal characteristics.

Moreover, electrical characteristics were optimized through a commercial laser simulator

to reduce the series resistance of the devices. In the following, we will focus on the wafer

107

Chapter 5. Double-sided Bragg laser design 108

design and performance of Fabry-Perot lasers. The nonlinear conversion experiments car-

ried out will be outlined and possible methods for tuning the phase-matching wavelength

will be investigated.

5.1 Wafer design

In the previous chapter, a single-sided wafer design was explored for nonlinear conversion,

as well as realization of integrated elements such as surface gratings and ring lasers. While

the thin cladding in the previous design lends itself well to the integration purposes, it was

shown that control of TIR modes can be much harder than double-sided Bragg lasers

in general. Due to its symmetric structure, a double-sided Bragg laser design allows

only for symmetric and anti-symmetric modes. This reduces the complexity of modal

discrimination and Bragg mode selectivity. A double-sided Bragg laser was considered

here for lasing at 775nm and parametric generation in the telecommunication band. The

laser was designed to emit in the Bragg mode of a Bragg laser structure at 775nm as

the DFG pump, where the light can be parametrically down-converted into conventional

TIR modes at 1550nm.

The material system used was AlxGa1−xAs with two strained InAlGaAs quantum

wells separated by 10nm Al0.28Ga0.72As barriers. At aluminum concentrations below

x < 0.45, AlGaAs bandgap is direct and equal to 1.424 + 1.247xeV. Given the selected

designed lasing wavelength, aluminum concentration of all the layers was kept above 0.2

to avoid bandgap absorption effect. Furthermore, due to the quantum well gain character-

istics, these diode lasers emit in the TE mode hence allowing for type-II phase matching

with TE second harmonic and TE/TM fundamental. The accurate concentration and

layer thickness of the quantum wells are defined by the grower (FBH Berlin) who did

not provide any information about the concentration, refractive index, or thickness of

the quantum wells. Given the well-established refractive index models for AlGaAs, we


decided to model the quantum well with an Al0.11Ga0.89As quantum well which has a

bandgap similar to the InAlGaAs. As will be shown later in the chapter, this assumption

may have been a major source of error in the phase-matching wavelength, and has to be

revisited.

Similar to what presented in the previous chapter, the phase-matched structure was

designed using a mode solver where we systematically solved for modes in the 1550nm

wavelength for a range of pump effective indices to find the suitable structure for phase

matching at the desired wavelengths. Various parameters were swept including the thick-

ness and aluminum concentration in the core layers and top and bottom matching layers,

seeking a local maximum for the normalized nonlinear conversion efficiency at the pre-

sumed wavelengths. A maximum 1D efficiency of 6.07 × 10−4%/W/cm2 was obtained.

Once more, to explore the maximum allowable conversion efficiency, the pump and idler

field profiles were assumed to be similar to that of the signal. The nominal upper limit to

the conversion efficiency was calculated to be 5.557× 10−2%/W/cm2, which is only two

orders of magnitude larger than the local maximum calculated for the current device.

Alongside the conversion efficiency optimization, confinement factor of the Bragg

mode was monitored and compared with all the available TIR modes. Fig. 5.1(b) depicts

the ratio of confinement factor of the Bragg mode to that of the 11 available TIR modes

at 775nm in the structure. As illustrated in the Bragg mode confinement factor is more

than 35 times larger than all the other available modes. Also, the confinement factor

of Bragg mode is more than two orders of magnitude larger than the lowest-order TIR

mode which incurs the smallest propagation loss among other TIR modes. Consequently,

the Bragg mode will be selected in the structure over all other available modes.

Figure 5.2 illustrates refractive index profile of the designed structure as well as mode

profile of the slab structure in 775 and 1550nm wavelengths. The designed upper and

lower transverse Bragg reflectors consist of 4 and 5 periods of Al0.70Ga0.30As/Al0.25Ga0.75As

respectively, with a thickness of 425/130nm. The matching layers are 395nm Al0.20Ga0.80As


‘

Table 5.1: The optimized double-sided Bragg laser structure.xm xc xb x1 x2 xcap0.20 0.70 0.28 0.70 0.25 0

tm tc tb t1 t2 tcap395nm 240nm 10nm 425nm 130nm 100nm

tc (nm)

x m

η (%/W/cm2)

210 220 2300.2

0.205

0.21

0.215

0.22

0.225

0.23

4.5

5

5.5

6x 10

−4

(a)

0 2 4 6 8 1010

1

102

103

104

105

TIR mode number

Γ BR

W/Γ

TIR

(b)

Figure 5.1: a) Calculated normalized nonlinear coupling efficiency, η, for SHG as afunction of (tc; xm) for double-sided Bragg laser. A maximum efficiency of 6.07 ×10−4%/W/cm2 is obtained at (tc; xm) = (240nm; 0.2) for a 2mm long test waveguide.Aluminum concentration was kept above 0.2 to minimize bandgap effects and core thick-ness was limited to 240nm to for confinement factor optimization purposes. b) Ratio ofoptical confinement factor of Bragg mode to that of all the available TIR modes for theoptimized structure. The lowest ratio is 35.3.

layers on top and bottom of the core, and bottom and top core layers of 240nm Al0.70Ga0.30As.

Two InAlGaAs quantum wells and three 10nm Al0.28Ga0.72As barriers are inserted be-

tween the two core layers. Finally, a 100nm GaAs cap layer is applied on top of the

structure. These parameters are listed in table 5.1 and full details of the designed struc-

ture are presented in a table as an appendix to this thesis.

After finalizing the layer compositions and thicknesses, the laser doping profile was

examined to improve the electrical performance. A commercial laser simulator from

Crosslight Inc. [82] was used to evaluate the laser output performance. The software

package used for the simulation takes into account self-heating, many-body, and quantum

tunneling effects. Here, we do not go through the details of the equations due to the


−2 0 22.8

3

3.2

3.4

3.6

x [µm]

Ref

ract

ive

inde

x [a

.u.]

Index profile at 2ω

−2 0 22.8

3

3.2

3.4

3.6

x [µm]

Ref

ract

ive

inde

x [a

.u.]

Index profile at ω

−4 −3 −2 −1 0 1 2 3−1

−0.5

0

0.5

1

x [µm]

Fie

ld p

rofil

e [a

.u.]

Figure 5.2: Refractive index profile and mode profile of the structure at 775 (red), and1550 (blue for TM and green for TE) wavelengths. The dashed lines together with theindex profiles represent the effective indices in the according wavelength.

limits of this thesis; the interested reader, however, is encouraged to refer to the model

equations presented elsewhere [99]. The interplay between doping levels, modal loss,

and series resistance/thermal conditions of the diode laser requires a rather complicated

tuning process for the doping levels in each layer of the structure.

Bragg lasers are multi-layered structures with complex energy band diagram which

further complicates the optimization process. Even though VCSELs are not edge emit-

ting, their structure is very similar to that of the Bragg lasers. In both VCSELs and

Bragg lasers series resistance is larger than that of conventional edge emitting lasers due

to the presence of multiple interfaces in the vertical structure. In both cases, doping

profile can be engineered to improve electrical and thermal characteristics. As such, a

doping profile similar to that of VCSELs previously presented in the literature was used

as a starting point for the Bragg laser doping profile. Through an engineered modifica-

tion of the initial doping levels, various profiles were tested and the doping profile which

provided higher output powers and lower voltage drops was chosen as the final profile.


0 1 2 3 4 5 6 7 8−1

0

1

2

3

4

x (µm)

Net

dop

ing

(× 1

018 /c

m3 )

Profile 1Profile 2Profile 3Profile 4

activeregion

(a)

0 10 20 30 40 500

5

10

15

20

25

30

Injected current (A/m)

Lase

r po

wer

(m

W)

0 10 20 30 40 501.4

1.5

1.6

1.7

1.8

1.9

2

Injected current (A/m)

Vol

tage

(V

)

Profile 1Profile 2Profile 3Profile 4

(b)

Figure 5.3: a) Some of the tested doping profiles, and b) simulated LIV characteristicsof the laser for the corresponding doping profiles.

Fig. 5.3 presents some of the doping profiles undertaken in the simulations, and the cor-

responding simulated LIV curves. Doping profile 4 was chosen to provide small enough

series resistance while providing an acceptable output power at the smallest doping levels

especially closer to the structure core. Note that even though the simulation software

takes free carrier absorption into account, introduction of doping at locations where the

light is highly confined can increase the impurity scattering losses which is not taken into

account in the simulation. As such, doping level is kept as low as possible at the location

of optical modal peak. The energy band diagram of the final device with the selected

doping profile is shown in Fig. 5.4(a). The chosen doping profile is presented in detail in

the appendix together with the wafer composition.

Lastly, tuning curve of the device was calculated based on the material and modal

dispersion and is plotted in Fig. 5.4(b). Close to the phase-matching point, the slope

is very abrupt; therefore, deviating from the designed wavelength can easily lead to

substantial changes in the signal and idler wavelength. Effects of such a characteristic

will be addressed more throughly in the nonlinear measurements, further in this chapter.


(a)

760 765 770 7751200

1300

1400

1500

1600

1700

1800

1900

2000

Pump wavelength (nm)

Sig

nal/I

dler

wav

elen

gth

(nm

)

(b)

Figure 5.4: a) Simulated energy band diagram of the unbiased laser for the selecteddoping profile; Ev, Ec, and Ef represent the valence and conduction band levels, andFermi level, respectively. b) Calculated tuning curve for the designed structure.

5.2 Laser fabrication and performance

The designed wafer was grown on 2-off [001] n-type GaAs using MOCVD and a set

of straight Fabry-Perot lasers were fabricated on the wafer through photolithography.

Ridge lasers 2-3µm wide and 1.8-2.4.5µm deep were patterned using plasma etching. The

structure was then passivated with a 300nm layer of silicon oxide, and contact windows

were etched on top of the waveguides to enable current flow through the deposited metal

contacts. A schematic of the device together with an SEM micrograph of a fabricated

device are shown in Fig. 5.5. Lasers were then cleaved into individual laser bars of 500-

1500 µm length which were mounted on a copper stage without bonding for further tests.

A sample LIV curve is illustrated in Fig. 5.6(a). The device under test here has a

width of 2.13µm and a length of 1.04mm. In this experiment, the laser was operated

at 20C in CW condition. The threshold current density of the device was measured

to be 1705A/cm2 and threshold voltage was 2.06V. The spectrum of the laser was in-

spected above threshold and is illustrated in Fig. 5.6(b). As can be seen, even though


(a) (b)

Figure 5.5: a) A schematic of the designed ridge structure, and b) a scanning electronmicrograph of a fabricated double-sided Bragg laser device before the metal deposition.The via opening for current transport is clearly seen in the SEM.

the device emits only at a single peak corresponding to a single transverse mode right

above threshold at 40mA, the spectral profile becomes multi-moded as the injected cur-

rent increases. This is a well-known phenomenon in Fabry-Perot diode lasers, and to

avoid such instances the diodes are usually cleaved to lengths shorter than a few hundred

micro-meters. However, given the equipment available to us, we were limited to devices

with sizes of the order of millimeters, hence the multiple spectral modes. Integration of

a surface DBR with the device can resolve this problem and lead to lasing in a single

spectral lobe with a side-band suppression ratios larger than tens of dB.

Figure 5.6(c) also shows a plot of emission spectra for temperatures ranging from

20-90C. For this experiment, the device was operated at 100mA CW, and the stage

temperature was increased in steps of 10C. A net shift of 0.261nm/C was measured in

the location of peak power. This number will later be used in conjunction with the shift

in phase-matching wavelength to provide a complete roadmap of temperature tuning.

To confirm that lasing takes place for the designed Bragg mode, near field profile

of the laser was measured and compared with the simulated mode profile. A sample

measurement together with the calculated theoretical predictions are also given in Fig. 5.7

to demonstrate the correspondence of the results. In the lasers etched 1.8-2.2µm, the near


0 20 40 60 80 1000

5

10


Pow

er/fa

cet (

mW

)

0 20 40 60 80 1001

2

3

Vol

tage

(V

)

(a)

784 785 786 787 788 7890

0.2

0.4

0.6

0.8

1

Wavelength (nm)P

SD

(A

.U.)

(b)

780 785 790 795 800 805 810 8150

0.2

0.4

0.6

0.8

1

Wavelength (nm)

PS

D (

A.U

.)

20oC

30oC

40oC

50oC

60oC

70oC

80oC

90oC

(c)

Figure 5.6: a) CW LIV curves for a sample laser operated at 20C, and b) normalizedoptical spectrum of the laser under test, operated CW at 20C at 40mA (solid) and100mA (dashed) injected currents. c) Normalized optical spectrum of the laser undertest at 100mA at various stage temperatures.

field resembles that of the Bragg mode and preserves its shape throughout the entire range

of tested bias currents up to four times the threshold current. Moreover, the measured

group index is very close to the simulated group index for such devices. However, devices

etched deeper, at 2.45µm, showed near field profiles and group indices akin to that of the

TIR mode as shown in Fig. 5.8. This is in accordance with the theoretical loss simulations

of the two modes as will be explained shortly. Contrary to the DFG wafer design in the

previous chapter, all the tested lasers etched 1.8-2.2µm exhibit the same near field, which

hints that lasing takes place in the same vertical mode. This is in contrast to the previous

design which would lase in Bragg/TIR mode depending on the modal loss of each mode.

Such a good modal discrimination towards choosing the Bragg mode shows capability of

the design methodology employed in the current design.

As discussed in section 2.2, modal properties of a 2D ridge Bragg waveguide including

its loss can vary depending on the ridge etch depth. An ensemble loss measurement

technique [69] was used to experimentally study the effect of etch depth on Bragg modal

loss. The differential efficiency, ηD, of various lasers cleaved from the same sample was

measured and fit to

1

ηD=

1

ηD,int

(1− αL

ln(R)), (5.1)


Figure 5.7: Near field of the laser under test at 20C and 100mA current. a) Calculated,and b) measured cross-sectional NF profile, c) calculated, and d) measured 2D NF profile.

Figure 5.8: Near field profile of a laser emitting in the TIR mode. a) Calculated, and b)measured cross-sectional NF profile, c) calculated, and d) measured 2D NF profile.

to calculate the internal efficiency, ηD,int, and loss, α. Here R is the net mirror reflectivity

and L is the laser length.

The modal propagation losses were measured for multiple lasers from various samples

etched to different depths. The results are presented in Fig. 5.9 together with theoretically

simulated loss for Bragg waveguide and TIR modes through a fully vectorial commercial

mode solver. Note that confinement of TIR mode lost at etch depths less than 2.27µm

and no mode profile can be simulated at shallower etch depths; this is why the TIR

modal loss is only plotted for etch depths above 2.27µm. From the theoretical results,

it is clear that the modal propagation loss increases significantly at certain etch depths

due to a loss of lateral confinement as discussed in section 2.2.

As shown in Fig. 5.9, in the vicinity of 2.45µm etch depth, simulated modal loss


0.7 0.8 0.9 1 1.1 1.2 1.36

8

10

12

14

16

18

20

Length (mm)

η D (

A.U

.)

α = 14.107 /cm, 1/ηD,int

= 0.997

MeasuredLinear fit

(a)

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8−100

0

100

200

300

400

500

Etch depth (µm)

BR

W m

ode

loss

(dB

/cm

)

BRW modeTIR mode

(b)

Figure 5.9: a) A sample plot of 1/ηD vs. length and the fitted parameters, and b)Theoretically simulated Bragg mode (solid) and TIR mode (dashed) loss, plotted togetherwith the measured losses for Bragg (circles) and TIR (squares). The TIR mode is onlyconfined at etch depths above 2.27µm where modal loss simulation was possible.

of TIR mode is significantly smaller than that of the Bragg mode. Threshold gain of a

mode for achieving lasing depends on modal loss as well as the optical confinement factor.

Figs. 5.10 show the simulated confinement factor for the two modes, and the simulated

threshold gain, assuming 30% mirror reflectivity and 1mm chip length. As illustrated

in the figures, at etch depths ranging from 2.38-2.5µm, the TIR mode reaches threshold

earlier than the Bragg mode. This is in line with our observation that lasers etched down

to 2.45µm emit in the TIR mode rather than the originally deigned Bragg mode (see

Figs. 5.7 and 5.8).

The experimental results provided in this section show that the devices within the

predicted low-loss etch depth range are lasing in the Bragg mode. Moreover, we ex-

perimentally confirmed the theoretically predicted modal loss of the devices. The large

measured modal loss at 1.79µm and emission in the wrong mode at 2.45µm etch depth

are all in line with the theoretical simulations. This is the first time that such complex

confinement characteristics are reported for Bragg waveguides. This study of laser per-

formance together with the assessed spectral and LIV characteristics will be used in the

future experiments to predict the nonlinear conversion performance.


1.4 1.6 1.8 2 2.2 2.4 2.6 2.810

−4

10−3

10−2

10−1

100

Etch depth (µm)

Con

finem

ent f

acto

r (A

.U.)

BRWTIR

(a)

1.4 1.6 1.8 2 2.2 2.4 2.6 2.810

1

102

103

104

105

106

Etch depth (µm)

Thr

esho

ld g

ain

(/cm

)

BRWTIR

(b)

Figure 5.10: Theoretically simulated Bragg mode (solid) and TIR mode (dashed) a)confinement factor, and b) threshold gain.

5.3 Nonlinear device performance

The devices were initially tested for second harmonic generation (SHG). Initially a tun-

able C-band mode-locked fiber laser was end-fire coupled into the ridge waveguide using

an anti-reflection coated 60x objective lens. Pulses with an FWHM of ≈ 100fs with a

repetition rate of 10MHz and an average power of 2mW were employed for the measure-

ment. A fiber polarization controller was used to manipulate the beam polarization and

a polarizing beam splitter (PBS) was used before the objective lens to only allow the

required linear polarization pass through. Also, any source background below 1450nm

was rejected before launching the beam into the sample, using a 1450nm long-pass filter.

At the sample output, the second harmonic was focused on a silicon detector and power

meter using a 40x objective lens. A schematic of the setup is shown in Fig. 5.11.

Due to limited tuning range of the source, no second harmonic was detected. In

order to extend the wavelength range available, the femto-second laser was injected into

an Erbium doped fiber amplifier to generate a broadband supercontinuum. A sample

spectrum of the EDFA input and output spectra are presented in Fig. 5.12. Initially,

type-I SHG was investigated where the input signal is polarized in the TE direction.

Due to the broadband nature of the injected signal, tuning the input was not possible.


Figure 5.11: Schematic of SHG experimental setup. A tunable source emitting at 1535-1565nm wavelength is injected into the sample after amplification, beam shaping, andpolarization control. SMF: single mode fiber; FPC: fiber polarization controller; FC:fiber collimator; LPF: 1450nm long-pass filter; PBS: polarization beam splitter; S: beamsampler; M: mirror; MF: flip-mount mirror; BRL: Bragg reflection waveguide laser; Ge-PD: Germanium photodetector.

Instead, a Horiba iHR320 spectrometer was employed to spectrally resolve the measured

second harmonic at the output. Fig. 5.13(a), shows a clear second harmonic spectral

peak at 807.4nm. The polarization of the measured power was confirmed to be mainly

TM as expected from a type-I process.

In addition to type-I processes, type-II SHG was studied by setting the input PBS to

45 degrees, therefore polarizing the input to a mixture of TE and TM polarizations. The

measured second harmonic spectrum is illustrated in Fig. 5.13(b). The peak at 816.4nm

is polarized in the TE direction manifesting type-II phase-matching, whereas the peak

at 807.4nm is TM polarized. This second peak occurs since a part of the TE polarized

input photons were converted to second harmonic through a type-I process rather than

mixing with TM polarized photons through the type-II process.

To further investigate the nonlinear properties of the device, a type-II DFG measure-

ment was also carried out. A CW tunable C-band laser, Agilent HP 8168F, was amplified

through the C-band EDFA and passed through a tunable filter, Alnair BVF-200CL, to

reject the EDFA background spontaneous emission at the unwanted wavelengths. The

obtained signal was mixed with the pump obtained from a CW tunable Ti:Sapphire laser,


1500 1520 1540 1560 1580 1600−60

−50

−40

−30

−20

−10

0

Wavelength (nm)

PS

D (

dBm

)

(a)

1500 1550 1600 1650 1700 1750−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

Wavelength (nm)

PS

D (

dBm

)

(b)

Figure 5.12: Power spectral density of the femto-second laser a) before and b) afteramplification through the EDFA. The laser and the EDFA were biased at 110mA and60mA, respectively.

795 800 805 810 815 8200

0.2

0.4

0.6

0.8

1

Wavelength (nm)

SH

pow

er (

A.U

.)

(a)

790 800 810 820 8300

0.2

0.4

0.6

0.8

1

Wavelength (nm)

SH

pow

er (

A.U

.)

(b)

Figure 5.13: Power spectral density of the generated second harmonic for a) type-I andb) type-II configurations. The femto-second laser and EDFA were biased at 110mA and60mA, respectively.

Coherent MBR 110, through a beam splitter, and end-fire coupled into the ridge waveg-

uide using an anti-reflection coated 60x objective lens. A fiber polarization controller

and PBS were used to manipulate the signal polarization, and a half-wave plate and PBS

were inserted in the pump beam path allowing for the required linear polarization to pass

through. At the sample output, idler was collected with a 40x objective lens and injected


Figure 5.14: Schematic of DFG experimental setup. Two tunable sources emitting around816nm and 1550nm wavelength are injected into the sample after beam shaping andpolarization control. SMF: single mode fiber; BPF: tunable band-pass filter; FPC: fiberpolarization controller; FC: fiber collimator; PBS: polarization beam splitter; BS: beamsplitter; S: beam sampler; M: mirror; MF: flip-mount mirror; BRL: Bragg reflectionwaveguide laser; Ge-PD: Germanium photodetector.

into a spectrometer. A strained InGaAs detector, EOS IGA-2.2-010-TE2-H, was used in

conjunction with a Stanford research SR830 lock-in amplifier to detect the idler power

at the spectrometer output port. A schematic of the setup is shown in Fig. 5.14.

The signal/pump were set to 21mW/90mW power in the TM/TE polarization and

the idler spectrum was recorded for various pump wavelengths. Figure 5.15(a) illustrates

a sample idler spectrum at pump wavelength of 816.3nm. Due to the proximity of signal

and idler wavelengths, separation of signal and idler waves at the waveguide output

was complicated. As such, the idler power was estimated by carefully calibrating the

spectrometer. Dependence of the calibrated idler power on the pump wavelength for a

constant signal wavelength of 1550nm is shown in Fig. 5.15(b). The signal/pump were set

to 21mW/90mW power similar to the previous test. A peak idler power of 1.82nW was

obtained for the phase-matched pump at 816.3nm and signal at 1550nm. The bandwidth

of the process was found to be 0.74nm.

In a DFG process, the idler power, Pi, is linearly related to the product of pump and


1710 1715 1720 1725 1730 1735 17400

0.2

0.4

0.6

0.8

1

1.2

1.4

Wavelength (nm)

Idle

r po

wer

(nW

)

(a)

814 815 816 817 818 8190

0.5

1

1.5

2


Idle

r po

wer

(nW

)

(b)

0 500 1000 1500 20000

0.5

1

1.5

2

2.5

Pp P

s (mW2)

Idle

r po

wer

(nW

)

(c)

815.8 816 816.2 816.4 816.6 816.8 8171500

1550

1600

1650

1700

1750

Pump wavlength (nm)

Sig

nal/I

dler

wav

leng

th (

nm)

(d)

Figure 5.15: a) A sample spectrum of the generated idler for pump/signal wavelengthof 816.3/1550nm. b) Idler power plotted against pump wavelength for a constant signalwavelength of 1550nm. The circles are the measured data and the solid line shows aLorentzian fit. c) Idler power plotted as a function of signal power for a constant pumppower of 90mW. The circles are the measured data and the solid line is a linear fit. d)Measured DFG tuning curve. All measurements carried out at room temperature (25C).

signal and powers, PpPs through

Pi = PpPsηL2 (5.2)

where L is length of the device and η is the normalized conversion efficiency. To confirm

this linear relationship, the idler power was measured as a function of signal power for

pump/signal wavelength of 816.3/1550nm as shown in Fig. 5.15(c). The DFG normalized

external conversion efficiency was estimated to be 1.84 × 10−2%/W/cm2, taking into

account the 1.038mm length of the sample and 70% objective lens collection efficiency


for the idler. The internal efficiency can be calculated by estimating the power inside

the sample. The coupling efficiency of the signal and pump beams were estimated to

be 20% and 5%, respectively. Note that the pump coupling efficiency is estimated to

be smaller than that of the signal due to the small spatial overlap of the input beam

and Bragg mode. The internal normalized conversion efficiency can then be estimated

to be 1.84%/W/cm2. The reported external coupling coefficient should be compared

with that reported previously for similar structures. For example, for a passive Bragg

waveguide, DFG external conversion efficiency of 2.5× 10−2%/W/cm2 [30] was reported.

Also, for a Bragg laser structure, SHG external conversion efficiency was estimated to

be 5 × 10−3%/W/cm2 [40]. As can be seen, our efficiency values are comparable with

those reported for similar passive structures, and more than three times larger than those

reported for similar active structures. Given the limitations in material choice and doping

induced losses, it is expected that the Bragg lasers offer smaller efficiencies compared to

similar passive devices. The relatively large conversion efficiency reported for the current

device confirms the design procedure for optimal nonlinear conversion.

The simulated DFG tuning curve previously presented in Fig. 5.4, clearly shows that

tuning the pump wavelength by a few nanometers moves the phase-matched signal and

idler wavelengths by hundreds of nanometers. Even though the experimental tuning curve

degeneracy point was found to be far from the initial design, a measured DFG tuning

curve can help understand the device behavior. To provide a DFG tuning curve, both

the signal and pump wavelengths were swept over a suitable range, input power was kept

constant, and the pump/signal wavelength combinations corresponding to the maximum

idler power were recorded together with the idler measured peak wavelength. The tuning

curve is plotted in Fig. 5.15. Because the device is operated near DFG degeneracy point,

a change of less than 1nm in the pump wavelength leads to change larger than 30nm

in the signal/idler wavelength. Except for the location of degeneracy point, this tuning

behavior was expected from the theory.


5.3.1 Tuning the phase-matching wavelength

Even though the current structure was initially designed to accommodate for type-II

phase-matching at 775nm, the phase-matching wavelength was red-shifted to 816.3nm

according to the measurements. This deviation of the phase-matching wavelength from

the design can be ascribed to various factors including inaccurate refractive index model,

metal-organic chemical vapor deposition growth variations, doping effects on the layer

refractive indices, and effect of current injection. Nevertheless, a major uncertainty in our

design was the quantum well indium and aluminum concentrations and lack of an accurate

index model for the quantum well material index. As stated earlier in this chapter, the

main source of error is likely the quantum-well optical properties as the concentration

and layer thickness of the quantum wells were not provided by the grower. Based on the

measured tuning curve in Fig. 5.15(d), with the current lasing wavelength around 790nm,

self-pumped DFG is possible for signal wavelengths in the 1250nm region. Due to lack of

resources in the group, we need to demonstrate self-pumped DFG with signal wavelengths

within the C-band. In order to shift the signal/idler phase-matching wavelength closer to

the C-band, a few paths are conceivable. The main path is to correct the quantum-well

model based on the current experimental data and redesign the wafer with the revised

model for the desired phase-matching wavelength. Also, control of lasing wavelength

thorough integration of surface Bragg gratings similar to that discussed in section 4.3

can provide lasing at the desired wavelength. In addition to these two approaches, we

studied the effect of current and temperature on moving the phase-matching point of the

currently available devices potentially closer to the originally designed wavelength. A

summary of both experiments will be outlined below.

Initially, a temperature controlled stage was used to hold the sample and temperature

was set to 10-100C with steps of 10C using a Keithly 2510 TEC sourcemeter. The signal

and pump were mixed in a 50/50 fiber splitter/combiner and the output was injected

into the sample through a cleaved facet fiber. The output was collected through a 40x


objective lens and the idler power was spectrally resolved using a spectrometer, similar

to the previous experiment. For every temperature point, the input fiber location was

optimized for maximum coupling, and pump wavelength was tuned while recording the

idler power. Signal power was kept constant at 1550nm throughout this experiment and

the pump/signal power was kept at 18/40mW. As shown in Fig. 5.16(a), temperature

tuning can vary the phase-matching wavelength by ∆λ/∆T = 0.1nm/C. By taking the

effect of temperature on lasing wavelength into account, a stage temperature of 182.5C

will be required to line up the lasing and phase-matching wavelengths. There are however,

many barriers in this path; not only holding the temperature at such high temperatures

needs additional equipment, but also operation of the diode laser at temperatures this

high is extremely weak, if even possible. As such, we focused on other methods for

attaining self-pumped DFG.

Injection of free carriers into the device active region modifies the material refrac-

tive index [100] and hence the phase-matching wavelength. Changes as large as -5%

could be anticipated in the refractive index of AlGaAs quantum wells corresponding to

a blue-shift of tens of nanometers in the phase-matching wavelength. This effect can

be studied in Bragg lasers based on InAlGaAs quantum wells. The device DFG phase-

matching wavelength was investigated while CW current was injected into the sample

through two gold-plated copper probes, at a constant 20C stage temperature. Once

more the signal wavelength was kept constant at 1550nm, pump wavelength was tuned,

and the idler power was monitored for a range of injected current levels of 0-90mA with a

step of 10mA. Fig. 5.16(b) depicts the normalized idler power plotted against the pump

wavelength for the tested currents. The figure shows less than 2nm blue-shift in the

phase-matching wavelength through current injection. Even though the stage tempera-

ture was kept constant, the device junction temperature can increase significantly due to

carrier injection. In the current case, the red-shift in phase-matching point caused by the

increase in junction temperature is offsetting the phase-matching wavelength blue-shift


Sample temperature (°C)

Pum

p w

avle

ngth

(nm

)

Normalized idler power (A.U.)

20 40 60 80 100815

820

825

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(a)


Pum

p w

avle

ngth

(nm

)

Normalized idler power (A.U.)

0 20 40 60

814.5

815

815.5

816

816.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(b)

0 20 40 60 80814

814.5

815

815.5

816

816.5


Pha

se m

atch

ed p

ump

wav

leng

th (

nm)

MeasuredCorrected

(c)

Figure 5.16: a) Idler power plotted against pump wavelength and stage temperature. Thetemperature step was 10C. b) Idler power plotted against pump wavelength and injectedcurrent at a constant stage temperature of 20C. The injected current step size was 10mA.Idler power is normalized to its maximum at each given temperature/current. c) Theraw and corrected phase-matching point as a function of injected current, extracted fromthe previous figure.

caused by carrier injection.

As the effect of current injection on junction temperature is known, effect of carrier

injection and junction temperature can be de-convolved to study the sole effect of carrier

injection on the phase-matching wavelength. Fig. 5.16(c) shows the DFG phase matching

pump wavelength extracted from the above experiment. The corrected data is also shown

in the figure where the effect of junction temperature on phase-matching point is offset

to only represent the effect of carrier injection on the phase-matching wavelength. The

linear blue-shift of phase-matching wavelength below the laser threshold can be ascribed

to the linear ascend of carrier concentration in the active region with the current. Above

threshold, however, carrier density is not dependent on current injection, and the excess

carriers are mainly consumed through radiative and non-radiative recombination. This

trend is clearly confirmed in the figure where the de-convolved phase-matching wavelength

remains nearly unchanged above threshold current. The effect of injected current on

phase-matching wavelength is estimated to be 0.076nm/mA under threshold.


5.3.2 Discussion

A double-sided Bragg laser for efficient nonlinear DFG was designed and tested as shown

in this chapter. In order to achieve self-pumped DFG, pump wavelength needs to be

supplied through electrical injection rather than external injection. Currently, this is not

possible for signal wavelengths near the C-band, due to the large separation between the

lasing wavelength and DFG phase-matching wavelength. However, the measurements

reported here lay out the background for future implementation of self-pumped DFG in

new device designs. The gathered DFG information includes the data regarding location

and efficiency of DFG in Bragg lasers in the current material system, which is critical

for future designs. This was the first time we worked with FBH Berlin for growth of

active AlGaAs wafers, and as such we did not have any information about the quantum

well content or its refractive index. Hence, an initial wafer was essential to identify all

these parameters. Moreover, study of operating conditions such as stage temperature

and injected current on DFG will help us better understand and predict the effect of

current injection for future implementation of electrically injected self-pumped DFG.

Absorption spectroscopy was suggested as one of the major areas of interests for

nonlinear integrated devices such as the one proposed here. The nanowatt power lev-

els achieved here may seem very small for any meaningful spectroscopy measurement.

However, this is only an initial measurement to characterize the material system, and to

provide information about the nonlinear properties. Specifically, power coupling into the

Bragg mode at pump wavelength is very inefficient. If the exact same device is redesigned

to lase effectively at the right mode and right wavelength, there will be easily tens of

milliwatts of pump power available for nonlinear conversion. Based on the measured

nonlinear conversion efficiency, assuming 100mW power in both the signal and pump

wavelengths and 2mm device length, a 0.73mW idler power will be attainable through

self-pumped DFG. Such a power level may not be sufficient for free space spectroscopy,

but is more than enough for on-chip spectroscopy, for example in capillary based sys-


tems [25]. In addition to self-pumped DFG, self-pumped SOPO is also possible with

the measured conversion efficiency. The measured nonlinear conversion efficiency can

be plugged in to the doubly-resonant OPO threshold power reported in [26] to better

illustrate this. Assuming 1mm long samples, and propagation loss of 2 /cm and high

reflection coatings of 95% reflectivity for both signal and idler, a threshold pump power

of 430mW can be calculated. Even though such power levels are not available in CW

operated lasers, this can easily be achieved by mode-locking the lasers. For example, a

diode laser with 40GHz repetition rate, 1ps temporal pulse width, and 16mW average

power can deliver the required power levels. Passive mode-locking of diode lasers can

be obtained by introducing a reverse biased ”saturable absorber” section along with the

diode laser gain section [101]. The SOPO design aspects including the threshold power

levels and dynamic characteristics when operated in pulsed regime will be discussed in

more detail in the next chapter.

5.4 Summary

We have designed a double-sided Bragg reflection waveguide laser which lends itself to

near-degeneracy difference frequency generation at 775nm and 1550nm. The method-

ology utilized to design the structure is discussed. Experimental results for laser char-

acterization are presented showing single mode lasing in the Bragg mode, and the laser

modal loss is studied as a function of ridge etch depth. Nonlinear properties of the device

are investigated and difference frequency generation is demonstrated for the first time

in an active semiconductor Bragg laser device. As the measured DFG degeneracy point

turned out to be far from the lasing wavelength, the effect of temperature and current

was studied on tuning the phase-matching wavelength. This study of temperature and

carrier effects on the phase-matching wavelength is the first systematic investigation of

DFG phase-matching wavelength tuning reported in the literature. Keeping the signal


wavelength constant allows for de-convolving the temperature and carrier effects on the

phase-matching wavelength without introduction of any additional variables.

The current DFG experimental results in the active structure are very important as

the current design is the stepping stone in realizing self-pumped DFG, and further down

the road, self-pumped parametric oscillation. The measurement results of the current

device implementation provide the background information required for correction of the

active region index model for successful implementation self-pumped DFG near the C-

band. Further, the current experimental results provide accurate prediction of phase

matching conditions for devices designed for self-pumped DFG at various operating con-

ditions. High quality factor cavities at signal/idler wavelengths can be incorporated onto

a device already designed for self-pumped DFG. Given the right amount of parametric

gain, and depending on the quality factor of the cavities, parametric generation can be

achieved in such a structure.

Chapter 6

Semiconductor Optical Parametric

Oscillators

Due to their vastly tunable output properties and versatility, optical parametric oscilla-

tors (OPOs) have fueled many domains of applications such as spectroscopy [102, 103],

sensing [104, 105] and various quantum optical experiments [106, 107]. In particular,

table-top intracavity optical parametric oscillators (IOPOs) have been investigated since

the late 60’s using various nonlinear elements in doubly-resonant [108, 109] and singly-

resonant configurations [22, 23, 110]. IOPOs offer distinct advantages over other OPO

configurations, especially due to the lower threshold pump power needed in the CW

mode of operation. In the case of IOPOs, parametric generation takes place in the

same cavity where the lasing takes place. This leads to a larger pump power available

inside the laser cavity and consequently to lower threshold levels compared with con-

ventional OPOs. A notable limitation of these systems is instability due to relaxation

oscillations [21]. Operating the pump laser in the Q-switched pulsed mode is one of the

solutions to overcome this stability issue [22, 23].

In the previous chapter, we showed DFG in the Bragg laser structure as a stepping

stone for realization of SOPOs. When sufficient parametric gain and feedback is made

130

Chapter 6. Semiconductor Optical Parametric Oscillators 131

available to the parametric process, both signal and idler can reach oscillation threshold

in the same cavity as the laser pump [26]. Direct modulation of lasers is a low cost,

low footprint, and low power consumption alternative to complex modulators such as

Mach-Zehnder modulators. Similar to directly modulated diode lasers, injected current

of SOPOs can be modulated for pulsed operation. Even though they are not as efficient

as conventional diode lasers, direct modulation of SOPOs can be beneficial in some areas

and requires investigation. Moreover, general investigation of SOPO pulsed operation is

essential for other applications. For example, in the previous chapter we discussed mode-

locked operation of SOPOs to attain the required OPO threshold levels. Understanding

the dynamic and static properties of SOPOs, specifically when operated in pulsed con-

dition, is essential to their optimal design and applicability to certain domains.

Akin to the optimization of the IOPO cavity that took place prior to realization of

efficient IOPOs, similar quantitative design tools and insight is needed for enabling real-

ization of functional SOPOs. Some SOPO design trade-offs including the OPO threshold

power have been studied recently [26]. This recent study focused on time-invariant prop-

erties, where the static operating regimes and dynamics of power exchange in the SOPO

were left unexamined. Insight into the device dynamics requires concomitant large signal

analysis of the rate equations of both the pump part and the OPO part of the device.

As such, in this chapter we will utilize existing rate equations of both diode lasers and

OPOs and modify them in order to represent the operation of SOPOs. This will help to

shed light on the device physics of operation and elucidate its static and dynamic prop-

erties. Some similar models have been used previously for static and dynamic analysis of

table-top intracavity doubly resonant [108, 109, 111] and singly resonant [22, 110] OPOs.

In this chapter, the nonlinear interactions are reformulated for waveguides rather than

bulk crystals and an explicit account for the phase of the interacting fields is introduced

in the equations allowing for chirp analysis of SOPOs.


6.1 Formalism: rate equations in active, nonlinear

media

The classical rate equations of quantum well (QW) lasers are well-studied in the litera-

ture [87]. The power and phase rate equations can be derived by solving the Helmholtz

electric field equation, assuming slowly varying envelope, multiplying by the field en-

velopes in x, y, and z and integrating over all three directions. The laser rate equations

can be expressed as follows for the carrier density, N , average laser optical power inside

the cavity, Pp, and radiation phase, φp:

dPp

dt= Ppvg;p(Γ

g

1 + βPp

− αp), (6.1a)

dφp

dt= −α

2vg;p(Γg − αp), (6.1b)

dN

dt=ηI

qV− N

τ− gvg;pζPp

1 + βPp

, (6.1c)

ζ =L

~ωpVphvg;p. (6.1d)

Here Γ is the optical confinement factor, g is the optical gain, β represents gain saturation,

vg;p is the group velocity at the laser wavelength, αp represents the sum of distributed

mirror loss and propagation losses, α is the linewidth enhancement factor, η denotes the

current injection efficiency, I is the injected current, q represents the electron charge, V

is the active layer volume, Vph is the optical cavity volume, τ is the carrier lifetime, ζ

is a conversion factor between the internal power and photon density in the cavity, L is

the length of the cavity, ωp is the angular frequency of the laser, and ~ denotes the Dirac

constant. In these equations, the spontaneous emission factor is neglected. Note that the

rate equations are given for the laser internal power so as to facilitate combining them

with those of the OPO later in the text. Also note that while the confinement factor, Γ,

shows up in (6.1a), this factor is excluded from (6.1c) due to the use of carrier density

rather than carrier numbers in this equation [112].


Figure 6.1: Schematic of a representative doubly resonant SOPO where the end facetsof the diode laser are high reflection coated (HR) at pump, signal and idler wavelengths.A scheme of a typical Bragg reflection waveguide SOPO is shown.

If the diode laser cavity is phase-matched for second order nonlinearities, efficient

optical parametric processes can take place within that cavity. A schematic of the device

is illustrated in Fig. 6.1, where pump photons are generated through lasing action in

the active medium and the pair of signal and idler are generated by parametric down-

conversion of these high energy pump photons. As such, a part of the laser power is

converted into signal and idler where their wavelengths are governed by the the phase

matching condition. This down conversion translates into an extra source of loss for the

pump laser.

Assuming a single longitudinal mode for all three interacting waves in the SOPO, and

taking z as the propagation direction, the overall scalar electric field can be expressed as:

Eσ(x, y, z, t) =1

2Fσ(x, y)fσ(z)Eσ(t)exp[−iωσt+ iφσ(t)] + c.c. , σ ∈ p, s, i (6.2)

Many diode laser designs operate in a single longitudinal mode. As SOPOs are essentially

diode lasers with the nonlinearity phase-matched, the single mode assumption can be

valid for SOPOs as well. In (6.2), Eσ(t) is the absolute value of the time envelope, Fσ


is the normalized field profile in the transverse plane (xy-plane), fσ is the field envelope

along the propagation direction, and c.c. denotes complex conjugate. Similar to the work

of Oshman and Harris in [108], the z envelopes are set to fp(z) =√

2/L cos(βpz), fs(z) =√

2/L sin(βsz), and fi(z) =√

2/L sin(βiz), where βσ are the propagation constants at

laser threshold. The laser acts as the pump, where ωp = ωs + ωi. The internal powers of

the pump, signal and idler are normalized such that Pσ = cnσǫ0/2L E2σ. By substituting

(6.2) into the Helmholtz equation, a set of nonlinear rate equations for SOPOs can be

derived similar to the derivation of diode laser rate equation. Under slowly varying

amplitude approximation, by multiplying both sides of the Helmholtz equations by Fσ

and fσ and integrating over x, y, and z, the rate equations for the powers of the interacting

waves can be derived. A detailed derivation is presented in Appendix E. The derived

SOPO rate equations can be summarized as:

dPp

dt= Ppvg;p(Γ

g

1 + βPp

− αp) +Kvg;pκ

λp

√

PsPiPp(− sin(∆φ))sinc(∆βL), (6.3a)

dφp

dt= −∆ωp +

K

2vg;p

κ

λp

√

PsPi

Pp

cos(∆φ)sinc(∆βL), (6.3b)

dPs

dt= −Psvg;sαs +Kvg;s

κ

λs

√

PsPiPp sin(∆φ)sinc(∆βL), (6.3c)

dφs

dt= −∆ωs +

K

2vg;s

κ

λs

√

PpPi

Ps

cos(∆φ)sinc(∆βL), (6.3d)

dPi

dt= −Pivg;iαi +Kvg;i

κ

λi

√

PsPiPp sin(∆φ)sinc(∆βL), (6.3e)

dφi

dt= −∆ωi +

K

2vg;i

κ

λi

√

PpPs

Pi

cos(∆φ)sinc(∆βL). (6.3f)

These equations can be coupled with the carrier density rate equation (6.1c) to describe

the interaction of carriers and photons for all three waves. In (6.3), ασ represent the sum

of propagation loss and distributed mirror losses for each wavelength, λσ are the free

space wavelengths, K = 1/2 for degenerate three-wave mixing process and K = 1 for

the non-degenerate case, ∆φ = φp − φs − φi, ∆β = βp − βs − βi, and κ is the nonlinear


coupling coefficient and is given by

κ =

√

√

√

√

< χ(2)eff >

24π2

nsninpǫ0cA(2)eff

, (6.4a)

< χ(2)eff >=

∫∫ +∞−∞ Fs(x, y)Fi(x, y)Fp(x, y)χ

(2)eff (x, y)dxdy

∫∫ +∞−∞ Fs(x, y)Fi(x, y)Fp(x, y)dxdy

, (6.4b)

A(2)eff =

∫∫ +∞−∞ F 2

s (x, y)dxdy∫∫ +∞−∞ F 2

i (x, y)dxdy∫∫ +∞−∞ F 2

p (x, y)dxdy(

∫∫ +∞−∞ Fs(x, y)Fi(x, y)Fp(x, y)dxdy

)2 . (6.4c)

Here χ(2)eff (x, y) is the local effective second order susceptibility of the material, and <

χ(2)eff > is the effective susceptibility of the device - a weighted average of the susceptibility

where the field profiles are the weighting functions. Additionally, in (6.3d) and (6.3f),

∆ωs,i are the deviations of signal and idler frequencies from their values at laser threshold

due to laser frequency chirp, ∆ωp. As shown in Appendix E, section E.2, for a small

change in the pump frequency, ∆ωp = α2vg;p(Γg − αp), the associated changes in the

signal and idler frequencies can be derived from the energy and momentum conservation

relations as:

∆ωp =α

2vg;p(Γg − αp), (6.5a)

∆ωs = ∆ωpnp − ng;i − ng;p

ng;s − ng;i

= γ∆ωp, (6.5b)

∆ωi = ∆ωp −∆ωs. (6.5c)

where nσ are the real parts of the corresponding effective indices and ng;σ represent the

group index at each wavelength.

In contrast to bulk IOPOs where frequency chirp of the pump is not usually of great

significance as the pump is either CW or Q-switched, SOPOs are self-pumped using an

electrically injected diode. As such, these devices can conceivably be operated in a pulsed

mode under direct current modulation. Operating in this mode entails appreciable pump


frequency chirp. This chirp of the pump can play a major role in shaping the output

properties of the signal and the idler. Therefore, the terms ∆ωp, ∆ωs, and ∆ωi which

are dependent on the injection current have to be taken into account in the study of the

SOPO chirp and power characteristics.

6.2 Steady-state analysis

The model derived here for doubly resonant SOPOs is similar in form to the doubly reso-

nant IOPO model discussed by Oshman and Harris [108], despite the differences between

both devices. In the case of the SOPO, waves propagate in guided modes in a cavity

with relatively smaller dimensions, which can support a smaller number of longitudinal

modes in comparison to conventional IOPO cavity. Another difference in the mathe-

matical expression of the two sets of equations is the manifestation of frequency chirp

in the pump frequency, ∆ωp, and the corresponding signal and idler chirp as described

in (6.5). As shown in the Appendix E, the effect of frequency chirp can be accounted for

in a first order approximation by utilizing the energy conservation condition, where the

chirp terms cancel out in d∆φ/dt. As such, when calculating the SOPO characteristics

which deal with ∆φ rather than individual phases of the interacting waves, the chirp

effects will not play a significant role. This is indeed the case when examining the SOPO

steady-state regimes, which relate closely to those of a doubly-resonant IOPOs as will be

shown in this section.

6.2.1 Stability conditions

The SOPO steady-state pump, signal, and idler internal cavity powers can be derived

using (6.3). Similar to the approach taken in doubly resonant IOPOs, by setting the

time derivatives of carrier density, powers, and ∆φ to zero, three distinct solutions can

be found for the SOPO output, defining three regions of operation.


It can be shown that if the pump laser power is below the OPO threshold power

POPO,th which is described by

POPO,th =1

4

λiλsαiαs

κ2, (6.6)

then parametric oscillation will not take place and the laser will operate similar to a

conventional un-phase-matched semiconductor laser. This regime will be termed as the

no-OPO regime since there will be no power available for either the signal or idler. The

pump power in this regime is described by:

Pp;no-OPO =Γgvgτp − 1

β. (6.7)

If the value of Pp,no-OPO is above POPO,th, there are two possible steady-state operating

regimes depending on the value of ∆φ. In the inefficient regime of operation ∆φineff 6= π2.

In this case, ∆φineff can take on any arbitrary number and the parametric interaction

changes the waves’ phases in addition to their amplitudes. Beside the SOPO threshold

condition, for the inefficient regime to be in effect it is necessary that Pp,ineff > 0 and

sin(∆φineff) ≤ |1| where the powers and ∆φineff in this regime are defined as:

Pp,ineff =gΓvg;p − αivg;i − αpvg;p − αsvg;sβ(αsvg;s + αpvg;p + αivg;i)

(6.8a)

Ps,ineff = Pp,ineffλp(vg;sαs + vg;iαi)

λsαsvg;s(6.8b)

Pi,ineff = Pp,ineffλp(αsvg;s + αivg;i)

λiαivg;i(6.8c)

sin2(∆φineff) =POPO,th

Pp;ineff

. (6.8d)

On the other hand, in the efficient regime, ∆φ = π/2 which leads to zero nonlinear

terms in (6.3b), (6.3d), and (6.3f). For this regime to be valid, the SOPO should be


operating above threshold, and the inefficient regime should be unstable; the second

condition implies that either Pp,ineff < 0 or sin(∆φineff) > |1| should be valid. The pump,

signal, and idler powers are defined as the following in the efficient regime:

Pp,eff = POPO,th (6.9a)

Ps,eff = Pp,eff

[

−λpαp

λsαs

+gΓ

1 + βPp

λpλsαs

]

(6.9b)

Pi,eff = Pp,eff

[

−λpαp

λiαi

+gΓ

1 + βPp

λpλiαi

]

. (6.9c)

Equations (6.9) elucidate that in the efficient regime any increase in the gain of the laser

will directly lead to an increase in the signal and idler powers, while the pump power

remains unchanged. Similar to doubly resonant IOPOs, there is an unstable SOPO

operating regime at extremely high pump powers [108]. SOPOs instability at extremely

high pump powers merits a separate study.

6.2.2 Numerical example

Here, we study the behavior of a type-II phase-matched Bragg reflection waveguide laser.

The active region for the pump is a double quantum well of InGaAs/GaAs with emission

wavelength at λp = 980nm (TE-polarized). A three-parameter gain relation similar to

that of [112] was chosen for the 6nm InGaAs wells. The wavelengths of the signal (TM-

polarized) and idler (TE-polarized) are taken to be at λs = 1550nm and λi=2665nm,

respectively. Table 6.1 summarizes the waveguide geometry and parameters of interest

used in simulations.

Fig. 6.2(a) shows the calculated powers of the pump, signal and idler as functions of

current. In the figure, the circles show the simulated powers obtained from numerical

solution of the rate equations in (6.3), whereas the solid curves show the analytically cal-

culated values obtained from the equations in [113]. The numerical values were obtained

through recording the final power values after solving the system of equations using a


Runge-Kutta algorithm [114]. A close agreement between the values of both calculations

is obtained.

The SOPO is fundamentally a diode laser lasing at the pump wavelength with the

second order nonlinearity of the structure phase-matched for nonlinear conversion within

the cavity. The pump power-current curve deviates significantly from a conventional

diode laser. The SOPO pump power has different characteristics in the three efficiency

regimes as indicated on Fig. 6.2(a). While in the no-OPO regime, the laser acts akin

to a conventional diode laser, in the efficient regime which ensues at currents between

25.5mA and 91.5mA, the pump output saturates at 250.5mW irrespective of the injected

current. In this regime, all the injected carriers translate into pump photons which are

all converted into signal and idler photons. Finally, at currents above 91.5mA, the SOPO

enters the inefficient regime of operation and the pump power increases with current, but

with a lower slope compared to the no-OPO regime. In this example, the pump slope

efficiency is 9.98W/A within the no-OPO regime, and 3.01W/A within the inefficient

regime. Such a reduction in the pump slope efficiency is due to the partial conversion of

pump photons into signal and idler in the inefficient regime.

As shown in Fig. 6.2(a), above the OPO threshold, signal and idler power increase

monotonically with current. This signal/idler power-current curve can be interpreted

similar to the power-current curve in a conventional diode laser. While in a conventional

laser current controls the gain, in the SOPO, current indirectly affects the parametric

gain of the device through changing the pump power and hence the associated parametric

gain. As predicted previously, the signal/idler slope efficiencies in the inefficient regime

are lower than those in the efficient regime. The slope efficiency is 6.39 (3.37)W/A in the

efficient, and 4.93 (2.61)W/A in the inefficient regime for signal (idler) respectively. This

change in their slope efficiencies demonstrates the reasoning behind naming both regimes.

The change in the SOPO signal power slope is attributed to a change in the mode of

operation due to the change in the parametric gain mechanism. This behavior is also


Table 6.1: Design parameters for the test structure.parameter value parameter valueλp (nm) 980 ασ αl,σ + αm,σ

λs (nm) 1550 αm,σ (ln√R1R2)/L

λi (nm) 2665 αl,σ (/cm) 2.00np 3.2765

√R1R2 0.97

ns 3.2547 L (µm) 250ni 3.2163 Γ 0.032vg;p (cm/s) 7.14×109 Vph (cm3) 1.25×10−10

vg;s (cm/s) 8.79×109 β (/W) 2.0706

vg;i (cm/s) 9.20×109 < χ(2)eff > /

√

A(2)eff (/V) 80.06×10−6

0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8


Ste

ady−

stat

e in

tern

al p

ower

(W

)

PumpSignalIdler

noOPO

efficient regime

(a)

inefficientregime

0

50

100

Pum

p ch

irp (

GH

z)

−2

−1

0

Sig

nal c

hirp

(T

Hz)

0 20 40 60 80 100 1200

1

2

Idle

r ch

irp (

TH

z)


inefficientregime

efficient regimenoOPO

(b)

Figure 6.2: a) Steady-state internal power of the pump, signal and idler and b) adiabaticfrequency chirp of the simulated SOPO plotted as functions of the injected current. Thelines and circles represent the calculated and simulated data, respectively. The steady-state regions of operation are separated with vertical dashed-lines, and are distinct fromthe change in the slope of the graphs. c©2005 IEEE [113]

similar to the change in the slope efficiency of a conventional diode laser due to nonlinear

gain mechanisms leading to lasing of other modes in addition to the fundamental mode.

Frequency chirp is defined as 1/2π dφ/dt and is usually divided into transient and


adiabatic components. Adiabatic chirp or the steady-state chirp can be calculated from

the steady-state powers and ∆φ using (6.3b), (6.3d), and (6.3f). Fig. 6.2(b) demonstrates

the dependence of the frequency chirp on injected current for the simulated SOPO. From

the figure, the analytically calculated chirp is in good agreement with those obtained

numerically. Note that the signal and idler chirp are not plotted in the no-OPO region,

where signal and idler powers are merely quantum fluctuations.

An important feature in Fig. 6.2(b) is the very large signal and idler adiabatic fre-

quency chirp, which is in the order of a few THz. This large frequency deviation can be

explained through the tuning curve of the structure. Fig. 6.3 shows the tuning curve of

the Bragg laser SOPO under study calculated through modal analysis. A small change

in the pump frequency/wavelength leads to relatively large change in the signal and idler

frequencies/wavelengths. For the device studied here, a shift in the emission wavelength

of the diode pump by an amount of 2nm results in the tuning of the signal wavelength

between 1550 − 1568nm and tuning of the idler wavelength between 2665 − 2627nm. It

can be shown that in the frequency chirp relations (6.3b), (6.3d), and (6.3f), the first

term is usually much larger compared to the second. Therefore, the chirp properties of

the device follow those of ∆ωσ. However the second terms have a significant effect on

∆φ which appears in the power rate equations and defines the steady-state regime of

operation. Due to carrier injection in the cavity, there is usually an appreciable adiabatic

frequency chirp on the order of tens of GHz induced in semiconductor lasers [115]. In

the case of SOPOs, this chirp is exhibited by the pump, which consequently translates

into an even larger chirp for the signal and idler. This transfer of chirp from pump to

signal and idler can be clearly seen in Fig. 6.2(b). It is important to note that the pump

chirp frequency is projected negatively onto the signal while the pump chirp translation

to idler is positive. This feature and its possible applications will be discussed in more

detail in the next section.


980 982 984 986 988 990 992

1600

1800

2000

2200

2400

2600

2800


Sig

nal/I

dler

wav

elen

gth

(nm

)

Figure 6.3: Wavelength tuning curve of the simulated SOPO showing the variation ofsignal and idler wavelengths as functions of the pump wavelength. A shift in the pumpwavelength by +2nm, results in a signal and idler wavelength tuning by 18nm and−38nm,respectively.

6.3 Dynamic analysis and large signal response

The importance of investigating the SOPO large signal dynamic response is two-fold; not

only because it sheds light on the transient properties of SOPOs in the CW regime, but

it also provides insight into their response when operated in pulsed regime. To start, the

time constants that represent the SOPO temporal response will be introduced. After,

the rate equations are solved to examine the transient behavior of power and frequency.

6.3.1 Rise time and build-up time: definition and closed-form

approximation

There are two main time constants that define the response speed of SOPOs: signal/idler

build-up time and rise time between 10% and 90% of the steady state value. They help

determine the ultimate direct modulation speed. Build-up time is the onset for the

signal and idler powers. We define the build-up time as the time needed for the input

step response to rise to 10% of the steady state value. The 10%-90% rise time is a popular

metric that allows for comparing the responses of various devices. It will be referred to as

the rise time. Fig. 6.4 shows a schematic of an example transient power trace to illustrate

the definition of these terms.


t=0Pmin

PmaxP2

P1

Time (A.U.)

P (

A.U

.) Rise time

Build−up time

Figure 6.4: The build-up time and rise time shown for a step response, assuming theturn-on time to be at t = 0s. Here P1 = Pmin+0.1∆P and P2 = Pmin+0.9∆P where∆P = Pmax− Pmin.

As opposed to numerical solutions, an analytical formula for the rise time or build-up

time can provide insight into the nature of the parameters affecting the response speed

and it can facilitate the process of tailoring the device design for high speed modulation.

A closed-form solution for the build-up time can be derived by solving the rate equations

described earlier with the appropriate initial conditions. In an initially unbiased SOPO,

before the build-up time the signal and idler powers are merely vacuum fluctuations,

and pump depletion can be neglected. As such, the solution of (6.3c) and (6.3e) result

in exponential responses for signal and idler powers. Assuming no pump depletion,

∆φ = π/2, and solving for the signal and idler, a solution can be derived which relate

the signal/idler power, Ps,i(t), to their initial value, Ps,i(0),

Ps,i(t) = Ps,i(0)exp

(

2t

√

vg;svg;iκ2

λsλiPp,fr

)

exp (−αs,ivg;s,it) . (6.10)

Here Pp,fr is the steady-state internal free running pump power, i.e. the pump power

available to the parametric processes which can be derived from (6.1a). To obtain a

closed-form relation for the build-up time, τr;s,i, it is sufficient to define r = 0.1Ps,i(∞)/Ps,i(0) =

Ps,i(τr;s,i)/Ps,i(0) and solve (6.10) for τr;s,i:

τr;s,i =ln r

2√

vg;svg;iκ2

λsλiPp,fr − αs,ivg;s,i

. (6.11)


The constant r should be derived through quantum optical calculations to account for

the quantum fluctuations which define Ps(0) [116]. However, the choice of r does not

strongly affect the calculation of the build-up time due to its logarithmic dependence.

Although a constant ∆φ is utilized to derive this approximation, equation (6.11) can

predict the build-up time for both SOPO steady-state regimes, efficient and inefficient as

will be demonstrated.

Equation (6.11) predicts that the OPO build-up time can be reduced by tuning phys-

ical device parameters such as loss and nonlinear coefficient, or external parameters such

as the pump power available for nonlinear conversion. Tuning the structural or physical

parameters are not easily achievable for a given device whereas the pump power can be

tuned easily through the injected current. Although the rise times can not be expressed

analytically similar to the build-up times, it can be shown numerically that the same

parameters will affect their values. The effects of the initial bias and current injection

step size on the build-up and rise times will be studied in the forthcoming subsections

alongside other dynamic properties.

6.3.2 Dynamic behavior for an initial condition of zero bias

In order to serve as a reference for the SOPO dynamics, the dynamic behavior of a con-

ventional laser which is not phase-matched for nonlinear conversion is provided. The

structure described in Table 6.1 is essentially a diode laser, which is phase-matched for

efficient nonlinear conversion. If the second order nonlinear interactions are excluded,

the device will perform as a conventional diode laser. The threshold current of this un-

phase-matched diode laser is as low as Ith = 0.252mA owing to the device small size

and high facet reflectivity. The response of the laser assuming a zero initial current is

plotted in Fig. 6.5 through solving (6.1). The behavior exhibits the well-known laser re-

laxation oscillations. These oscillations become less pronounced as the current increases.

The changes in the laser carrier density together with the relaxation oscillations induce


0

50

100

Pum

p po

wer

(m

W)

0

2

4

6

0

I/Ith

0 1 2 3 4 5

−20

0

20

40

60

time (ns)

Pum

p ch

irp (

GH

z)

(a)

(b)

Figure 6.5: a) Internal pump power, and b) frequency dynamics of the un-phase-matchedlaser for current steps of 2Ith, 4Ith, and 6Ith. The inset shows the injected current as afunction of time.

transient chirp on the order of tens of GHz. This increase in the frequency shift is often

called “positive” chirp and it usually negatively impacts the performance of dispersive

telecommunication systems, which rely on direct modulation of lasers as a source.

The response of the conventional diode laser for currents in the vicinity of those

typically needed to reach oscillation threshold in SOPOs is also studied to serve as a

reference. The SOPO discussed above has an OPO threshold current of 25.5mA which is

about two orders of magnitude larger than the pump laser threshold value. The dynamic

behavior is shown in Fig. 6.6, where only one overshoot rather than damped relaxation

oscillations are observed due to the significant level of current injection. Moreover, the

laser transient and adiabatic chirp are much larger due to the large swing in the injected

carrier density.

Power dynamics

If nonlinear conversion is taken into consideration when analyzing the example given

above, the large-signal response of a phase-matched SOPO should be calculated through

the solution of equations (6.1c) and (6.3). The pump, signal, and idler internal power

and chirp of the SOPO detailed in table 6.1 were calculated for a current step at t = 0

s rising from zero to nIOPO,th, n = 2, 3, .., 10, where IOPO,th = 25.5mA as can be seen


0

1

2

3

4

Pum

p po

wer

(W

)

0 0.2 0.4 0.6 0.8−200

0

200

400

Pum

p ch

irp (

GH

z)

Time (ns)

00

10

I/IO

PO

,th

(a)

(b)

Figure 6.6: a) Internal power, and b) frequency dynamics of the un-phase-matched laserfor currents changing from 2IOPO,th to 10IOPO,th in steps of IOPO,th. The inset shows theinjected current as a function of time.

in Fig. 6.7. This range of bias conditions leads to the SOPO operation in efficient and

inefficient regimes. By comparing the pump power dynamics in presence and lack of

of phase matching, it is clear that the pump behavior is altered at the onset of its

conversion into the signal and idler. The onset of this change is the signal/idler build-

up time at which signal and idler powers increase significantly while the pump power

is depleted. Parametric gain can be seen as a power-dependent loss mechanism for the

pump. Consequently, after the signal and idler build up, the pump laser encounters not

only the cavity and mirror losses, but also the parametric conversion losses. The behavior

of both signal and idler are merely identical.

Also Fig. 6.7 highlights the presence of relaxation oscillations in the SOPO response

akin to the un-phase-matched laser modulated near the threshold current. Comparing the

signal and idler output responses of the SOPO with the internal power of a conventional

un-phase-matched laser, unveils a notable distinction between the responses. Contrary

to the case of the conventional un-phase-matched pump laser, in the SOPO there is no

visible signal and idler relaxation oscillation in vicinity of the SOPO threshold, where

the signal and idler powers monotonically increase to their steady-state values. In this

example, relaxation oscillations take place at currents above 3IOPO,th. The oscillations


0

2

4P

ump

pow

er (

W)

0

1

2

Sig

nal p

ower

(W

)

0 0.5 1 1.50

0.5

1

Time (ns)

Idle

r po

wer

(W

)

00

10

I/IO

PO

,th

(a)

0

200

400

Pum

p ch

irp (

GH

z)

−6

−4

−2

0

Sig

nal c

hirp

(T

Hz)

0 0.5 1 1.50

2

4

6

Time (ns)

Idle

r ch

irp (

TH

z)

(b)

Figure 6.7: a) Internal power, and b) frequency dynamics of the SOPO under-study forcurrent steps of 2IOPO,th to 10IOPO,th in steps of IOPO,th. The inset shows the injectedcurrent as a function of time.

amplitude and their damping time increase as the the pumping level is raised.

The current at which the SOPO shifts from the efficient to the inefficient regime of

operation was found to be 95mA for this example as can be seen in Fig. 6.2. Hence, the

plots representing 2IOPO,th and 3IOPO,th in Fig. 6.7(a) show the operation of the device

in the efficient steady-state regime. The other plots fall into the inefficient regime. It

is evident that for this example, the relaxation oscillations appear only in the inefficient

regime. In order to investigate these fluctuations and their sources in more detail, a

transient power analysis should be performed similar to those carried out in [110].

The relaxation oscillations of the signal and idler are due to the depletion of the

pump into the signal and idler to a level below the steady state power, which leads to

an undershoot in the pump power. This leads to back-conversion of the parametrically

generated signal and idler to increase the power to a level closer to the steady state

value. This cycle may continue as a damped relaxation as can be seen in Fig. 6.7(a).

The pronounced conversion of the parametric powers in the inefficient regime can be

attributed to the intermittent change of ∆φ whereas in the efficient regime ∆φ does not

change and has a value of π/2. Relaxation oscillations have been shown to happen before

in doubly-resonant [111] and singly-resonant IOPOs [110].


Chirp dynamics

Frequency chirp dynamics of the SOPO are plotted for the same current bias conditions

described in the previous subsection in Fig. 6.7(b). To compare the phase matched laser

/ SOPO with a conventional laser, Fig. 6.7(b) should be compared to Fig. 6.6(b). In the

conventional un-phase-matched pump laser, the laser frequency shift reaches a steady-

state value in the order of GHz after the laser rise time. On the other hand, for the SOPO,

although the pump chirp properties behave in a similar fashion before the build-up time,

pump frequency encounters additional transient chirp after the build up of the signal and

idler pulses. This effect can be attributed to the depletion of the pump into the signal

and idler, which changes the pump photon density, and consequently varies the carrier

density and hence pump frequency. Moreover, additional transient chirp components

can be seen for the pump for currents above 3IOPO,th due to the presence of relaxation

oscillations. Relaxation oscillations alter the level of pump power as well as the carrier

density leading to oscillations in the pump output wavelength.

The transient and adiabatic pump chirp characteristics get transferred to the signal

and idler chirp, which reach THz levels for the signal and idler, compared to the GHz level

in the pump. One of the most important features in Fig. 6.7(b) is the negative frequency

chirp in the signal as opposed to the positive chirp which is obtained in a conventional

laser. The signal frequency chirp is opposite to that of the pump and idler in its sign.

Such a negative chirp can be explained through the tuning curve which translates how

the pump frequency shift influences that of the signal due to the presence of ∆ωσ terms in

the model. This negative chirp could be of great benefit in chirp engineering applications

in some optical communication systems.

Build-up and rise times

The signal and idler build-up times were calculated for various currents both numerically

and analytically from (6.11) assuming r = 107 - taken after the work in [116]. Fig. 6.8(a)


0

200

400

600

800

1000

1200

Bui

ld−

up ti

me

(ps)

Signal−calculatedSignal−analyticalIdler−calculatedIdler−analytical

0 100 200 300 400 5000

100

200

300


Ris

e−tim

e (p

s)

SignalIdler

(b)

(a)

Figure 6.8: Dependence of signal and idler power a) build-up times and b) 10%-90% risetimes on injected current simulated for the example SOPO. The initial current is 0 mA.

shows the analytically calculated results from (6.11) (dotted line and triangles) and the

build-up time obtained from the numerical solutions (solid line and circles). The figure

demonstrates a good agreement between the analytical results and those calculated from

the simulations. The signal and idler 10%-90% power rise times were calculated from

the simulation data. The results are plotted in Fig. 6.8(b) showing rise times of tens of

picoseconds. Similar to the build-up time, rise time is inversely dependent on the value

of the injected current step. Moreover, it can be seen that the signal and idler rise times

are nearly equal. This can be explained by the Manley-Rowe relations and the similarity

of the signal and idler power ratio in a lossless OPO [117].

6.3.3 Dynamic behavior for device biased above OPO threshold

In order to achieve faster response time and lower transient chirp, it is common to set

the initial current of diode lasers to a bias point above threshold. The interested reader

is encouraged to refer to [113] for full details on the dynamics when the bias is non-zero.

Here, we will outline the effect of non-zero initial bias point on the SOPO rise and build-

up times by setting the initial bias current to values above the OPO threshold. The

dynamics of the reference structure described earlier were examined when the initial bias


20

40

60

80

Bui

ld−

up ti

me

(ps)

Signal−1.1IOPOthIdler−1.1IOPOthSignal−2IOPOthIdler−2IOPOth

0 100 200 300 400 5000

100

200

300


Ris

e−tim

e (p

s)

Signal−1.1IOPOthIdler−1.1IOPOthSignal−2IOPOthIdler−2IOPOth

(a)

(b)

Figure 6.9: Dependence of signal and idler power a) build-up times and b) 10%-90%rise times on injected current simulated for the example SOPO. Solid and dashed curvesshow the response to initial currents of 1.1IOPO,th and 2IOPO,th, respectively.

is set to 1.1IOPO,th and 2IOPO,th in two separate cases.

In the case of non-zero initial conditions, the no-pump-depletion assumption is not

valid and consequently equation (6.11) does not hold anymore. However, the build-up

time can still be calculated numerically as plotted in Fig. 6.3.3(a). The figure depicts

a significant decrease in the build-up time in this example compared to the zero initial

current case. This was expected as the signal and idler have already built-up in the

cavity. Furthermore, the figure shows that the build-up time is inversely related to the

initial bias current value.

The corresponding 10%-90% rise times are also plotted and compared to those plotted

in Fig. 6.3.3(b) for both 1.1IOPO,th and 2IOPO,th currents. The figure illustrates that the

rise time is reduced modestly with increasing the initial current due to the reduced time

needed for the signal and idler to get to their steady-state values when starting from a

non-zero power. The rise time converges to nearly 30ps in all three examples studied

at sufficiently high current steps. It can be concluded that while the main advantage of

biasing the device above OPO threshold is to decrease the build-up time to realistic values

and tuning the build-up time, tuning the initial current at for values above threshold will

only modestly affect the rise time depending on the region of operation. The SOPO rise


time can be tuned through other parameters such as the current step side.

6.4 Discussion

The SOPO dynamic behavior was predicted in this work through a self-consistent analysis

of the diode laser pump rate equations in conjunction with the OPO rate equations. It was

evident from the analysis that the build-up time is the limiting factor in the response time

of these devices. The build-up time is largely determined by the values of the nonlinear

gain and the propagation losses in the cavity, and will likely continue to be the limiting

factors even after improving these parameters significantly. In order to circumvent the

build-up time limitations, the DC bias for these devices can be set to a value above the

SOPO threshold akin to the strategies employed for directly modulating semiconductor

lasers.

In the structure used here to study the various current injection examples, the device

suffers from lower conversion efficiency and larger chirp components in the output fre-

quency when it is operated in the inefficient regime, compared to the efficient regime of

operation. However, the former regime of operation provides superior rise and build-up

times. As such, operation of the SOPO at very large currents which essentially lead to

operation in the inefficient regime provides enhanced dynamics as a modulated source.

Given the nature of the gain in SOPOs they will likely require significantly higher powers

for their bias in comparison to conventional un-phase-matched laser counterparts in order

to obtain reasonable transient response times. However given the SOPO tunability and

diverse wavelength coverage there may exist regions of operation where they may cater

to unmet needs for certain applications. The performance of this class of devices when

directly driven for ASK modulation is remarkable as the slope efficiency varies widely de-

pending on whether the SOPO is biased in the efficient or inefficient regimes. For a given

extinction ratio in the output, bias conditions can be devised to require minimum current


modulation swing. Moreover for higher modulation current steps, significant transient

and adiabatic chirp values are obtained. This excessive chirp in the signal and idler can

be utilized in a beneficial fashion. A bandpass filter with a suitable narrow bandwidth

can be used to engineer the output extinction ratio.

Moreover, sign of the frequency chirp obtained in the signal is of great interest for

dispersion limited optical communication links. The chirp properties of the pump laser

are translated to the signal while inverting their sign, and hence lead to negative chirp in

the signal frequency. This property can be utilized for use in pre-chirping the signal to

act as a source for extended link lengths in optical links at 1550nm in a fashion similar

to [115,118].

In this study of the dynamic behavior, we mainly focused on directly modulated lasers.

However, nearly all the proposed concepts and analysis can be generalized to SOPOs

working in the pulsed regime. For example, SOPOs can be operated in laser Q-switched

or mode-locked regime. In such a case, the phase-matched diode laser will be mode-

locked, and presumably if the pump power reaches OPO threshold, the phase-matched

diode laser will become an SOPO. However, in such a system, signal/idler build-up time

should also be taken into account. Such parameters can be calculated through numerical

solution of the SOPO model presented above, or the proposed analytical formulation.

This analysis will provide insight into practical devices which provide the required watt-

level powers and efficient parametric generation. Referring to Fig. 6.8, mode-locked

SOPOs with pump pulse temporal widths smaller than a few hundred picoseconds may

have trouble achieving parametric generation. As such, either the pump initial condition

should be modified as discussed in section 6.3.3, or longer pulses should be employed for

successful implementation of SOPO.


6.5 Summary

By merging the analysis tools available for diode lasers and OPOs, a set of novel nonlin-

ear differential equations were developed which relate the carrier density with the pump,

signal, and idler temporal characteristics in an electrically injected intracavity semicon-

ductor OPO. The model was used to elucidate the characteristics of SOPO two stable

regions of operation: the efficient and inefficient regimes. The efficient regime leads to

lower transient chirp and more efficient generation of signal and idler, compared to the

inefficient regime of steady-state operation. However, the inefficient regime takes place

at higher injection levels which offer higher output powers and faster rise times.

The effect of initial conditions of the SOPO on its dynamic properties were studied

to investigate applications of such devices for direct modulation. This study highlights

the ability to tune the build-up time through the initial conditions through closed-form

analytical and numerical solution to the proposed model. Given the nature of parametric

gain in SOPOs, their direct-modulated operation requires significantly higher powers in

comparison to conventional un-phase-matched laser diodes. However given the SOPO

tunability and diverse wavelength coverage there exist regions of operation where they

could cater to unmet needs for certain applications. For example, such devices can be

used in sensing, widely tunable light generation, and possibly some telecommunications

applications. Some of these areas of interest such as signal negative chirp dynamics were

discussed and possible applications in optical communication systems were proposed.

Chapter 7

Conclusions

In this dissertation we showed design, fabrication, and characterization of Bragg reflec-

tion waveguide lasers as active devices for nonlinear conversion. To fabricate high quality

diode lasers with our resolution and flexibility requirements, we developed a full micro-

fabrication process using electron beam lithography. In addition to the the sub-micron

resolution of ebeam lithography which allows for realization of structures with small

features such as DFBs, the lack of need for a metal mask allows for design flexibility

and versatility. Some of the previously available processes such as plasma etch and de-

oxidization had to be modified for better correlation with the developed ebeam processes.

Along with working on the three-step lithography process, a metal deposition recipe was

also developed for n-type and p-type metal contact to avoid dealing with third-party fa-

cilities. The developed processes allow for full fabrication of semiconductor diode lasers

in the TNFC cleanroom eliminating the need for shipping the samples out for some of

the steps, and ultimately leads to faster and higher quality fabrication process.

Following the theoretical design guidelines provided in the dissertation, initially a

single-sided Bragg laser wafer was designed for lasing emission around 980nm, and effi-

cient phase-matched DFG in the C-band and mid-IR wavelength regimes. A mixture of

fabrication recipes developed both in this thesis and previously were utilized to prepare

154

Chapter 7. Conclusions 155

the samples. It was shown through a combination of experiments and simulations that

the single-sided design does not lend itself to lasing in the Bragg mode due to the com-

plications of modal discrimination in the asymmetric structure. To provide insight into

this problem, dependence of 2D modal confinement on the etch depth was investigated

in quarter-wave ridge Bragg waveguides. We used a semi-analytical method, namely

effective mode theory, to provide better insight into the physics of such characteristics.

This showed that Bragg mode confinement is lost at certain points due to loss of index

contrast in the ridge and slab regions. We showed that the same effect holds for any

other generic Bragg structure and the confinement properties were confirmed experimen-

tally through measurement of modal loss of a ridge Bragg laser at different etch depths.

It is clear that this novel study is essential for designing functional ridge waveguides

with suitable confinement properties. A similar investigation revealed that this peculiar

non-monotonous etch depth dependance of Bragg modal loss plays a major role in the

sub-optimal mode discrimination in the single-sided Bragg laser design. The large Bragg

mode loss together with the moderate confinement factor values for a higher-order TIR

mode have lead to the observed mode discrimination problems. The insight provided

through this investigation was used to correct the Bragg laser design procedure for the

future Bragg laser designs.

Based on the above-mentioned information another Bragg laser wafer, this time a sym-

metric double-sided Bragg laser, was designed and fabricated for lasing around 775nm

and phase-matching near degeneracy in the C-band. Near field measurements of the

fabricated devices demonstrated lasing in the Bragg mode which shows the efficiency

of the corrections taken in the design procedure. We reported observation of nonlinear

conversion mechanisms such as externally injected pulsed second harmonic generation

and externally injected CW difference frequency generation in Fabry-Perot double-sided

Bragg lasers. An internal DFG conversion efficiency of 1.84%/W/cm2 with a pump accep-

tance bandwidth of 0.74nm was reported. The measured nonlinear characteristics were


compared with similar devices previously reported in the literature, and improvements

in the design were highlighted. Moreover, device spectroscopy, including the dependance

of phase-matching wavelength, λPM on temperature and injected current was investi-

gated. A rate of ∆λPM/∆T of 0.1nm/C and ∆λPM/∆I of 0.073nm/mA were measured

for temperature and current dependance. The measured dependency of phase-matching

wavelength on the operating conditions will be essential in realizing self-pumped DFG

in the next generation of devices. It was shown that milliwatt-level power levels are

attainable through self-pumped DFG with some modifications to the current structure.

Such powers provide a good solution for current and emerging applications in on-chip

sensing and spectroscopy.

Gratings and ring cavities are essential components for monolithic integration with

other devices. Aside from investigation of nonlinear conversion, implementation of dif-

ferent devices such as DFB and ring lasers was studied using the developed fabrication

process on the single-sided Bragg laser platform. DFB lasers were designed using coupled

mode theory and laterally corrugated surface gratings were fabricated on the single-sided

Bragg laser platform with the developed processes. Ring lasers with large ring radii were

also designed using a commercial mode solver, and fabricated on the same wafer with

ebeam lithography. Test results of both sets of devices showed unwanted effects which

were ascribed mainly to the sub-optimal mode selectivity characteristics of the single-

sided Bragg laser wafer. Nevertheless, the preliminary characterization results provide

valuable information for future implementation of ring and DFB lasers on a Bragg laser

wafer which favor lasing in the Bragg mode. For example, uni-directional lasing charac-

teristics of single-sided Bragg laser ring lasers was studied and documented.

This dissertation explored some further challenges for the design of efficient devices

for phase-matching second-order nonlinearities. With the presented implementation of

DFG and the clear path to self-pumped DFG, realization of integrated intracavity self-

pumped semiconductor OPOs is only steps away. To provide insight into design and


dynamic characteristics of SOPOs, a theoretical model was developed. The proposed

model combines the well-known laser rate equations with nonlinear effects for the first

time in an integrated SOPO. Static and dynamic operation of the SOPO in the different

stability regions was studied using the developed model. It was shown that even though

the efficient regime of operation allows for optimal nonlinear conversion, the inefficient

regime of operation provides lower rise times. Further, the notable chirp dynamics of

SOPOs including the negative chirp exhibited by the signal were discussed and a possible

application in optical communication systems was proposed. Even though this study

of dynamics was focused on directly modulated SOPOs, the time-domain model and

discussions can be used for devices operated in other pulsed conditions such as mode-

locked SOPOs.

In addition to the SOPO properties, Bragg waveguide far-field characteristics is also

important in the design process, specifically for in- and out-coupling from Bragg lasers.

The far-field properties were studied in this work through a Gaussian approximation of

the fundamental Bragg mode near-field profile. Based on the near-field approximation,

an analytical formula for far-field diffraction pattern of the Bragg mode was calculated

and design guidelines for single-lobed far-field operation were provided. The proposed

methodology and study provides insight into different far-field regions of operation of

Bragg waveguides, and allows for design optimization for optimal coupling from Bragg

lasers.

7.1 Summary of contributions

Below is a short summary of the major accomplishments in this dissertation. The future

roadmap of this research topic is discussed as another section for utilizing the discussed

results to expand and improve the goals of this thesis and beyond.

• Bragg waveguide modal confinement: Dependence of 2D confinement properties of


ridge Bragg waveguides on the etch depth was investigated systematically. This

novel study is extremely beneficial to designing 2D ridge waveguides with suitable

confinement properties.

• Bragg waveguide far-field behavior: The far-field regions of operation of Bragg

waveguides was systematically investigated. A Gaussian approximation of the

Bragg mode profile was proposed for analytical extraction of the far-field diffraction

pattern. This study provides the insight for optimal coupling to other integrated

systems.

• Ebeam lithography and contact deposition process development: The full fabrica-

tion process of semiconductor diode lasers using ebeam lithography in the TNFC

cleanroom was developed. No such processes were available prior to this research.

• Wafer design for mid-IR generation: A single-sided Bragg laser wafer was designed,

fabricated, and tested for mid-IR generation. The mode selection mechanism in the

wafer was experimentally shown to be sub-optimal. The underlying physics was

investigated and was corrected for the next wafer design.

• Wafer design for near-degeneracy DFG: A double-sided wafer was designed and

fabricated for idler generation near the C-band. A DFG conversion efficiency of

1.84%/W/cm2 was reported. Moreover, tuning the phase-matching wavelength

with temperature and current injection was investigated for prediction of self-

pumped DFG characteristics. The measurements provide the background infor-

mation for future implementation of self-pumped DFG in a new wafer design.

• DFB and ring laser investigation: Realization of different devices such as DFB and

ring lasers was investigated on the single-sided Bragg laser platform for integra-

tion purposes. Uni-directional emission characteristics of ring lasers were explored.

Nevertheless, it was shown that poor mode selectivity in the wafer limited the


effectiveness of both ring and DFB lasers.

• Time-dependent SOPO model: A theoretical model for investigation of SOPOs akin

to the laser rate equations was developed. Using the model, static and dynamic

operation of the SOPO in the different stability regions was studied and a possible

application in optical communication systems was proposed. This study provides

the required insight for design optimization of SOPOs especially when operated in

pulsed condition.

7.2 Future directions

There are multiple improvements along this work towards viable widely tunable non-

linear sources of light. Even though the diode lasers tested in this work showed clear

improvements over the previous devices fabricated in the group, there is still more room

to improve their performance. The output power of the lasers under test did not exceed

more than tens of milliwatts in the CW regime. Compared to the commercially avail-

able lasers with similar quantum wells, there is room for at least an order of magnitude

increase in the power. This can be achieved through improvement of etch and contact

quality, accurate design of the etch depth for maximal lateral confinement, improvement

of growth quality, and introduction of tapered ridge structures. Also, p-side bonding of

the fabricated lasers can reduce thermal effects in the laser cavity.

We reported on fabrication of ring and DFB lasers on the single-sided Bragg laser

wafer in chapter 4. However, there were major difficulties in Bragg mode selection in

those devices due to the unwanted modal properties of the wafer. These include relatively

large confinement factor of higher-order TIR modes and complex etch depth dependence

of the Bragg mode. The double-sided wafer design presented in chapter 5 shows far more

improved modal discrimination characteristics, allowing for single vertical mode operation

of lasers in the Bragg mode. As such, ring and DFB lasers can be much more easily


realized on this platform and need to be further investigated. Moreover, as suggested

in section 4.3, laterally coupled gratings can alleviate the etch imperfection obstacle

observed in sidewall corrugated gratings. The shallow etch depth of the gratings in the

former setting can allow better control over the etch and consequently coupling coefficient

of the grating. Further, DBR lasers provide much larger tunability ranges compared to

DFB lasers. The fabrication process, however, requires a two-step etch which will lead

to complications in the alignment and plasma etching. Process development for such

a two-step etch can be very important step in implementing grating based diode lasers.

Further, the next step to successful realization of DFB lasers will be demonstrating widely

tunable DBR lasers with three sections on the current platform.

Aside from the device implementation, a focus of this thesis was nonlinear conversion

in the active Bragg laser platform. In this work, we showed DFG results in an active Bragg

laser structure and investigated the thermal and current injection effects. However, due

to the large deviation of the phase-matching degeneracy wavelength from the originally

designed location, self-pumped DFG was left unexamined. We are still investigating the

integration of surface gratings with the current lasers to shift the lasing wavelength close

to the position of degenerate phase-matching wavelength. Moreover, a new wafer design

is prepared with corrections to the model to provide near degeneracy DFG close to the

lasing wavelength. The wafer design will be submitted for wafer growth and will need

to be processed and tested for its self-pumped DFG results. Mid-IR generation through

self-pumped DFG and parametric generation provides great flexibility and tuning range

to the 2-3µm mid-IR regime. Self-pumped DFG for mid-IR generation should also be

investigated through another wafer design. After providing self-pumped DFG, optical

parametric generation should be investigated as well by a combination of mode-locking

the lasers for higher peak powers, and high-reflection facet coatings.

Finally, in the quantum optics domain, Bragg waveguides have been subject of intense

study as sources of correlated photon-pairs. Recently, correlated photon pair generation


was realized in Bragg lasers [40]. However, the work did not present any data on the

spectral properties of the photons. The devices which will be processed for near degen-

eracy self-pumped DFG can as well be used for self-pumped parametric down-conversion

to generate entangled photon pairs. Realization of widely tunable laser sources through

distributed Bragg gratings can provide an excellent source of photon pairs, wavelength

of which can be easily tuned to the right phase matching wavelength.

Appendix A

Epitaxial design of the grown wafers

A.1 Wafer 1: single sided Bragg laser

A.2 Wafer 2: double sided Bragg laser

162

Appendix A. Epitaxial design of the grown wafers 163

Table A.1: Detailed epitaxial structure of the single-sided design.

Layer Material ThicknessDopinglevel

Dopant Dopant

No (Al composition) (nm) (cm−3) Species Type

23 GaAs (cap layer) 50 > 1018 C p+Grading 27 1018 C p

22 0.75% AlGaAs 1500 1018 C pGrading 27 1018 C p

21 GaAs 316 5× 1017 C pGrading 27 5× 1017 C p

20 24% AlGaAs 125 1017 C p19 24% AlGaAs 100 - - undoped18 GaAs 6 - - undoped17 InGaAs 10 - - undoped16 GaAs 6 - - undoped15 InGaAs 10 - - undoped14 GaAs 6 - - undoped13 24% AlGaAs 100 - - undoped12 24% AlGaAs 183.6 1.2× 1017 Si n

Grading 27 1.2× 1017 Si n11 GaAs 514 1.2× 1017 Si n

Grading 27 5× 1017 Si n10 35% AlGaAs 912.4 5× 1017 Si n


Grading 27 1.2× 1018 Si n8 35% AlGaAs 912.4 1.2× 1018 Si n


Grading 27 1.2× 1018 Si n6 35% AlGaAs 912.4 1.2× 1018 Si n

Grading 27 1.2× 1018 Si n

5 GaAs 170 1.2× 1018 Si nGrading 27 1.2× 1018 Si n

4 35% AlGaAs 912.4 1.2× 1018 Si nGrading 27 1.2× 1018 Si n

3 GaAs 170 1.2× 1018 Si nGrading 27 1.2× 1018 Si n

2 35% AlGaAs 912.4 1.2× 1018 Si n1 35% AlGaAs 1500 2× 1018 Si n+

02-off GaAs(substrate)

- - Si n+


Table A.2: Detailed epitaxial structure of the double-sided design.

Layer Material ThicknessDopinglevel

Dopant Dopant

No (Al composition) (nm) (cm-3) species type

32 GaAs 100 > 1019 C p+Grading 25 > 1019 C p

31 25% AlGaAs 105 3× 1018 C pGrading 25 3× 1018 C p









22 70% AlGaAs 188 5× 1017 C p21 70% AlGaAs 40 - undoped20 28% AlGaAs barrier 10 - undoped19 InAlGaAs QW - - undoped18 28% AlGaAs barrier 10 - undoped17 InAlGaAs QW - - undoped16 28% AlGaAs barrier 10 - undoped15 70% AlGaAs 40 - undoped14 70% AlGaAs 188 5× 1017 Si n

Grading 25 5× 1017 Si n13 20% AlGaAs 370 5× 1017 Si n

Grading 25 2× 1018 Si n12 70% AlGaAs 400 2× 1018 Si n

Grading 25 2× 1018 Si n


11 25% AlGaAs 105 2× 1018 Si nGrading 25 2× 1018 Si n








3 25% AlGaAs 105 2× 1018 Si n2 Grading 25 2× 1018 Si n1 GaAs 200 2× 1018 Si n+

02-off GaAs(substrate)

Si n+

Appendix B

Detailed step-by-step fabrication

process

Stage 1: Fabricating the ridge waveguides

1. Cleave the required number of 1x1 cm samples using a diamond scribe and ruler.

2. Clean the samples using the nitrogen gun to remove any dust created during the

cutting. Remove the Aluminum Oxide from the surface using 30s of HCl and DI

water. Further clean the sample with acetone and iso-propanol (IPA), ultrasonic

bath in IPA then dry using the nitrogen gun. IPA should be the final solvent used

as it leaves no residue and quickly evaporates.

3. Bake each piece at 160C for 5 minutes.

4. Spin HMDS primer on a sample at 3000RPM for 60 seconds. Set ACL to 589.

5. Spin Fox15:MIBK (1:1) ebeam resist on the sample at 3000RPM for 60 seconds.

Set ACL to 589. Inspect for defects, bubble streaks or other inconsistencies.

6. Soft-bake the sample at 160C for 2 minutes. Let sample return to room tempera-

ture for 1 minute.

166

Appendix B. Detailed step-by-step fabrication process 167

7. Load the sample on the holder and measure the sample center position with regards

to the Faraday cup on the holder. If a height adjustable holder is being used, the

sample surface should also be adjusted to have maximum ±30µm height.

8. Fracture GDSII pattern file into GPF file format: layer 4, 17, 12: res 0.025; layer

16: res 0.005

9. Expose the resist using the following parameters: 100kV HT voltage for all; layer

4, 25nA beam current, 750µC/cm2 dose; layer 16, 5nA beam current, 700µC/cm2

dose; layer 17, 25nA beam current, 650µC/cm2 dose; layer 12, 25nA beam current,

600µC/cm2 dose.

10. Develop in CD-26 for 6 minutes. Quench the sample into de-ionized (DI) water.

11. Inspect the pattern under the microscope. If the sample is under-developed, dip in

developer again for 1-2 minutes.

12. Hard bake the samples at 180C for 5 minutes.

13. Prepare Trion Mini-lock etcher for AlGaAs etching. Open chlorine (Cl2) gas cylin-

der in the service corridor behind the etcher. Turn on both RF power supplies.

Reduce the chiller temperature to 5C.

14. Place the 8” clear quartz carrier into the chamber. Run both the hydrogen clean

and oxygen clean recipes for 15 and 10 minutes respectively (titled H2-O2 clean).

Both recipes require manual tuning. Keep an eye on the reflected power routinely.

15. Remove quartz carrier and insert the 8” black graphite carrier with 3” quartz plate

into the chamber. Be sure to clean it with IPA before hand. Run the oxygen clean

recipe for 5 minutes.

16. Prepare the chamber by running the etch recipe for 45 seconds. Settings are 200

W ICP power, 50W RIE power, 5mTorr pressure, 8sccm BCl3 flow rate, 4.5sccm


Cl2 flow rate, 5sccm Ar flow rate.

17. Pre-bake one sample for 5 minutes at 100C to remove any surface moisture.

18. Remove the carrier with quartz plate. Attach the sample onto the quartz using

Santovac 5 vacuum grease. Clean the sample of any dust using the nitrogen gun.

19. Place the quartz back onto the graphite carrier and return them both to the cham-

ber. Leave the chamber under vacuum for 5 minutes. This is not just to reduce

the base pressure but to also give the chamber a chance to cool down.

20. Run the etch recipe in a pulsed mode of 30-40 second etching bursts and leave 150-

180 seconds for between successive bursts. This is because the sample can become

quite hot with this recipe.

21. Remove the sample and inspect for damage, micromasking and other features under

the microscope.

22. Clean the chamber as before and repeat for all samples.

23. Follow shut-down procedure for Mini-lock etcher. Close chlorine cylinder in back

service room.

24. Place the samples in BOE (Buffered Oxide Etchant) for 20 seconds to remove the

HSQ resist. Dip in DI water right away, and clean with acetone and IPA. Beware

of the dangers of HF/BOE and the procedure for safely working with such acids.

Stage 2: Electrical Isolation of ridges and patterning oxide opening

1. Prepare the Oxford Plasmalab 100 for deposition. This includes turning on the

instrument, cleaning the chamber and setting the table temperature to 400C.

2. Insert all samples into the Oxford Plasmalab loadlock chamber on a silicon wafer.

Place shards of silicon around the samples to eliminate edge effects. Deposit silica

(SiO2) for 6 minutes at 400C. Inspect the result to ensure no defects.


3. Use the clean recipe in the Oxford Plasmalab 100 and follow the shut-down proce-

dure.

4. Spin HMDS primer on a sample at 3000RPM for 60 seconds. Set ACL to 589.

5. Spin Fox15 ebeam resist on the sample at 1500RPM for 60 seconds. Set ACL to

589. Inspect for cracks, defects, bubble streaks or other inconsistencies.

6. Soft-bake the sample at 90C for 5 minutes. Let sample return to room temperature

for 1 minute.

7. Heat up the sample at 390C for5 minutes in the rapid thermal annealer using the

nima 390C recipe. This includes two ramp up periods of 150s and 300s, a 5 minute

heating at 390C, and a 180s cool down period.

8. Prebake the sample at 180C for 3 minutes to remove any surface moisture.

9. Spin two layers of ZEP-520A ebeam resist on the sample at 1500RPM for 60 sec-

onds. Set ACL to 589. Bake the sample at 180C for 3 minutes after each spinning.

Inspect for defects, bubble streaks or other inconsistencies.

10. Fracture GDSII pattern file into GPF file format: layer 2: res 0.01.

11. Expose the resist using the following parameters: 100kV HT voltage , layer 10,

5nA beam current, 380µC/cm2 dose. You will need to measured the position of the

alignment marks beforehand to do the exposure.

12. Develop the samples in ZED-N50 developer for 70 seconds. Immediately dip the

sample into an MIBK:IPA (9:1) solution for 30 seconds and blow dry with nitrogen

gun.

13. Inspect the opening under the microscope. If the opening is under-developed or

closes at points along the ridge, dip in developer again for 5 seconds. If the vias are


misaligned the sample has to be dipped in ZDMAC to remove the ZEP and redo

the whole via alignment process.

14. Prepare the Trion Phantom etcher by physically cleaning the chamber with IPA.

Nitrogen blow gun fry the chamber and run the oxygen clean recipe (titled CLEAN)

for 5 minutes.

15. Run the silica etch recipe without the sample to prepare the chamber. Settings

are: 400W ICP power, 70W RIE power, 15mTorr pressure, 50sccm CHF3 flow

rate, 8sccm He flow rate, and 120 second time (titled Bhavin sio2 v2). Recipe

parameters can be changed in the manual mode, if required.

16. Vent chamber and affix all samples to the black anodized aluminum carrier using

Santovac 5 vacuum grease. Clean samples on carrier lightly using nitrogen gun.

17. Place carrier back into chamber and close lid. Evacuate the chamber to vacuum

using the manual controls for at least 5 minutes. Run silica etch recipe as mentioned

above.

18. Vent chamber and remove samples. Gently clean back of samples to remove San-

tovac 5 on cleanroom cloth that has IPA on it.

19. Clean chamber using oxygen clean recipe.

20. Do not use buffered oxide etchant (BOE) on the samples if the Al concentration of

some of the layers is above 60%.

21. Inspect sample under the microscope for any new damage or defects.

22. Heat ZDMAC resist stripper in a petri dish to 80C. Place the samples in the

stripper for >1 hour. Ultrasonic the samples with the stripper for 30 seconds in

ultrasonic. Clean with acetone and IPA.


23. Inspect the sample surface for any remaining resist. Sometimes the sample has to

be left in the stripper overnight to completely remove the resist. If the resist was

still persisting, a 40 second oxygen ashing step can be performed using the clean

recipe in the Phantom etcher.

Stage 3: Contacts deposition, thinning and cleaving

1. Prebake the sample at 180C for 3 minutes to remove any surface moisture.

2. Spin two layers of ZEP-520A ebeam resist on the sample at 1500RPM for 60 sec-

onds. Set ACL to 589. Bake the sample at 180C for 3 minutes after each spinning.

Inspect for defects, bubble streaks or other inconsistencies.

3. Fracture GDSII pattern file into GPF file format: layer 10: res 0.01; layer 7: res

0.1

4. Expose the resist using the following parameters: 100kV HT voltage for all; layer

10, 100nA beam current, 360µC/cm2 dose; layer 7, 25nA beam current, 180µC/cm2

dose.

5. Develop the samples in ZED-N50 developer for 60 seconds. Immediately dip the

sample into an MIBK:IPA (9:1) solution for 30 seconds and blow dry with nitrogen

gun.

6. Inspect the exposed areas under the microscope. If the metal contact patterns are

under-developed, dip in developer again for 5 seconds.

7. Deposit the top p-type contact in the ebeam evaporator. The contact composition

is 8nm of Ti and 220nm of Au. Be careful not to increase the current much higher

than that necessary for melting the source. A rate of 0.1-0.6nm/s is usually suitable.

8. Place samples with top contact into petri dish with ZDMAC resist remover heated

to 60C. Let sit for >1 hour. Place in ultra-sonic bath till photo-resist peels off


completely. Do not put in ultrasonic bath for greater than 20 seconds as the

ridges could be damaged. Remove left-over resist with swab.

9. Inspect the metal surface under the microscope without removing the sample from

the resist remover. If some of the metal is not lifted off, removing the sample from

the resist remover may lead to the metal sticking to the sample surface and make

it harder to remove. Redo the above step until the excess metal is completely

removed.

10. Prepare lapping machine for sample thinning. Clean surface pad and ensure there

is 30µm and 5µm alumina powder for thinning. Wear two or three layers of nitrile

gloves for protection as well as a face mask.

11. Heat sample holder to 110C and melt mounting wax onto it. Affix samples to

holder and turn off hotplate.

12. Periodically flatten samples to holder with tweezers as mounting wax cools. This

will ensure flatness. Wait 5 minutes.

13. Set lapping fixture to a setting of 0.16 inches and attach sample holder to fixture

with screw. Install a new silicon carbide 12000 grit paper on the lapping machine.

14. Place some 30µm alumina powder and water onto the lapping surface, mix till it is

a paste. Begin rotation and set voltage to 15V.

15. Carefully bring fixture to contact with rotating surface. Slowly move the fixture

allowing for various angles of thinning and to utilize all the alumina paste. Measure

the thickness of the sample with the thickness monitor.

16. Set lapping fixture to a setting of 0.14 inches. Place some 5µm alumina powder

and water onto the lapping surface, mix till it is a paste. Begin rotation and set

voltage to 20-25V.


17. Repeat thinning procedure for another 10 minutes or till sample has reached thick-

ness setting.

18. Clean lapping surface and fixture with water to remove used alumina. Remove

sample holder from fixture and place on hotplate. Set hotplate to a setting of

110C to melt mounting wax.

19. Carefully remove thinning samples. Note their thickness and ease of damage.

20. Clean area and lapping machine. Follow shut-down procedure.

21. Place samples into a petri dish with acetone for 10 minutes. Gently agitate the

dish to allow all the mounting wax to dissolve away. Clean with IPA.

22. Deposit the bottom n-type contact using ebeam evaporator. The contact compo-

sition is 45nm of Au, 25nm of Ge, 35nm of Ni, and 120nm of Au. Be careful not

to increase the current much higher than that necessary for melting the source. A

rate of 0.1-0.6nm/s is usually suitable.

23. Heat up the sample at 390C for 1 minute in the rapid thermal annealer using the

nima 390C short recipe. This includes two ramp up periods of 180s and 180s, a 1

minute heating at 390C, and a 180s cool down period.

24. Cleave the samples by utilizing a two layer plastic sheet. One side should have a

mild adhesive to hold the sample. With the sample on the adhesive, carefully mark

it with a diamond scribe at the lengths you wish to cleave.

25. Place the second layer on top of the first, effectively confining the sample.

26. Place the sample onto a glass slide. Using a microscope, carefully push the sample

over the edge of the glass slide. This should cleave at the scribe marked lengths.

27. Carefully remove the cleaved devices. Inspect the facets and measure the device

lengths under a high-magnification microscope.


28. Place cleaved devices in a suitable package for transportation such as a gel pack.

Appendix C

Other developed ebeam processes

This appendix summarizes the ebeam processes which were developed to pattern the

mesa structures on AlGaAs semiconductor diode lasers but were discarded later in favor

of the finalized recipe presented in chapter 3.

Based on the ebeam resists available in the ECTI cleanroom, we had to propose

a few different processes before we decided on the most versatile and least expensive

process for defining the features etched in the AlGaAs wafer. The ebeam resists which

were examined for defining the features etched in the AlGaAs wafer included ma-N 2410,

ZEP-510A, and Hydrogen silsesquioxane (HSQ). While negative tone resists are more

suited for patterning small form factor features such as waveguides, positive resists can

be better used in patterning trenches. In this section, we will present a short description

of the developed recipes for the two first resist and its advantages and disadvantages.

C.1 ma-N 2410 resist recipe: mesa structures

Microresist Technology’s ma-N 2410 is a negative tone electron-beam resist which we

initially chose to define the waveguides due to lack of other suitable negative tone resists

in the ECTI cleanroom. Generally speaking, negative tone resists are better suited for

patterning waveguides because a small area has to be exposed, and eventually time/cost

175

Appendix C. Other developed ebeam processes 176

Table C.1: Detailed ma-N 2410 recipe for defining mesa structures.Spin coat Soft Beam Exposure Fracture Development Rinse Hardspeed bake current dose resolution time time bake

3000RPM 90oC 500pA 30µC/cm2 10nm 180s in 30s in 100oC584accl (150s) ma-D 525 DI water (300s)

of the process will be minimized through use of such resists.

ma-N 2410 can be spin coated in layers as thick as 1µm at a spin speed of 3000RPM.

While such a thick layer of resist can lead to good masking for deep etches, it can also

lead to lower attainable resolutions and severe proximity effects - unwanted exposure of

the areas close to the exposed area. Table C.1 shows the details of the process developed

for ma-N.

The ma-N ebeam resist series is well-resistant to CHF3 and CF4 plasma etching,

hence it is an ideal negative tone resist for etching silica and silicon. However, due to its

lower resistivity to chlorine based plasma etch, we could not use the patterned ma-N to

etch our AlGaAs samples directly in the III-V etcher; alternatively, we had to spin coat

the resist on top of 200nm of silica deposited on the GaAs sample. The patterned resist

would then be used to etch the silica to make a ”hardmask”. This etched silica hardmask

would then be resistant enough for GaAs etch depths of 2µm and more.

Fig. C.1 shows developed and etched samples using the ma-N 2410 resist. The suitable

dose was determined through a dose test, which steps the desired pattern over a range of

doses. The resulting patterns are inspected using scanning electron microscopy (SEM) to

find the optimal dose. Similar to many other ebeam resists, for a given exposure dose, the

resist development time varies depending on the pattern size and shape beside the resist

thickness. The development time for lower exposure doses was generally found to be

less dependent on the feature size in the present resist series. Fig. C.1(a) shows that the

spacing between the two waveguides in a directional coupler was fully developed after the

180s development time where Fig. C.1(b) shows the quality of the etched structures using

the current recipe and a silica hardmask. Even though the etch quality is acceptable, the


(a) (b)

Figure C.1: a) Microscope image of an evanescent coupler patterned on silica/AlGaAs,using the ma-N 2410 resist. The exposure dose was 30µc/cm2. b) An SEM micrographof an etched ridge prepared using ma-N 2410 resist. The etch time was 146s in the III-Vetcher.

sidewall roughness seen in Fig. C.1(b) is clearly more than that of the devices patterned

with HSQ (see Fig. 3.6(b)). This is ascribed to the lower plasma etch resistivity of Ma-N

compared to HSQ. Moreover, even though the resist exposure was relatively fast and

straightforward, we noticed the exposure dose needed was changing with time. This was

attributed to the approaching resist expiry date. Eventually, we had to give up on this

resist due to purchase cost issues and inconsistencies in the exposure results.

C.2 ZEP resist recipe: mesa structures

ZEP 520A, by Zeon Corp. - here referred to as ZEP - is a positive tone electron-beam

resist which was chosen to define the waveguides after ma-N 2410 failed. Similar to ma-N,

ZEP was used as a soft mask to etch a 200nm silica layer deposited on the GaAs/AlGaAs

samples. The patterned silica layer then acted as a hardmask for the III-V etch.

Being a positive resist, the exposed regions of ZEP will be washed away during devel-

opment. Consequently, the waveguides have to be defined by defining 40µm trenches on

each side of the waveguides thus defining the waveguide structure in between after the


Table C.2: Detailed mesa structure development recipe for ZEP-520A.Spin coat Soft bake Development time Rinse time Hard bake

6000RPM 100oC 60s in 30s in 100oC(584accl) (180s) ZED-N50 MIBK:IPA (9:1) (300s)

Table C.3: EBL exposure parameters for the two exposed areas in the 10µm (high reso-lution) and 10-40µm (low resolution) vicinity of the mesa structures.

Exposure area Beam current Exposure dose Fracture resolution

High resolution 5nA 120µC/cm2 10nmLow resolution 30nA 240µC/cm2 100nm

development and etch. In order to decrease the long write time stemming from the large

exposure area, only the first 10µm on each side of the waveguides were exposed with

high resolution (10nm) and the rest of the trench area was exposed at a lower resolution

(100nm). Table C.2 shows the details of the process developed for ZEP including the

various exposure conditions.

Fig. C.2 shows developed and etched samples using the ZEP-520A resist. Ideally,

due to its high resolution, ebeam lithography should lead to very smooth lithographi-

cally defined features and hence smooth etched sidewalls. However, Fig. C.2(b) shows

sidewall irregularities with an estimated peak-to-peak roughness of 80nm. Part of these

roughness can be explained through the slight over exposure of the waveguide due to

the backscattered electrons in the large exposure areas in the vicinity of the waveguide.

Another process which adds up to these etch irregularities is the additional step of silica

etch. Any irregularities which are defined in the silica hardmask will be augmented in

the AlGaAs etch profile.

Due to the low confinement of the waveguide mode in the ridge waveguide, the

trenches were designed to be 40µm on each side of the waveguides to minimize the leakage

losses. Such a large exposure area demands a long exposure time leading to expensive

ebeam lithographic processes. The process cost issues together with the issues in the

quality of the lithographically defined and etched features lead us to use Dow Corning’s


(a) (b)

Figure C.2: a) Microscope image of a 2µm wide waveguide patterned on silica/AlGaAs,using the ZEP-520A resist. The exposure dose was 120µc/cm2 for the 10µm vicinity ofthe sample and 240µc/cm2 for the rest of the exposed area. The resist remaining at theunexposed area can be seen at the top and bottom. b) An SEM micrograph of the crosssection of an etched sample prepared using ZEP-520A resist. The etch time was 110s inthe III-V etcher.

Fox15 in the future experiments.

C.3 Summary

To enable the fabrication of ring and DBR lasers, a few new processes based on ebeam

lithography had to be established. Some of these processes were finalized in a full ebeam

lithographic recipe, as presented in chapter 3. However, two other processes based on

ma-N 2410 and ZEP-520A which were developed for defining the mesa structures were

discarded in favor of the recipe developed for Fox-15. The details of these processes were

explained and their advantages and drawbacks were discussed briefly.

Appendix D

Verification of 2D mode solver

As stated within the text, a commercial 2D mode solver [65] was used to analyze the 2D

mode profile in this thesis. The software package is based on Finite Difference method

and as such, it is imperative to study the parameters chosen for the simulation, and

to confirm its convergence. We will focus on the 2D mode simulations carried out for

section 2.2.2. Nevertheless, the chosen parameters are valid for simulations carried out

for other devices such as those presented in chapters 4 and 5.

a finite difference mode simulation can be implemented using different boundary con-

ditions such as metal or perfectly matched layers. If metal boundary conditions are

chosen for simulating a ridge waveguide, light reflection from the boundaries can reduce

the simulation accuracy. This will be more severe when the the light is not well con-

fined beneath the ridge. For simulation of ridge waveguides, perfectly matched boundary

conditions can absorb the light that leaks to the boundaries and hence imitate infinite

boundaries.

The boundaries were chosen to be well-away from the ridge region, to assure the light

does not leak into the perfectly matching layers. We chose a boundary of 10× 15µm to

keep the simulation time within reach. The choice of mesh size is also very important

in carrying out finite difference simulations. Assuming a homogeneous mesh, the rule of

180

Appendix D. Verification of 2D mode solver 181

0 50 100 1503.033

3.0335

3.034

3.0345

3.035

3.0355

3.036

3.0365

Mesh size (nm)

Effe

ctiv

e in

dex

(a)

y(µm)

x(µm

)


−5 0 5

−4

−3

−2

−1

0

1

2

3

4

0

0.2

0.4

0.6

0.8

(b)

Figure D.1: a) The calculated effective index as a function of mesh size for the samplechosen here. b) Two-dimensional mode profile of the sample structure simulated with amesh size of 50nm.

thumb is to have the mesh size to be considerably smaller than the feature size of the

structure which is being tested. To pick the right mesh size, the calculated effective index

was plotted as a function of mesh size as seen in Figure D.1. It can be clearly seen that

the simulation has converged at mesh sizes smaller than 50nm. As such, this mesh size

was chosen which provides an accurate meshing while keeping the simulation time the

shortest.

Appendix E

Full derivation of the SOPO model

E.1 Formulation

The classical rate equations for quantum well (QW) lasers have been studied to per-

fection thus far [87, 112]. In this appendix, a similar derivation to that of diode lasers

will be pursued, but while including the parametric second order nonlinear effects. A

triply resonant cavity and a single longitudinal mode is assumed for all three interacting

wavelengths similar to equation (6.2) repeated below:

Eσ(x, y, z, t) =1

2Fσ(x, y)fσ(z)Eσ(t)exp[−iωσt+ iφσ(t)] + c.c. , σ ∈ p, s, i (E.1)

In this equation, the index σ = p, s, i denotes the variable for pump, signal, or idler,

Eσ(t) is the absolute value of the time envelope, fx,l, fy,l, and fz,l are the normalized

field profiles in the x, y, and z directions, and c.c. denotes complex conjugate. Similar

to Oshman et al. [108], we will assume fp(z) =√

2Lcos(βpz), fs(z) =

√

2Lsin(βsz), and

fi(z) =√

2Lsin(βiz) where kσ are the z-components of the corresponding wave vectors

at the laser threshold.

182

Appendix E. Full derivation of the SOPO model 183

The nonlinear Helmholtz equation reads as the following

∇2 ~E(x, y, z, t)− ǫ(x, y, z, t)

c2∂2 ~E

∂t2= µ0

∂2 ~PNL

∂t2(E.2)

where the scalar nonlinear polarization can be expanded as

PNLp,s,i(x, y, z, t) =

1

2Kǫ0χ

(2)eff (x, y)Fs,i,pfs,i,pFi,p,sfi,p,sEs,i,p(t)Ei,p,s(t)

× exp[−iωp,s,it+ i(+,−,+)φs,i,p(t) + i(+,−,−)φi,p,s(t)] + c.c. (E.3)

K = 1/2 for degenerate and K = 1 for non-degenerate. By substituting equation (6.2)

into (E.2), assuming slowly varying envelope, multiplication by Fσ and fσ, and integrating

over x, y, and z, the following set of equations can be derived

2iωp

c2(ǫp +

ωp

2

ǫp∂ωp

)1

2

dEpdt

+ (ω2p

c2ǫp − β2

p)1

2Ep +

2ωp

c2(ǫp +

ωp

2

ǫp∂ωp

)1

2Epdφp

dt

= (L

4(2

L)3/2)

1

2

< χ(2)eff >

A(2)eff

K(−ω2p

c2)EsEie−i∆φ(−sinc(∆βL)) (E.4a)

2iωs

c2(ǫs +

ωs

2

ǫs∂ωs

)1

2

dEsdt

+ (ω2s

c2ǫs − β2

s )1

2Es +

2ωs

c2(ǫs +

ωs

2

ǫs∂ωs

)1

2Esdφs

dt

= (L

4(2

L)3/2)

1

2

< χ(2)eff >

A(2)eff

K(−ω2s

c2)EpEiei∆φ(−sinc(∆βL)) (E.4b)

2iωi

c2(ǫi +

ωi

2

ǫi∂ωi

)1

2

dEidt

+ (ω2i

c2ǫi − β2

i )1

2Ei +

2ωi

c2(ǫi +

ωi

2

ǫi∂ωi

)1

2Eidφi

dt

= (L

4(2

L)3/2)

1

2

< χ(2)eff >

A(2)eff

K(−ω2i

c2)EpEsei∆φ(−sinc(∆βL)) (E.4c)

Note that∫ L

0fp(z)fs(z)fi(z)dz = (L

4( 2L)3/2)(−sinc(∆βL)) = 1/2

√

2/L(−sinc(∆βL)).

Here L is the length of the cavity, < χ(2)eff > and A

(2)eff were defined earlier in equation (6.4),

and

∆β = βp − βs − βi (E.5a)


∆φ = φp − φs − φi (E.5b)

Also, ǫσ can be described as the following [119]

ǫp ≈ np2 + 2np(∆np + i∆n′′

p) = np2 + 2inp∆n

′′p(1 + iα) = np

2 − inp(Γg

1 + βPp

− αp)c

ωp

(1 + iα).

(E.6a)

ǫs ≈ ns2 + insαs

c

ωs

(E.6b)

ǫi ≈ ni2 + iniαi

c

ωi

(E.6c)

In equations (E.6), nσ is the real part of the corresponding effective index, ∆nσ and

∆n′′σ are the carrier induced change in the real and imaginary parts of effective index,

respectively, α = ∆np

∆n′′

pis the linewidth enhancement factor, Γ is the optical confinement

factor, g is the optical gain, β represents gain saturation, vg;σ is the group velocity, and

ασ represents the optical and distributed mirror loss.

We will do some manipulations for pump to reach to a suitable form for the pump

rate equation; changes in the signal and idler should be very similar:

2iωp

c2(npng;p)

dEpdt

+ (−inp(Γg

1 + βPp

− αp)c

ωp

ω2p

c2(1 + iα))Ep +

2ωp

c2(npng;p)Ep

dφp

dt

= −1

2

√

2

Lχ(2)effK

ω2p

c2EsEi(cos(∆φ)− i sin(∆φ))sinc(∆βL) (E.7)

Note that 2iωp

c2(npng;p) = 2iωpnp

cvg;p, hence,

2iωpnp

cvg;p

dEpdt

+ (−inp(Γg

1 + βPp

− αp)ωp

c)Ep = +

1

2

√

2

Lχ(2)effK

ω2p

c2EsEi(−i sin(∆φ))sinc(∆βL)

(E.8a)

(+np(Γg

1 + βPp

− αp)ωp

c(+α))Ep + 2

ωpnp

cvg;pEpdφp

dt= +

1

2

√

2

Lχ(2)effK

ω2p

c2EsEi(cos(∆φ))sinc(∆βL)

(E.8b)


Multiplying by the according constant and taking the d/dts to one side:

dEpdt

=1

2vg;p((Γ

g

1 + βPp

− αp))Ep +1

4np

vg;p

√

2

Lχ(2)effK

ωp

cEsEi(− sin(∆φ))sinc(∆βL)

(E.9a)

dφp

dt= +

α

2vg;p(Γ

g

1 + βPp

− αp) +1

4np

vg;p

√

2

Lχ(2)effK

ωp

c

EsEiEp

(cos(∆φ))sinc(∆βL) (E.9b)

Assuming Aσ =√Pσ =

√

cnσǫ02L

Eσ, we multiply both sides of the top equation by√

cnpǫ02L

.

dAp

dt=

1

2vg;p((Γ

g

1 + βPp

− αp))Ap +1

4np

vg;p

√

2

Lχ(2)effK

2π

λpAsAi

√

cnpǫ02L

cniǫ02L

cnsǫ02L

(− sin(∆φ))sinc(∆βL)

(E.10a)

dφp

dt= −α

2vg;p(Γ

g

1 + βPp

− αp) +1

4np

vg;p

√

2

Lχ(2)effK

2π

λp

AsAi

Ap

√

cnpǫ02L

cniǫ02L

cnsǫ02L

(cos(∆φ))sinc(∆βL)

(E.10b)

And finally:

dAp

dt=

1

2vg;p((Γ

g

1 + βPp

− αp))Ap

+K

2vg;pAsAi

1

λp

[

πχ(2)eff

√

2

Ln2p

√

cnpǫ02L

cniǫ02L

cnsǫ02L

]

(− sin(∆φ))sinc(∆βL) (E.11a)

dφp

dt= −α

2vg;p(Γ

g

1 + βPp

− αp)

+K

2vg;p

AsAi

Ap

1

λp

[

πχ(2)eff

√

2

Ln2p

√

cnpǫ02L

cniǫ02L

cnsǫ02L

]

(cos(∆φ))sinc(∆βL) (E.11b)

The term in brackets is defined as κ, defined in equations (6.4).

Following the same approach for signal and idler, all the equations for the three

wavelengths can be derived as shown below:

dAp

dt=

1

2Apvg;p(Γ

g

1 + βPp

− αp) +K

2vg;p

κ

λpAsAi(− sin(∆φ))sinc(∆βL), (E.12a)


dφp

dt= −α

2vg;p(Γ

g

1 + βPp

− αp) +K

2vg;p

κ

λp

AsAi

Ap

cos(∆φ)sinc(∆βL), (E.12b)

dAs

dt= −1

2Asvg;sαs +

K

2vg;s

κ

λsAsAi sin(∆φ)sinc(∆βL), (E.12c)

dφs

dt= −∆ωs +

K

2vg;s

κ

λs

ApAi

As

cos(∆φ)sinc(∆βL), (E.12d)

dAi

dt= −1

2Aivg;iαi +

K

2vg;i

κ

λiAiAs sin(∆φ)sinc(∆βL), (E.12e)

dφi

dt= −∆ωi +

K

2vg;i

κ

λi

ApAs

Ai

cos(∆φ)sinc(∆βL). (E.12f)

The terms −∆ωs and −∆ωi were inserted in the above equations to allow for satisfaction

of the phase-matching condition when the laser is biased above threshold. Derivation of

these terms will be discussed in the following section. Lastly, the dAσ/dt equations can

be easily converted to dPσ/dt to reach to equations (E.12) by simply multiplying the two

sides by 2Aσ.

The output power of the laser at each facet can be calculated from the internal

power by Pout = 1/2FP ln 1r1r2

= 1/2FP ln 1√R1R2

where the pre-factor F arises from the

scattering losses in the mirror [112].

E.2 Chirp terms in the SOPO model

The terms ∆ωs and ∆ωi in (6.3d) and (6.3f) represent the deviation of signal and idler

frequencies from their values at laser threshold due to laser frequency chirp, ∆ωp. To

derive the numerical value of these terms based on ∆ωp =α2vg;p(Γ

g1+βPp

−αp) it is assumed

that ∆ωp is much larger than the frequency change due to nonlinear effects - the right

terms in the above-mentioned equations. From the energy and momentum conservation

relations,

∆ωp = ∆ωs +∆ωi (E.13)

(ωp +∆ωp)(np +∆np) = (ωs +∆ωs)(ns +∆ns) + (ωi +∆ωi)(ni +∆ni), (E.14)


where nσ are the real parts of the corresponding effective index and ∆nσ are the changes

in the effective index due to carrier injection in case of pump, and frequency shift for

signal and idler.

By injection of carriers into the laser/SOPO cavity, the pump effective index varies,

and consequently the pump angular frequency shifts as much as ∆ωp = −∆npωpvg;p/c.

By neglecting the second order changes such as ∆ω2σ and ∆n2

σ, (E.14) can be simplified

to

∆ωpnp +ωp∆ωp

−ωpvg;s/c= ∆ωsns + ωs∆ns +∆ωini + ωi∆ni. (E.15)

The group index at signal/idler is defined as ng;s,i = ns,i + ωs,i∆ns,i

∆ωs,i. If this expression is

substituted in the above, ∆ωs can be derived as reported in equation (6.5b).

Lastly, note that ∆ωσ terms were derived by utilizing the energy conservation condi-

tion - equation (E.13). Hence, ∆ωp −∆ωs −∆ωi = 0 and d∆φ/dt does not include the

∆ωl terms as shown below.

d∆

dφ= −κK

2

[

vg;pλp

√

PsPi

Pp

− vg;sλs

√

PpPi

Ps

− vg;iλi

√

PsPp

Pi

]

cos(∆φ)sinc(∆kL). (E.16)

This property has a major effect in the steady-state power and regimes of operation of

SOPOs as outlined in section 6.2.

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