design, fabrication and characterization of plasmonic ...reza sanatinia, maz naiini, reyhaneh...

Design, fabrication and characterization of

plasmonic components based on silicon nanowire

platform

FEI LOU

Doctoral Thesis in Physics

Stockholm, Sweden, 2014

TRITA-ICT/MAP AVH Report 2014:05 KTH school of Information and

ISSN 1653-7610 Communication Technology

ISRN KTH/ICT-MAP/AVH-2014:05-SE S-164 40 Kista

ISBN 978-91-7595-060-0 SWEDEN

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan

framlägges till offentlig granskning för avläggande av teknologie doktorsexamen

fredagen den 25 April 2014 klockan 10:00 i Sal D, Forum, Kungliga Tekniska

Högskolan, Isafjordsgatan 39, Kista, Stockholm.

©Fei Lou, March, 2014

Tryck: Universitetsservice US AB

III

Abstract

Optical interconnects based on CMOS compatible photonic integrated circuits are

regarded as a promising technique to tackle the issues traditional electronics faces, such

as limited bandwidth, latency, vast energy consumption and so on. In recent years,

plasmonic integrated components have gained great attentions due to the properties of

nano-scale confinement, which may potentially bridge the size mismatch between

photonic and electronic circuits. Based on silicon nanowire platform, this thesis work

studies the design, fabrication and characterization of several integrated plasmonic

components, aiming to combine the benefits of Si and plasmonics.

The basic theories of surface plasmon polaritons are introduced in the beginning,

where we explain the physics behind the diffraction-free confinement. Numerical

methods frequently used in the thesis including finite-difference time-domain method

and finite-element method are then reviewed. We summarize the device fabrication

techniques such as film depositions, e-beam lithography and inductively coupled

plasma etching as well as characterization methods, such as direct measurement

method, butt coupling, grating coupling etc.

Fabrication results of an optically tunable silicon-on-insulator microdisk and III-V

cavities in applications as light sources for future nanophotonics interconnects are

briefly discussed. Afterwards we present in details the experimental demonstrations

and novel design of plasmonic components.

Hybrid plasmonic waveguides and directional couplers with various splitting ratios

are firstly experimentally demonstrated. The coupling length of two 170 nm wide

waveguides with a separation of 140 nm is only 1.55 µm. Secondly, an ultracompact

polarization beam splitter with a footprint of 2×5.1 μm2 is proposed. The device

features an extinction ratio of 12 dB and an insertion loss below 1.5 dB in the entire

C-band. Thirdly, we show that plasmonics offer decreased bending losses and enhanced

Purcell factor for submicron bends. Novel hybrid plasmonic disk, ring and donut

resonators with radii of ~ 0.5 μm and 1 μm are experimentally demonstrated for the

first time. The Q-factor of disks with 0.5 μm radii are 90 ± 30, corresponding to Purcell

factors of 127 ± 42. Thermal tuning is also presented. Fourthly, we propose a design of

electro-optic polymer modulator based on plasmonic microring. The figure of merit

characterizing modulation efficiency is 6 times better comparing with corresponding

silicon slot polymer modulator. The device exhibits an insertion loss below 1 dB and a

power consumption of 5 fJ/bit at 100 GHz. At last, we propose a tightly-confined

waveguide and show that the radius of disk resonators based on the proposed

waveguide can be shrunk below 60 nm, which may be used to pursue a strong

light-matter interaction.

The presented here novel components confirm that hybrid plasmonic structures can

play an important role in future inter- and intra-core computer communication systems.

Key words: Planar integrated circuit, silicon photonics, plasmonics, subwavelength,

directional coupler, polarization beam splitter, disk resonator, ring resonator,

finite-difference time-domain, photonic crystal, electro-optic polymer, Purcell factor.

V

Acknowledgments

First and for most, I would like to express my greatest gratitude to my principle

supervisor Assoc. Prof. Lech Wosinski for his continuous guidance and considerate

support during past few years. The thesis work could only be done with his guidance

and expertise. I am very grateful for his kindness and encouragement during these

years.

I also would like to thank my co-supervisors Prof. Lars Thylen and Prof. Sebastian

Lourdudoss. I appreciate very much the opportunities to work with and learn from them

and their group members. It has been a very valuable experience and my horizons have

been largely expanded from interacting with them.

Special thanks to Dr. Zhechao Wang at Ghent University, who had taught me

fabrications in the first month of my journey at KTH. I also specially thank Doc. Min

Yan, Prof. Min Qiu, Dr. Yiting Chen, Dr. Yanting Sun and Yu Xiang all at KTH for their

valuable guidance with partial of my work.

Thank Dr. Yuechun Shi, Xi Chen, Xu Sun, Maofeng Dou, Himanshu Kataria, Dr.

Carl Junesand, Wondwosen Metaferia, Assoc. Prof. Sergei Popov, Gleb Lobov, Dr.

Petter Holmström at KTH, and Prof. Daoxin Dai, Dr. Yaosheng Shi, Xiaowei Guan at

Zhejiang University for the constructive discussions and fruitful cooperation.

Thank our administrator Ms. Madeleine Printzsköld for her warm support and

considerations.

Thank KTH Electrumlab cleanroom staff and IT-service group for their professional

work. Specially, thank Albanova cleanroom administrator Assoc. Prof. Anders

Liljeborg who is constantly ready to help with all kinds of EBL problems.

Thank Prof. Saulius Marcinkevicius, Assoc. Prof. Anand Srinivasan, Assoc. Prof.

Henry Radamson, Prof. David Haviland for their interesting, informative and educative

courses.

Special thanks to Prof. Lena Wosinska for her invitations and nice treats in her

house.

Thank the friends and colleagues I am luckily enough to meet at KTH: Jin Dai,

Kunli Xiong, Miao Zhang, Yi Feng, Min Cen, Dr. Lin Dong, Sohail Ahmed, Zaher

Elbeck, Oscar Rino Granström, Chenzhi Xu, Fan Pan, Dr. Jiantong Li, Dr. Zhiying Liu,

Dr. Xiaodi Wang, Yichen Zhao, Dr. Jiajia Chen, Dr. Qin Wang, Dr. Yongbin Wang,

Reza Sanatinia, Maz Naiini, Reyhaneh Soltan, Sam Vaziri, Xingang Yu, Bote Liu, Song

Lu, Dr. Jing Wang, Dr. Yi Song, Dr. Qiang Li, Dr. Sergey Dyakov, Bikash Dev

Choudhury, Chen Hu, Dr. Naeem Shahid, …

I also would like to express my gratitude to Prof. Xinliang Zhang, without whom I

could not make it so far on this academic road.

At last, thank sincerely my parents and my family who are unconditionally loving

me, caring about me, and encouraging me, and thank Lei Lei, you are the best gift

heaven sent to me.

VII

Table of the Contents

Abstract......................................................................................................................................... III

Acknowledgments ...................................................................................................................... V

List of publications .................................................................................................................... IX

Acronyms ...................................................................................................................................... XI

1. Introduction ............................................................................................................................ 1

1.1 Background ....................................................................................................... 1

1.2 Objectives and Main Achievements ................................................................. 3

1.3 Thesis Outline ................................................................................................... 4

References ............................................................................................................... 5

2. Surface Plasmon Polaritons ............................................................................................... 9

2.1 Plasma model .................................................................................................... 9

2.2 Surface plasmons at a metal-insulator interface ............................................. 11

2.3 SPP waveguide with subwavelength confinement ......................................... 12

References ............................................................................................................. 14

3. Design and Simulation Methods ..................................................................................... 15

3.1 Finite-difference time-domain method ........................................................... 15

3.2 Finite element method .................................................................................... 19

References ............................................................................................................. 22

4. Fabrication and Characterization Techniques ........................................................... 25

4.1 Photonic integrated circuits: overview ........................................................... 25

4.2 Fabrication techniques .................................................................................... 26

4.2.1 Plasma enhanced chemical vapor deposition ........................................... 26

4.2.2 Electron beam evaporation ....................................................................... 28

4.2.3 Electron beam lithography ....................................................................... 29

4.2.4 Inductive coupled plasma -reactive ion etching ....................................... 31

4.3 Characterization methods ............................................................................... 32

4.3.1 Material characterization .......................................................................... 33

4.3.2 Device characterization ............................................................................ 33

4.4 Device demonstrations .................................................................................... 36

4.4.1 Tunable SOI microdisk assisted by perfect absorbers .............................. 36

4.4.2 III-V cavities ............................................................................................. 37

References ............................................................................................................. 39

5. Ultracompact Plasmonic Components ......................................................................... 43

5.1 Hybrid plasmonic directional couplers ........................................................... 43

5.2 Polarization beam splitters based on three-core directional couplers ............. 46

5.3 Hybrid plasmonic resonators .......................................................................... 49

5.3.1 Ultrasharp 90o bends ................................................................................ 49

VIII

5.3.2 Hybrid plasmonic disk resonators ............................................................ 52

5.3.3 Hybrid plasmonic ring and donut resonators ........................................... 54

5.4 Electro-optic polymer modulators based on HP ring resonators .................... 57

5.4.1 Integrated optical modulators: overview .................................................. 57

5.4.2 Performance evaluations .......................................................................... 58

5.4.3 Discussion of fabrication feasibility ......................................................... 61

5.5. Nanodisks based on layered metal-dielectric waveguide .............................. 62

5.5.1 Strongly confined cavities: overview ....................................................... 62

5.5.2 Guiding principle of layered metal-dielectric waveguides ....................... 62

5.5.3 Nanodisk resonator based on the proposed waveguide ............................ 63

References ............................................................................................................. 66

6. Conclusions and Future Work ........................................................................................ 71

6.1 Conclusion ...................................................................................................... 71

6.2 Future work ..................................................................................................... 73

7. Guide to Appended Papers ............................................................................................... 75

IX

List of publications

Publications included in the thesis

A. Fei Lou, Zhechao Wang, Daoxin Dai, Lars Thylen, and Lech Wosinski,

“Experimental demonstration of ultra-compact directional couplers based on

silicon hybrid plasmonic waveguides,” Applied Physics Letters, 100(24), 241105

(2012).

B. Fei Lou, Daoxin Dai, and Lech Wosinski, "Ultracompact polarization beam splitter

based on a dielectric–hybrid plasmonic–dielectric coupler," Optics Letters, 37(16),

3372-3374 (2012).

C. Fei Lou, Lars Thylen, and Lech Wosinski, “Experimental demonstration of

silicon-based metallic whispering gallery mode disk resonators and their

thermo-tuning,” Optical Fiber Communication Conference/National Fiber Optic

Engineers Conference (OFC/NFOEC), paper Tu2E.1, (2014).

D. Fei Lou, Daoxin Dai, Lars Thylen, and Lech Wosinski, “Design and analysis of

ultra-compact E-O polymer modulators based on hybrid plasmonic microring

resonators,” Opt. Express 21, 20041-20051 (2013).

E. Fei Lou, Min Yan, Lars Thylen, Min Qiu, and Lech Wosinski, “Whispering gallery

mode nanodisk resonator based on layered metal-dielectric waveguide,” to be

published in Opt. Express (2014).

F. Fei Lou, Lars Thylen, and Lech Wosinski, “Ultra-sharp bends based on hybrid

plasmonic waveguides,” manuscript (2014).

Publications not included in the thesis

Journal papers

G. M. Dou, F. Lou, M. Boström, I. Brevik, and C. Persson, “Casimir quantum

levitation tuned by means of material properties and geometries”, Submitted to

Phys. Rev. B, (2014).

H. L. Lei, Y. Yu, F. Lou, Z. Zhang, L. Xiang and X. Zhang, “A simple experimental

scheme for M-QAM optical signals generation,” Frontiers of Optoelectronics,

5(2), 200-207 (2012).

I. Y. Shi, X. Chen, F. Lou, Y. Chen, M. Yan, L Wosinski and M.

Qiu, ”All-optical-switching in silicon disk resonator based on photothermal effect

of metal-insulator-metal absorber,” manuscript, (2014).

J. X. Chen, Y. Shi, F. Lou, Y. Chen, M. Yan, L Wosinski and M. Qiu,

“Photothermally tunable silicon microring-resonator-based optical add-drop filter,”

manuscript, (2014).

Conference contributions

K. F. Lou, X. Zhang, L. Wosinski, “Transmission characteristics of a novel grating

X

assisted microring,” Proc. of SPIE 8308, 83080A-1 (2011).

L. F. Lou, Z. Wang, D. Dai, L. Thylen, and L. Wosinski, “A sub-wavelength

microdisk resonator based on hybrid plasmonic waveguides”, 5th International

Photonics and OptoElectronics Meetings (POEM 2012), November 1-2, 2012,

Wuhan, China. (Best Student Paper)

M. F. Lou, Z. Wang, D. Dai, L. Thylen, and L. Wosinski, “Photonic devices based on

silicon hybrid plasmonic waveguides”, Asia Communications and Photonics

Conference (ACP), November 7-10, 2012, Guangzhou, China, paper: AS2H.2.

N. F. Lou, L. Thylen, and L. Wosinski, “Hybrid plasmonic microdisk resonators for

interconnect applications”, Optics + Optoelectronics International Symposium,

15-18 April 2013, Prague, Czech Republic, SPIE Proc. (2013).

O. L. Wosinski, F. Lou and L. Thylen, “Silicon- and plasmonics-based nanophotonics

for telecom and interconnects”, invited talk presented at 16th International

Conference on Transparent Optical Networks, ICTON 2014, Graz, Austria, July

6-10, 2014, Proceedings of the IEEE.

P. L. Wosinski, F. Lou and L. Thylen, " Novel hybrid plasmonic devices on silicon

platform”, invited talk, 35th Progress in Electromagnetics Research Symposium

(PIERS), Aug 25-28, 2014 Guangzhou, China.

Q. L. Wosinski, F. Lou and L. Thylen, "Nanoscale Si-based photonics for next

generation integrated circuits", invited talk, 15th International Conference on

Transparent Optical Networks, ICTON 2013, Cartagena, Spain, June 23-27, 2013,

Proceedings of the IEEE.

R. L. Wosinski, F. Lou and L. Thylen, " Silicon platform-based nanophotonics for

interconnect applications”, invited talk, 34th Progress in Electromagnetics

Research Symposium (PIERS), Aug 12-15, 2013 Stockholm, Sweden.

S. L. Wosinski, F. Lou and L. Thylen, “Hybrid plasmonics for computer

interconnects”, invited talk presented at the Asia Communications and Photonics

Conference (ACP), November 12-15, 2013, Beijing, China, paper: ATh4A.1.

T. X. Sun, F. Lou and L. Wosinski, “Study of Plasmonic Analogue of EIT Effect

based on Hybrid Plasmonic Waveguide System,” Asia Communications and

Photonics Conference (ACP), Beijing, China, Nov. 12-15 (2013).

U. L. Wosinski, Z. Wang, F. Lou, D. Dai and L. Thylen, “Novel plasmonic

waveguides and devices”, invited talk presented at the 5th International Photonics

and OptoElectronics Meetings (POEM 2012), November 1-2, 2012, Wuhan,

China.

V. L. Wosinski, Z. Wang, F. Lou, D. Dai and L. Thylen, “Silicon- and

plasmonics-based nanophotonics for telecom and interconnects”, special invited

talk presented at the Asia Communications and Photonics Conference (ACP),

November 7-10, 2012, Guangzhou, China, paper: AW1A.3.

W. L. Wosinski, Z. Wang, F. Lou, D. Dai, S. Lourdudoss and L. Thylen, “Advanced

silicon device technologies for optical interconnects”, invited talk presented at the

Photonics West 2012 Conference, January 21-26, San Francisco, California, USA,

Proc. SPIE 8265, 826506 (2012).

XI

Acronyms

AFM Atomic Force Microscopy

α-Si:H Hydrogenated Amorphous Silicon

BPM Beam Propagation Method

CMOS Complementary Metal Oxide Semiconductor

CMP Chemical-Mechanical Polishing

DUT Device Under Test

WDM Wavelength-Division Multiplexing

EBL Electron Beam Lithography

EBE Electron Beam Evaporation

ELOG Epitaxial Lateral Overgrowth

FFT Fast Fourier Transforms

FEM Finite Element Method

FDTD Finite-Difference Time-Domain

FIB Focused Ion Beam

HPWG Hybrid Plasmonic Waveguide

HSQ Hydrogen Silsesquioxane

HVPE Hydride Vapor Phase Epitaxy

ICP-RIE Inductively Coupled Plasma- Reactive Ion Etching

IL Insertion Loss

LMD Layered Metal-Dielectric

MDM Metal-Dielectric-Metal

MRR Micro Ring Resonator

PBS Polarization Beam Splitter

PECVD Plasma Enhanced Chemical Vapor Deposition

PhC Photonic Crystal

PICs Photonic Integrated Circuits

PL Photoluminescence

PML Perfectly Matched Layer

RC Resistor-Capacitor

SEM Scanning Electron Microscope

SOI Silicon-On-Insulator

SOG Spin-of-Glass

SPPs Surface Plasmon Polaritons

TE Transverse Electric

TM Transverse Magnetic

TO Thermo-Optic

WF Writing Field

1

Chapter 1

Introduction

1.1 Background

Advances in semiconductor technology have led us to current era of big data and

super-computing; the whole society is unprecedentedly connected and computerized.

All this convenience is largely attributed to the success of complementary

metal-oxide-semiconductor (CMOS) - based electronic integrated circuits. Since the

invention of semiconductor transistors around 1950s, the progress in electronic circuits

has been following the famous Moore’s law (Gordon Moore, 1965), which states that

the number of transistors per chip doubles every two years. The strong driving forces of

continuous chip miniaturization are not only to shrink the device size, but more

importantly to enhance the performance and reduce the cost and power consumption.

This is especially the case in nowadays multi-core and multi-board cascaded circuits in

supercomputers and datacenters. Thousands and millions of computer processor units

are scaled and interconnected, and the cost and power consumption are tremendous.

However, as the number of transistors per chip continues growing, the challenge in chip

miniaturization shifts gradually from how to integrate more transistors per unit area to

how to interconnect them with other functional components. As the scaling of chip size

and communication bandwidth, using traditional copper-based interconnects is

reaching its physical limits in terms of heat dissipation, signal latency, cross talking, etc.

[1], researchers began eagerly looking for other solutions.

To break through the limitations traditional electronics faces, optical interconnects

by using photons as information carriers have been proposed [2]. The proposal

combines the advantages of both worlds i.e. photons and electrons, which may

potentially trigger another round of information technology revolution. The history of

light-based communication can actually date back to ancient times. One such example

is the building of Great Walls started around 220 BC, where smoke was lighted in case

of intrusions so that distant defending force was warned. In 1960, Theodore Maiman

shed a new form of light to the world [3], which does not exist in nature i.e. laser. The

invention, together with several other emerged techniques such as ultra-low-loss fibers,

erbium doped fiber amplifiers, wavelength-division multiplexing (WDM), etc., became

the foundations of modern optical communication. Similarly to electronics, from the

date of birth, modern optical communication has been pushed toward device

integration and chip miniaturization. A variety of material platforms such as silica on

Chapter 1. Introduction

2

silicon [4], III-V semiconductors [5], polymers [6], LiNbO3 [7], silicon on insulator

(SOI) [8-9], etc. have been examined towards this end. One most economic and perhaps

most promising platform is silicon-based photonics [8-10]. The reasons are mainly two

fold: firstly, silicon has a very high refractive index and it is transparent (loss of ~1

dB/cm) in the telecommunication wavelength range; secondly but equal-importantly,

fabrication of silicon-based photonic devices is compatible with the advanced CMOS

processes available in billion dollar foundries hitherto used to create electronic

processors. However, as nothing is perfect, neither is silicon photonics due to following

issues.

One issue has to do with silicon itself. A working optical commutation system needs

some basic components, for light guiding, generation, detection, modulation, routing,

and so on. Although passive components being relatively easy to implement in silicon

photonics, realizing of active photonic devices based on Si platform faces various

challenges. Firstly, silicon has an indirect bandgap, and lasing only occurs under

demanding conditions with extremely poor efficiency [11]; secondly, since silicon is

transparent at telecom wavelength, it is not suitable for detection [12]. As for light

modulation, although there have been demonstrations of Si modulators in recent years

[13-14], the device footprint is normally large due to material’s poor electro-optic (EO)

coefficient, and the achievable speed is fundamentally limited due to the

resistor-capacitor (RC) circuit latency (latest speed record: 50 Gb/s [14]). As a result, Si

by itself is not suitable for future photonic integrated circuits (PICs). One needs to

incorporate versatile and complementary materials onto Si platform, exploiting the best

of each world [15-18]. A recent European project PhoxTroT [19] is an example of

efforts towards such hybrid circuit. The project goal is to combine Si photonics, III-V

semiconductors, polymers, glass, plasmonics, electronics, etc. for optical interconnects.

Selecting appropriate materials for specific needs may potentially enhance the chip

performance, reduce the cost and power consumption.

Another issue of Silicon photonics is related to photons. We have discussed that like

electrons, photons can also act as an information carrier, even with better performance.

However, realizing optical computing is very challenging. The problems are that

photons are bosons and stopping and storing them are very difficult [20]. Moreover, the

basics of optical computing i.e. optical transistors (based on nonlinearities) are far from

maturity yet [21]. Hence we will continue relying on electrons for data computing for

quite a long time. Correspondingly, in the near future, as proposed and implemented by

giants like IBM [22], Intel [23] etc., integrated circuits can consist of multiple layers,

where information is stored and processed using electrons in electronic layers, while

guided and routed using photons in photonic layers. The idea has already been

implemented and commercial products are expected in the next few years [24]. This

approach, however, will eventually face another intrinsic problem: the size mismatch

between photonic components and electronic counterparts [25]. To be more specific, a

state of-the-art transistor has a feature size of about 30 nm. In comparison, the width of

a silicon waveguide is normally beyond 450 nm due to the diffraction limit of light;

footprints of functional photonic devices are even larger, e.g. the typical radius of a SOI

microring resonator is around 5 micron or more. As the integration density increases,


3

millions of photonic and electronic components will be integrated, and the huge size

mismatch becomes essential.

Plasmonics has been regarded as next-generation chip technology [25-26], since it

can enable circuits with sizes comparable to electronics and transfer information at a

photonic speed. Plasmonic waveguides are normally composed of metals and

dielectrics. By guiding the so-called surface plasmon polaritons (i.e. density waves of

electrons oscillations) at metal-dielectric interfaces, they can enable diffraction free

light confinement [27-28], however at a cost of metal dissipation loss. Various

plasmonic waveguide geometries have been proposed and demonstrated, including

dielectric-loaded plasmonic waveguide [29-30], long range SPP waveguide [31],

metal-dielectric-metal waveguide [32-33], hybrid plasmonic waveguide [34-35], etc.

Beside compact light confinement, plasmonics is equally interesting for other desirable

properties, such as strong light-matter interaction useful for enhancement of

nonlinearities [36-37] and Purcell factor [38], improved RC circuit latency [39],

capability to guide electrons and photons simultaneously [40-41], etc. Hence, it might

be very useful to incorporate plasmonics into the above mentioned hybrid circuit, as

long as we properly design and evaluate the losses and gains. A practical solution of

such hybrid circuit would be: low-loss and compact light guiding is realized by SOI

waveguides, while functional components can embrace diverse materials (III-V,

germanium, polymer, plasmonics, graphene, etc.), targeting better performance, more

compact footprint and a lower cost.

1.2 Objectives and Main Achievements

Summarizing discussions in section 1.1, we come to the objectives of this thesis:

- to explore and bring up new concepts of functional plasmonic components

based on Si platform,

- aiming to combine the benefits of plasmonics and other functional materials for

applications in next-generation photonic integrated circuits.

Main part of our work focuses on a so-called hybrid plasmonic waveguide (HPWG). It

was firstly proposed by a UC Berkeley group in 2008 [34], and later demonstrated by

various research groups [42-45]. We think such a waveguide is interesting mainly for

three reasons. (1) HPWG is composed of Si and metal with a SiO2 slot sandwiched in

between. The materials and fabrication can be readily CMOS-compatible. (2) There’s

an extra design of freedom in HPWG by selecting the thickness of SiO2 slot. (3) By

guiding a hybrid mode (partially plasmonic and partially photonic), HPWG achieves

relatively compact confinement and long propagation length; the insertion loss (IL) of

functional devices are relatively low as a result.

In the thesis work, we have achieved following results:

Fabrication and evaluation of ultracompact directional couplers based on

HPWG with splitting ratios ranging from ~ 100:0 to 50: 50 to 0:100.

New design of ultracompact polarization beam splitters (PBSs) based on

HPWG with an insertion loss below 1.5 dB and a footprint of 2×5.1 μm2.

Design and experimental realization of submicron-radius hybrid plasmonic disk,

ring, donut resonators with free spectral ranges of ~ 200 nm and a Purcell factor


4

over 100. The waveguide-loaded disk resonator with 525 nm radius was the

smallest to date fabricated device that got acknowledgment as a best student

paper and received attention in many popular magazines.

Design and concept evaluation of an ultracompact EO polymer modulator based

on HP microring resonators (radius ~ 540 nm) with insertion loss of about 1 dB

and power consumption of about 5 fJ/bit at100 GHz.

We have also proposed another type of tightly confined plasmonic waveguide: layered

metal-dielectric (LMD) waveguide, for pursuing even smaller resonator and more

intense light-matter interaction. We have shown that a disk resonator with radius of

around 60 nm can be achievable and the proposed devices are potentially useful in

strong coupling system.

The achievements presented in this thesis are an important contribution in the

development of future optical interconnects in inter- and intra-core computer

communication systems.

1.3 Thesis Outline

The rest of the thesis is organized as follows:

In Chapter 2, we discuss the basic principles and fundamentals of surface plasmon

polaritons. Plasma models of noble metals are introduced to describe metal’s optical

properties. Dispersion relation of a two-dimensional metal-dielectric interface is

derived from Helmholtz equation. We also compare a metal-insulator-metal waveguide

with a traditional photonic waveguide, explaining SPP’s diffraction-free confinement.

Chapter 3 introduces two frequently used numerical methods for design and

simulations in this thesis. Finite-difference time-domain method (FDTD) is employed

to rigorously simulate the lightwave propagation. Finite element method (FEM) is used

as solvers for optical modes as well as coupled-multiphysics problems. The

implementation principles and practical examples of FDTD and FEM simulations are

given for a deep understanding.

In Chapter 4, we explain the fabrication and characterization techniques used in our

experiments. We firstly briefly introduce the techniques of film deposition, electron

beam lithography and inductively coupled plasma etching. Then characterization

methods including grating couplers, direct measurement, butt coupling and an optical

pump system are discussed. Finally we present some of our experimental results

including a tunable silicon-on-insulator microdisk integrated with perfect absorbers

and III-V laser cavities.

Chapter 5 presents our main results on plasmonic devices. Experimental

demonstrations of hybrid plasmonic directional couplers are firstly discussed. Then we

propose a novel design of a PBS based on three-core directional couplers. Afterwards,

hybrid plasmonic ultra-sharp 90o bends and submicron disk, ring and donut resonators

are analyzed and demonstrated. Based on hybrid plasmonic microring, the concept of

an ultra-compact electro-optic polymer modulator is proposed and evaluated. Finally,

we discuss a new plasmonic waveguide i.e. layered metal-dielectric waveguide and

investigate the optical properties of the nanodisk based on such strongly-confined

waveguides.


5

In Chapter 6 the discussion and conclusion of this work are presented, and some

guidelines for the future research directions are given.

Finally Chapter 7 lists the appended papers and summarizes the achievements.

References

[1] J. A. Davis, R. Venkatesan, A. Kaloyeros, M. Beylansky, S. J. Souri, K. Banerjee,

K. C. Saraswat, A. Rahman, R. Reif, and J. D. Meindl, "Interconnect limits on

gigascale integration (GSI) in the 21st century," Proc. IEEE 89, 305 (2001).

[2] D. A. B. Miller, "Rationale and challenges for optical interconnects to electronic

chips," Proc. IEEE 88, 728-749 (2000).

[3] T. H. Maiman, "Stimulated optical radiation in ruby," Nature 187, 493−494 (1960).

[4] M. Kawachi, "Recent progress in silica-based planar lightwave circuits on silicon,"

IEE Proc. Optoelectronics 143, 257-262(1996).

[5] T. L. Koch, "Semiconductor photonic integrated circuits," IEEE J. Quantum.

Electron. 27, 641-653 (1991).

[6] H. Ma, A. K.-Y. Jen, and L. R. Dalton, "Polymer-based optical waveguides:

materials, processing, and devices, " Adv. Mater. 14, 1339-1365 (2002).

[7] E. L. Wooten et al. "A review of lithium niobate modulators for fiber-optic

communications systems," IEEE J. Sel. Top. Quantum Electron. 6, 69-82 (2000).

[8] L. Pavesi and D. J. Lockwood, Silicon Photonics (Springer-verlag, New York,

2004).

[9] G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley,

West Sussex, 2004).

[10] B. Jalali, M. Paniccia, and G. Reed, “Silicon photonics,” IEEE Microw. Mag. 7(3),

58–68 (2006).

[11] H. Rong, et. al "A continuous-wave Raman silicon laser," Nature 433, 725-728

(2005).

[12] S. Fama, L. Colace, G. Masini, G. Assanto, H.-C. Luan, High performance

germanium-on-silicon detectors for optical communications, Appl. Phys Lett. 81,

586-588 (2002).

[13] L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky,

and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,”

Electron. Lett.43(22), 1196–1197 (2007).

[14] Takeshi Baba, Suguru Akiyama, Masahiko Imai, Naoki Hirayama, Hiroyuki

Takahashi, Yoshiji Noguchi, Tsuyoshi Horikawa, and Tatsuya Usuki, "50-Gb/s

ring-resonator-based silicon modulator," Opt. Express 21, 11869-11876 (2013).

[15] D. Liang, G. Roelkens, R. Baets, and J. Bowers, “Hybrid integrated platforms for

silicon photonics,” Materials 3(3), 1782–1802 (2010).

[16] R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8),

495–497 (2010).

[17] J. Leuthold, C. Koos, W. Freude, L. Alloatti, R. Palmer, D. Korn, J. Pfeifle, M.

Lauermann, R. Dinu, S. Wehrli, M. Jazbinsek, P. Günter, M. Waldow, T. Wahlbrink,

J. Bolten, H. Kurz, M. Fournier, J. Fedeli, H. Yu, and W. Bogaerts,


6

“Silicon-organic hybrid electro-optical devices,” IEEE J. Sel. Top. Quantum

Electron.19(6), 3401413 (2013).

[18] S. I. Bozhevolnyi, ed., Plasmonic Nanoguides and Circuits, Pan Stanford Publ.,

(2008).

[19] PhoxTroT project: http://www.phoxtrot.eu/

[20] T.F. Krauss, "Why do we need slow light?" Nat. Photonics 2, 448-449 (2008).

[21] D. A. B. Miller, “Are optical transistors the logical next step?” Nat. Photonics4(1),

3–5 (2010).

[22] http://researcher.ibm.com/researcher/view_project.php?id=2757

[23] http://www.intel.com/content/www/us/en/research/intel-labs-silicon-photonics-re

search.html

[24] M. Streshinsky, R. Ding, Y. Liu, A. Novack, C. Galland, A. E.-J. Lim, P.

Guo-Qiang Lo, T. Baehr-Jones, and M. Hochberg, "The Road to Affordable,

Large-Scale Silicon Photonics," Optics & Photonics News 24(9), 32-39 (2013).

[25] R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, "Plasmonics: the next

chip-scale technology," Mater. Today 9, 20-27 (2006).

[26] E. Ozbay, "Plasmonics: Merging photonics and electronics at nanoscale

dimensions," Science 311, 189-193 (2006).

[27] A. V. Zayats and I. I. Smolyaninov, "Near field photonics: surface plasmon

polaritons and localized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50

(2003).

[28] A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface

plasmon polaritons," Phys. Rep. 408, 131-314 (2005).

[29] A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on

dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett.90(21),

211101 (2007).

[30] T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereux, A. V. Krasavin,

and A. V. Zayats, “Bend- and splitting loss of dielectric-loaded surface

plasmon-polariton waveguides,” Opt. Express 16(18), 13585–13592 (2008).

[31] R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, “Demonstration of

integrated optics elements based on long-ranging surface plasmon polaritons,” Opt.

Express 13(3), 977–984 (2005).

[32] Z. Han, A. Y. Elezzabi, and V. Van, "Experimental realization of subwavelength

plasmonic slot waveguides on a silicon platform," Opt. Lett. 35, 502-504 (2010).

[33] G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal

subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87(13), 131102 (2005).

[34] R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid

plasmonic waveguide for subwavelength confinement and long-range

propagation,” Nat. Photonics 2(8), 496–500 (2008).

[35] D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap

for a nano-scale light confinement,” Opt. Express 17(19), 16646–16653 (2009).

http://www.phoxtrot.eu/

http://researcher.ibm.com/researcher/view_project.php?id=2757

http://www.intel.com/content/www/us/en/research/intel-labs-silicon-photonics-research.html

http://www.intel.com/content/www/us/en/research/intel-labs-silicon-photonics-research.html


7

[36] M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics6(11),

737–748 (2012).

[37] G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear

surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).

[38] A. N. Poddubny, P. A. Belov, P. Ginzburg, A. V. Zayats, and Y. S. Kivshar,

“Microscopic model of Purcell enhancement in hyperbolic metamaterials,” Phys.

Rev. B86(3), 035148 (2012).

[39] J. A. Conway, S. Sahni, and T. Szkopek, "Plasmonic interconnects versus

conventional interconnects: a comparison of latency, crosstalk and energy costs,"

Opt. Express 15, 4474-4484 (2007).

[40] M. L. Brongersma, R. Zia, and J. A. Schuller, “Plasmonics—the missing link

between nanoelectronics and microphotonics,” Appl. Phys., A Mater. Sci. Process.

89, 221–223 (2007).

[41] H. A. Atwater, “The promise of plasmonics,” Scientific American Reports 56,

(2007).

[42] M. Wu, Z. Han, and V. Van, "Conductor-gap-silicon plasmonic waveguides and

passive components at subwavelength scale," Opt. Express 18, 11728-11736

(2010).

[43] I. Goykhman, B. Desiatov, and U. Levy, “Experimental demonstration of locally

oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett. 97(14), 141106

(2010).

[44] S. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, "Silicon-based horizontal

nanoplasmonic slot waveguides for on-chip integration," Opt. Express 19,

8888-8902 (2011).

[45] Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L.

Wosinski, "Experimental Realization of a Low-loss Nano-scale Si Hybrid

Plasmonic Waveguide," in Optical Fiber Communication Conference/National

Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical

Society of America, 2011), paper JThA017.

Chapter 2. Surface Plasmon Polaritons

9

Chapter 2

Surface Plasmon Polaritons

Surface plasmon polaritons (SPPs) are density waves of coherent electrons oscillating

at the interface between any two materials whose real parts of permittivities have

opposite signs (e.g. metal-dielectric interfaces) [1-2]. Similar to photonics, surface

plasmons (propagating or localized) are referred as plasmonics. As a primer, this

chapter discusses the fundamentals and basics of surface plasmon polaritons. Firstly,

we present plasma models for describing optical properties of noble metals. We then

consider a simple example of a two-dimensional metal-dielectric interface, in order to

explain the concept of surface plasmons. In the chapter end, we compare a typical

plasmonic waveguide i.e. metal-insulator-metal waveguide with a traditional photonic

waveguide, explaining SPP waveguide’s diffraction-free confinement.

2.1 Plasma model

Since SPPs originate from the electron oscillations, metals with numerous free

electrons are natural materials used in plasmonics. Plasma model of metals is the basis

to study SPPs [3-5]. It depicts the interaction of the mobile electrons at the metal

surface with external electromagnetic excitations, which is also referred as the metal’s

dielectric function or permittivity. Drude model, developed by a German physicist Paul

Drude in 1900, provides a fairly accurate description of metal’s conductivities. The

model neglects the detailed lattice potential and interactions between electron-electron

or electron-ion, and free electrons oscillating in one dimension are assumed to obey the

classical kinetic equation expressed as

mx + mγx = - eE, (2.1)

where 𝑚 and 𝛾 are averaged effective optical mass and collision frequency of the free

electron, respectively, e is the elementary charge and E = E0e-iωt is the external

oscillating electrical field. Solving the differential equation Eq. 2.1, we obtain a

solution given by

x = - e/m(ω2 + iγω)E. (2.2)

The solution can be inserted into the expressions of polarization density P = - nex (n is

the electron density) and electrical displacement D = ε0E + P. By combining the

equations, the metal’s dielectric function is derived as


10

εm=1 - ωp2/(ω2 + iγω), (2.3)

where ωp is the plasma frequency given by ωp2 = ne2/ε0m. For some cases (e.g. in

noble metals), the bands are filled till close to the Fermi surface [5] and a background

permittivity ε∞ is introduced. More commonly, we use an extended form of Eq. 2.1

given by

εm= ε∞ - ωp2/(ω2 + iγω) . (2.4)

It’s worth mentioning that Eq. 2.4 is obtained by modelling the free electron excitations.

However, at high frequencies, interband transitions of bound electrons in some metals

(for example gold) are significant, hence Drude model fails to apply. In these cases, we

refer to Drude-Lorentz model, which emulates the interband transition of bound

electrons by a spring with a restoring force. We denote the resonance frequency of the

spring as ω0. The kinetic equation of electrons is then modified as

mx + mγx + mω02x = - eE. (2.5)

Solving Eq. 2.5, we obtain the expression of distance as

x = - e/m(ω2 - ω02 + iγω)E. (2.6)

Similarly, combing Eq. 2.6 with macroscopic polarization and electrical displacement

equations, we derive the metal’s permittivity as

εm = ε∞ - ωp2/(ω2 - ω0

2 + iγω). (2.7)

When taking into account bounds from multiple nuclei, a more general form of

Drude-Lorentz model can be written as

εm = ε∞ - ∑ ωp2/(ω2 - ω0i

2 + iγω)i . (2.8)

In this thesis, we use Drude model of Eq. 2.4 to describe silver, while Drude-Lorenz

model of Eq. 2.8 is used to describe gold, unless otherwise mentioned [6-7]. The chosen

parameters in the models are fitted by the experimental data from Johnson and Christy

[8]. Fig. 2.1 shows the real (ε′) and imaginary (ε") parts of the fitting results. One can

see that in our concerned communication wavelength range (1.3 μm to 1.6 μm), the

models provide very accurate description of the metals’ optical properties.


11

Figure 2.1. Imaginary and real parts of permittivities given by plasma models, fitted with

experimental data from Johnson and Christy [8]. (a) Silver modelled by Drude model. (b) Gold

modelled by Drude-Lorentz model.

2.2 Surface plasmons at a metal-insulator interface

Since metals can be described by classic plasma models, the study of the lightwave

behavior of SPP waves is a classic problem, governed by Maxwell’s equations. To

explain the concept of surface plasmon polaritons, we consider a planar SPP waveguide

composed of a metal layer (of a permittivity 𝜀1 ) and a dielectric layer (of a

permittivity 𝜀2) as schematically shown in Fig. 2.2(a). Here, the wave vector is along

x+ direction and no spatial variation along y direction is assumed. Thus, the

propagation wave can be written as E = E(z)eiβx and satisfies Helmholtz equation [9]

0k22 EE . (2.9)

Figure 2.2. Surface plasmon polaritons at a metal-dielectric interface. (a) Schematic diagram of

the electron oscillations. (b) Dispersion curve of SPPs supported by a silver-air interface. (c) Hy

field distribution along the metal-dielectric interface.

0 0.5 1 1.5 2-250

-200

-150

-100

-50

0

50

0 0.5 1 1.5 20

2

4

6

8

'' (Johnson & Christy)

'' (Drude Model)

' (Johnson & Christy)

' (Drude Model)

0 0.5 1 1.5 2-200

-150

-100

-50

0

50

0 0.5 1 1.5 20

5

10

15

20

25

30

' (Johnson & Christy)

' (Drude-Lorentz Model)

'' (Johnson & Christy)

'' (Drude-Lorentz Model)

Wavelength (μm)

ε(A

u)

imagin

ary p

art

ε(

Au

) re

al p

art

Wavelength (μm)

(a) (b)

ε(A

g)

imag

inar

y p

art

ε(

Ag)

real

par

t


12

Similar expression also stands for the magnetic field H. For a planar transverse

magnetic (TM) polarized light, there exist only 𝐸𝑥, 𝐸𝑧 and 𝐻𝑦 components. Solving

the Maxwell’s equations gives their explicit expressions as

z ≥ 0

E = (iA2k2, 0, -A1β) eiβx - k2z/ωε0ε2, (2.10)

H = (0, 1, 0)A2eiβx - k2z (2.11)

z < 0 E = (-iA1k1, 0, -A1β)eiβx + k1z/ωε0ε1, (2.12)

H = (0, 1, 0)A1eiβx + k1z. (2.13)

In addition, E and H need to satisfy the boundary conditions along the metal-dielectric

interface (𝑧 = 0), i.e. Ex1 = Ex2, Hy1 = Hy2 and ε1Ez1 = ε2E

z2. By combining these

conditions with Eq. 2.10 - 2.13, we derive the propagation constant of the TM-polarized

SPP mode as

β = k0√ε1ε2/(ε1 + ε2). (2.14)

From Eq. 2.14, the effective refractive index of the plasmonic mode can be given:

ne = R(β)/k0. To evaluate the propagation loss due to metal dissipation, propagation

length can be defined as the 1/e plasmon decay length [5]; and it is evaluated by

Lp = k02/2I(β). For a silver-air interface, the supported SPP wave has a dispersion

relation as shown by the solid line in Fig. 2.2(b). The gray area is leakage region below

the airline, and the singularity point (𝜔/𝜔 ~ 0.51) corresponds to the condition when ε’

= -1. Furthermore, by inserting Eq. 2.14 into Eq. 2.10 - 2.13, we get the electrical field

distribution along the normal direction of the interface, as schematically illustrated in

Fig. 2.2(c). One may find that the skin depth of metal is significantly smaller than this

of dielectric, suggesting that sub-wavelength confinement can be potentially achieved.

It’s worth mentioning that for TE polarization, one can perform a likewise

theoretical analysis. However, only null solutions to above equations can be derived,

meaning that SPP waveguides do not support TE modes.

2.3 SPP waveguide with subwavelength confinement

As discussed in Section 2.2, a metal-dielectric interface supports propagating confined

surface plasmon polaritons. However, one can see from Fig. 2.2(c) that although

electromagnetic fields of the SPP mode decays rapidly in the metal side, there exhibit

slow-decaying tails in the dielectric side. Hence, such waveguide cannot provide the

desired subwavelength confinement. A straightforward solution is to add another

metal-dielectric interface and form a so-called metal-dielectric-metal (MDM)

waveguide in order to pursue a more compact confinement [10]. Fig. 2.3(a) shows the

schematic diagram of the sandwich structure of a 2D MDM waveguide. A traditional

waveguide is shown in Fig. 2.3(b) for comparison. Here, the wave propagates along x+

direction; silver is chosen as the plasmonic material; the dielectric core is silicon with a


13

permittivity of 12; cladding material is air. Similarly, the dispersion relations of TM

mode in SPP waveguide and TE mode (most compact) in Si waveguide can be derived.

The effective indices and propagation length (of SPP waveguide) as functions of

waveguide core w are then calculated, as shown in Figs. 2.3(c)-(d). Figs. 2.3(e)-(f)

show the corresponding field distributions. One can see that in traditional dielectric

waveguide, optical field penetrates through the waveguide core and extends with a long

tail into the low-index claddings. In contrary in MDM waveguide, light can be tightly

confined in the slot between the metal slabs, even when the slot width decreases

dramatically, suggesting that subwavelength confinement beyond the diffraction limit

of light is enabled. However, highly localized surface plasmons also imply tremendous

losses. In the studied MDM waveguide, propagation length is typically of the order of

10 μm, as shown in Fig. 2.3(c).

Figure 2.3. (a) Schematics of a metal-dielectric-metal (MDM) waveguide; here, the dielectric is

silicon and metal is silver. (b) Schematics of a traditional optical waveguide (Air-Si-Air). (c)

Effective index and propagation length of TM mode in MDM waveguide as functions of

waveguide width w. (d) Effective index of TE mode in Si waveguide as a functionsof w. (e) Hy

field distributions of MDM waveguide’s TM mode along z axis for w = 50 nm, 100 nm and 200

nm. (f) corresponding Ey field distributions of Si waveguide’s TE mode.


14

References

[1] J. J. Burke, G. I. Stegeman, T. Tamir, “Surface-polariton-like waves guided by thin,

lossy metal films,” Phys. Rev. B 33, 5186-5201 (1986).

[2] G. I. Stegeman, D. G. Hall, and J. J. Burke, "Surface-polaritonlike waves guided

by thin, lossy metal films," Opt. Lett. 8, 383-385 (1983).

[3] L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press,

Cambridge, 2006), p. 408.

[4] M. Fox, Optical properties of solids (Oxford University Press, New York, 2003).

[5] S. A. Maier. Plasmonics: Fundamentals and Applications. (Springer, 2007.)

[6] A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable

for FDTD simulations,” Appl. Phys. B93(1), 139–143 (2008).

[7] P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical

properties of gold,” J. Chem. Phys.125(16), 164705 (2006).

[8] P. B. Johnson and R. W. Christy, "Optical Constants of the Noble

Metals,"Phys. Rev. B6, 4370 (1972).

[9] J. D. Jackson. Classical Electrodynamics. Wiley, New york, 3th edition, 1998.

[10] G. Veronis and S. Fan, "Guided subwavelength plasmonic mode supported by a

slot in a thin metal film," Opt. Lett. 30, 3359-3361 (2005).

15

Chapter 3

Design and Simulation Methods

Since the formulation in 1873, Maxwell’s equations have stated the fundamentals to

analyze electromagnetic (EM) waves. As a set of partial differential equations (PDEs),

Maxwell’s equations normally have no analytical solutions except for certain simple

problems (e.g. the 2D planar waveguides as discussed in Chapter 2). Numerical

methods with the help of powerful computational resources are required in order to

study sophisticated photonic components in optical fiber telecommunication systems,

photonic integrated circuits and nanophotonics. In this chapter, we introduce two

frequently used design and simulation methods: finite-difference time-domain method

(FDTD) and finite element method (FEM). We derive the basic implementation

principles and some practical examples are given for a deep understanding.

3.1 Finite-difference time-domain method

In this section, Finite-difference time-domain method (FDTD) and its working

principle are introduced. FDTD was firstly proposed by K. S. Yee in 1966 [1]. After

nearly half-century’s development [2-3], it has become a very sophisticated tool for

modeling electromagnetics. In this thesis, 3D-FDTD is frequently used to simulate the

lightwave propagation properties (e.g. transmission, reflection, filtering, coupling, etc.)

of photonic as well as plasmonic components, such as bends, directional couplers,

resonators, etc. Compared with other methods such as beam propagation method

(working under a slow-varying envelope approximation) [4], transfer matrix method

(simplifying EM fields into rays) [5], FDTD is rigorous and accurate because very few

approximations are made during the implementations. The basic idea of FDTD is to

discretize Maxwell’s equations (a set of time-dependent PDEs) both in space and time

domains. At one time node, FDTD solves the electromagnetic (EM) fields in each

special unit cell. Then at next time node, EM fields are updated based on the fields from

previous time node. Given enough running time and high gridding resolutions (time

and space), FDTD simulation results can be very accurate. In addition, since FDTD is a

time-domain method, a wide wavelength range can be simulated with a single run,

which significantly saves the computational time. It’s also noted that diverse materials

(dispersive, nonlinear and gain materials) can be incorporated into FDTD

implementation.

In order to deeply understand the FDTD algorithm, here we consider FDTD

implementation process of simulating a nondispersive and isotropic medium. We start

with Maxwell equations

Chapter 3. Design and Simulation Methods

16

0t

BE , (3.1)

t

DH j . (3.2)

Combining Eq. 3.1-3.2 with , and B H D E j E , we get

EH

1

t, (3.3)

EHE

1

t, (3.4)

where , and are the material permittivity (in a unit of F/m), permeability (in a unit

of H/m) and electric conductivity (in a unit of S/m, contributing to the dissipation of

SPP propagations). Then, we discretize the time-dependent partial derivatives in Eq.

3.3-3.4 with a time step of t . At a time node t n t , we get

n2

1n

2

1n

1

tE

HH

, (3.5)

2

1n

2

1n

1nn 1

t

HE

EE

. (3.6)

Here, a central difference approximation is applied. Eq. 3.5 and Eq. 3.6 can be written

in scalar expressions as

1 1

2 2 1( )

n n nnyx x z

EH H E

t y z

, (3.7)

11

( )

nn n nynx x z

x

HE E HE

t y z

. (3.8)

Note that, Eq. 3.5 (3.6) gives Eq. 3.7 (3.8) and other two equations with similar forms.

Here only Eq. 3.7 (3.8) is shown for conciseness.

Figure 3.1. Yee lattice in a Cartesian coordinate system. , and x y z are the grid sizes in

respective directions.

Next, in the spatial domain, the space-dependent partial derivatives can also be


17

discretized. Fig. 3.1 shows the schematics of one element (also known as Yee lattice) of

the computational regions in a Cartesian coordinate system. Here, , and x y z are the

grid sizes in respective directions; , and i j k are integers and the lattice center

coordinates are ( , , i x i y k z ). Then, Eq. 3.7 and Eq. 3.8 can be re-written as

1 1

2 2

1 1( , 1, ) ( , , )

1 1 1 1 2 2( , , ) ( , , ) [2 2 2 2

1 1( , , 1) ( , , )

2 2 ], 3.9

n n

z zn n

x x

n n

z z

E i j k E i j kt

H i j k H i j ky

E i j k E i j k

z

1 1

2 2

1

1 1

2 2

1 1 1 1( , , ) ( , , )

1 1 2 2 2 2( , , ) ( , , ) [2 2

1 1 1 1( , , ) ( , , )

2 2 2 3.102 ],

n n

z zn n

x ijk x ijk

n n

y y

H i j k H i j k

E i j k A E i j k By

H i j k H i j k

z

where

1 1( , , ) ( , , )

2 2(1 ) / (1 )1 1

2 ( , , ) 2 ( , , )2 2

ijk

i j k t i j k t

A

i j k i j k

, (3.11)

1( , , )

2( ) / (1 )1 1

( , , ) 2 ( , , )2 2

ijk

i j k tt

B

i j k i j k

. (3.12)

Then, we obtain the central equations for FDTD simulations i.e. Eq. 3.9-3.10 (and

other four equations not shown). Maxwell’s equations are simplified into these simple

algebraic formulas. One may find that in space domain, only E fields in the line centers

and H fields in the face centers need to be calculated, as illustrated by the arrows in

Fig. 3.1; while in time domain, H fields at time node 1

( )2

n t i.e. 1

2n

H can be

calculated by nE and

1

2n

H ; while 1nE are derived by n

E and 1

2n

H . Given an

initial condition, the evolutions of EM fields with time can be iteratively solved by

computers. The updating of E fields is done at time steps of 0, t , 2 t …, while H fields

are calculated at time steps of 0.5 t , 1.5 t , 2.5 t ...

In FDTD simulations, perfectly matched layers (PMLs) are normally used as

boundary conditions [6]. Their permittivity and permeability are specially designed so

that optical waves propagating from nonPML to PML decay rapidly but experience

negligible reflection. FDTD simulations also need to satisfy the Courant stability


18

condition in order to obtain convergent solutions, which is written as [7]

2 2 21 1 11/ ( ) ( ) ( )c t

x y z

. (3.13)

It’s noted that in practical simulations, 2 dimensional (2D) FDTD assisted by effective

index method can be used to simplify 3D models [8]. This is extremely useful for

large and slow-varying photonic components. However, in more general cases, 3D

FDTD simulation is recommended for accurate solutions. Fig. 3.2 shows two relevant

examples using MEEP based FDTD simulations [9]. Fig. 3.2(b) studies the beating

length of a directional coupler (schematically shown in Fig. 3.2(a)) [10]. Here, the 2D

model is simplified from a 3D silicon-on-insulator circuit by equivalent effective

index method [11]; the excitation source in FDTD simulations is continuous wave at

1550 nm. When using a pulse light as excitation, the wavelength-dependent splitting

ratios can be studied by frequency analysis using discrete Fourier transforms (DFT).

Fig. 3.2(d) simulates a 3D L3 photonic crystal (PhC) cavity (with hexagonal lattice,

schematically shown in Fig. 3.2(c)) [12]. In the first study, we employ a transient

pulse light to excite the cavity. Then, by performing DFT analysis of the decay of

electric fields, the cavity’s resonant frequencies and quality factors can be extracted. In

the second study, we use a continues wave at the resonant frequency as excitation, and

the field distributions of a cavity mode can be simulated, as shown in Fig. 3.2(d).

Figure 3.2. (a) Schematics of a two-dimensional directional coupler. The core is assumed as Si

with dimensions of 300×300 nm2; the cladding is SiO2. After equivalence by effective index

method, ε1 = 6.85 and ε0 = 2.1. (b) Ey field distributions of the 2D directional coupler at a

continuous wave excitation. Computational domain [x, z] = [(-1,1) , (0, 20)] μm. (c) Schematics

of a 3D L3 photonic crystal cavity. The permittivities of cladding and core are ε2 = 1 and ε3 =

11.2, respectively. (d) Ey field distributions of a resonant mode of the L3 cavity.


19

3.2 Finite element method

This section discusses finite element method (FEM). We know that normally practical

physics problems can be simplified into boundary value models governed by different

kinds of nonlinear partial differential equations (PDEs) such as Maxwell’s equations,

the laws of thermodynamics, Newton’s laws of motions, structural mechanic laws, etc.

As a powerful algorithm discretizing PDEs, FEM is useful not only in computational

electromagnetics (e.g. photonics) but also in other areas of physics as well as solving

coupled multi-physics problems [13]. In this thesis, we use FEM primarily as optical

mode solvers; it is also used for solving multiphysics problems. FEM is a nice

supplement to FDTD techniques. We note that mode analyses of optical waveguides

are fundamental for investigation of photonic components (with slow variations along

the propagation axis). Studying the mode effective index can largely simplify the

model’s complexity. Beside FEM, frequently used mode solvers also include finite

difference method [14], film mode matching method [15], etc.

In FEM implementations [16-17], the computational domain is firstly meshed into

smaller subdomains i.e. finite elements (with shape of triangular, quadrilaterals, etc.).

Then complicated PDEs are transferred into simple equations by discretizing spatial

partial derivatives. In each subdomain, local residual function is defined to depict the

solutions’ convergence, and then all local functions are recombined and systematically

re-assembled into a group of global residual equations. Finally, by combing with initial

values and boundary conditions, user-desired solutions at specific elements can be

computationally obtained. Note that in the acquisition of stable and convergent

solutions, variational methods are used to minimize the residual functions.

Figure 3.3. A triangle element in the FEM implementation.

In the next paragraphs, we consider a simple example: a 2D FEM analysis of an

optical waveguide mode, in order to get a deeper understanding of FEM

implementations. As discussed in previous sections, the basis of solving the guiding

electromagnetic wave is to find solutions to the governing Helmholtz equation

2 2 0k , (3.14)

where denotes the desired electric or magnetic field. A residual function can then be

defined as


20

2 2 2 21( ) ( ) ( ) )

2S

R k dSx y

, (3.15)

depicting the error or convergence of the obtained solutions. Since the computational

domain is discretized into finite elements (with a total number of N), the global residual

can be re-written as the sum of the local residual functions in all elements:

2 2 2 2

1

( ) [( ) ( ) ]2

Ne e e

e

e

AR k

x y

. (3.16)

Here, e denotes one triangular element as illustrated in Fig. 3.3. The element area is Ae,

and 1, 2 and 3 denotes the element’s three nodes. We assume that at a random point O

in the element, e can be approximated as a polynomial function of x and y,

2 2 ...e a bx cy dx fy gxy . Note that higher power of the polynomial

function ensures higher accuracy, but more computational resources are required. For

simplicity, e is taken as a linear function of x and y in our following analysis

e a bx cy . (3.17)

Applying Eq. 3.17 in the nodes 1, 2, 3, we obtain three linear equations

( 1, 2, 3)ei i i ia b x c y i . Combining these equations, we derive the expressions

of a, b and c as

, , ea b c

a

b

c

, (3.18)

where 1 2 3 1 2 3 1 2 3 1 2 3, , , , , , , , , , ,e e e ea a a b b b c c c a b c ,

1 2 2 1( ) / (2 )i i i i i ea x y x y A , 1 2( ) / (2 )i i i eb y y A and 2 1( ) / (2 )i i i ec x x A . Then,

Eq. 3.18 can be inserted into Eq. 3.17, and we obtain

T

e e u , (3.19)

where 1 2 3, , and i i i iu u u u a b x c y u .

Moreover, x and y dependent partial derivatives can be discretized, and according to

Eq. 3.19, we obtain

Tee

x

b , (3.20)

Tee

y

c . (3.21)


21

Then, we can insert Eq. 3.20-3.21 in Eq. 3.16, and the residual function can be

rewritten in a matrix form as

2

1

( ) { }2

NT Te

e e e e e e

e

AR k

K L , (3.22)

where T T

e K b b c c and

2 1 11

1 2 112

1 1 2

e

L .

If assuming the nodes’ number in the whole computational domain is M, Eq. 3.22 can

be recombined and reassembled, and we derive a global residual equation given by

2( ) { }2

g T g TeAR k K L , (3.23)

where 1 2, ... M is the matrix of electromagnetic fields in M nodes;

1

=N

g g

e

e

K K and 1

=N

g g

e

e

L L are M×M global matrices obtained by adding all local

matrices eK and eL . Hence, all except a 3×3 submatrix (corresponding to eK and eL ),

elements in g

eK and g

eL are all zero.

Until now, we have obtained the central equation Eq. 3.23 for FEM simulations.

PDE is simplified into the linear and matrix form, and the numerical analysis can be

readily implemented by e.g. Matrix-based MATLAB when incorporating with

boundary conditions and initial values.

In this thesis work, we use commercial software COMSOL Multiphysics for the

FEM simulation [18]. For complicated problems which are computationally costly, we

run COMSOL in remote shell servers at Royal Institute of Technology (KTH) i.e. HP

Proliant (with 12 cores and a RAM of 82 GB) [19]. Fig. 3.4 shows an example of

COMSOL simulations of a multi-physics problem, which studies the thermo-optic

(TO) effect of a micro heater placed on top of a SOI waveguide. Here, Si waveguide

has a core size 450×250 nm2, and it’s embedded in SiO2 with a micro heater placed

500 nm on top. Fig. 3.4(a) shows the optical mode distribution in the SOI waveguide;

while Fig. 3.4(b) shows the temperature distributions when the temperature of the

micro heater increases from 200C to 40

0C. By coupling these two models together,

influence of micro heater on the optical waveguide can be predicted.


22

Figure 3.4. (a) Optical mode distribution of a Si waveguide at room temperature. (b)

Temperature distribution when increasing the micro heater’s temperature from 200C to 40

0C.

References

[1] K. S. Yee, “Numerical solution of initial boundary value problems involving

Maxwell's equations in isotropic media,” IEEE Trans. Antennas Propagation, vol.

14, pp. 302-307 (1966).

[2] A. Taflove, “Review of the formulation and application of the finite-difference

time-domain method for numerical modeling of electromagnetic wave infractions

with arbitrary structures”, Wave Motion, vol. 10, pp. 547-582 (1988).

[3] A. Taflove, “Computational Electrodynamics: The Finite-difference Time-domain

Method”, Artech House, Norwood, MA (1995).

[4] J. van Roey, J. van der Donk, and P. E. Lagasse. Beam-propagation method:

analysis and assessment. J. Opt. Soc. Am., 71:803–810, (1981).

[5] J. Hong, W. Huang, and T. Makino, “On the transfer matrix method for

distributed-feedback waveguide devices,” J. Lightwave Technol. 10(12), 1860–

1868 (1992).

[6] W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, “The perfectly matched layer

(pml) boundary condition for the beam propagation method,” IEEE Photon.

Technol. Lett., vol. 8, pp. 649-651 (1996).

[7] F. Zheng, Z. Chen, and J. Zhang, “A finite-difference time-domain method without

the Courant stability conditions,” IEEE Microw. Guided Wave Lett.9(11), 441–

443 (1999).

[8] E. I. Smotrova, A. I. Nosich, T. M. Benson, and P. Sewell, "Cold-cavity thresholds

of microdisks with uniform and nonuniform gain: quasi-3-D modeling with

accurate 2-D analysis," IEEE J. Sel. Top. Quantum Electron. 11, 1135-1142

(2005).

[9] Ardavan F. Oskooi, David Roundy, Mihai Ibanescu, Peter Bermel, J. D.

Joannopoulos, and Steven G. Johnson, “MEEP: A flexible free-software package

for electromagnetic simulations by the FDTD method,” Computer Physics

Communications 181, 687–702 (2010).

[10] A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J.

Lightwave Technol.3(5), 1135–1146 (1985).

[11] G. B. Hocker and W. K. Burns, "Mode dispersion in diffused channel waveguides

by the effective index method," Appl. Opt. 16, 113-118 (1977).


23

[12] Y. Akahane, T. Asano, B.S. Song, and S. Noda, "High-Q photonic nanocavity in

two-dimensional photonic crystal," Nature 425, 944 (2003).

[13] G. Strang and G. Fix. An Analysis of The Finite Element Method. Wellesley

Cambridge Press, 2nd edition, 2008.

[14] M. S. Stern, "Semivectorial polarized finite difference method for optical

waveguides with arbitrary index profiles," IEE Proc. J. Optoelectron. 135, 56-63

(1988).

[15] A. S. Sudbo, "Film mode matching: a versatile numerical method for vector mode

field calculations in dielectric waveguides," Pure Appl. Opt. 2, 211-233 (1993).

[16] M. N. O. Sadiku, "A simple introduction to finite element analysis of

electromagnetic problems", IEEE Trans. Educ., vol. 32, pp.85 -93 (1989).

[17] J. P. Bastos and N. Sadowski Electromagnetic Model by Finite Element

Methods, 2003.

[18] COMSOL Multiphysics: http://www.comsol.com/

[19] http://www.kth.se/ict/2.9136/computer-systems/shell-servers

http://www.comsol.com/

http://www.kth.se/ict/2.9136/computer-systems/shell-servers

Chapter 4. Fabrication and Characterization Techniques

25

Chapter 4

Fabrication and Characterization Techniques

In this chapter, we firstly give an overview of the fabrication process of photonic

integrated circuits (PICs). Then the fabrication techniques for film deposition, litho and

etching which are frequently used in this thesis are summarized. After discussing the

material and device characterization methods, we present experimental results of some

photonic devices in the chapter end.

4.1 Photonic integrated circuits: an overview

In modern optical fiber communications and optical interconnects systems, a large

number of sophisticated optical components are usually required. To bring down the

overall cost, reduce the system volume, increase the performance stability etc., it’s

essential to replace the conventional bulk components with photonic integrated circuits

(PICs).

Various material platforms can be used for PICs, among which, silica-on-silicon is

commonly used in current telecommunication systems such as dense wavelength

division multiplexing (DWDM) [1]. The advantages include low-loss and convenient

coupling, etc. However, the integration density is limited because the low index

contrast between the core and the cladding is not suitable for sharp bends. As an

example, an arrayed waveguide grating (AWG) which is frequently used as

(de)multiplexers has a typical size of cm2 [2]. III-V semiconductor platform, on the

other hand, is widely used in optoelectronics to realize active photonic devices

including detectors, optically/electrically pumped lasers, amplifiers, modulators, etc.

[3-4]. The refractive index of III-V semiconductors is large, enabling denser

integrations, e.g. size of AWG based on III-V can be decreased to mm2 [5]. However,

the technology has certain drawbacks such as expensive material, high absorption,

and low fabrication throughput (typical wafer size is 3 inch) [6]. On the contrary,

PICs based on silicon-on-insulator (SOI) platform are very promising. Si has a very

high refractive index (comparable to III-V, much larger than silica), and it is transparent

in telecom wavelength. As an element, it is abundant in nature. Most importantly, Si

wafer is much less fragile than III-V wafer, thus large wafer-scale (SOI wafer size can

reach 12 inch) processing is feasible; and the fabrication is highly compatible with the

existing CMOS processes which are already used to fabricate nowadays electronic

circuits [7-8].

Fig. 4.1 shows the flow chart of the main processes in semiconductor fabrications.

Starting with a wafer or a small piece of sample (used in research e.g. in our


26

experiment), film depositions are firstly performed. Plasma enhanced chemical vapor

deposition (PECVD) is used for deposition of amorphous silicon (a-Si), silicon dioxide,

silicon nitride, etc. Electron beam evaporation (EBE) is normally used for coating of

metal layers. After film deposition, the GDS (a file format used for pattern generation)

designs are transferred to resists by lithography. Widely used litho methods include:

photolithography, nanoimprint, electron beam lithography (EBL), etc. Then etching

processes are used to transfer the patterns from photoresists or Ebeam resists to

semiconductors. We use dry etching technique e.g. inductive coupled plasma - reactive

ion etching (ICP-RIE) for anisotropic and deep etchings. Wet etching is applied for

creating undercuts.

In practical fabrications, the chips are normally processed for multiple rounds, and

several other fabrication processes might be included, such as doping,

chemical-mechanical polishing (CMP), annealing, oxidization, etc.

Figure 4.1. Flow chart of a typical semiconductor fabrication process.

After finishing the chip fabrication, characterizations are performed to test the

overall performance. Normally, light from a tunable laser source can be coupled into

fabricated devices by grating couplers or butt coupling. We also use an evanescent

coupling method to couple fiber mode into hybrid plasmonic modes. The transmission

properties can be tested by monitoring the outputs with infrared (IR) CCD camera. An

optical pump system is also built up to characterize the spontaneous emission from

III-V cavities.

The reminder of this chapter is organized as follows: section 4.2 introduces the

major used micro/nano fabrication tools. Section 4.3 explains the characterization

methods and section 4.4 summarizes the experimental results.

4.2 Fabrication techniques

4.2.1 Plasma enhanced chemical vapor deposition

Commercial SOI wafer normally has standard thicknesses of oxide buffer and top

silicon film. To form SOI wafers with any desired film thicknesses, we use plasma

enhanced chemical vapor deposition (PECVD) technology for hydrogenated

amorphous silicon (a-Si:H) and SiO2 deposition. Very high-quality materials and

accurate control of film thicknesses can be achieved by recipe optimization. Figure 4.2

illustrates a simple sketch of the PECVD system we use in the Electrum lab at KTH


27

[9-11].

The deposition takes place mainly in following steps. At first, the PECVD chamber

is evacuated and pumped down. Then the precursory gas mixtures are injected

uniformly into the chamber through a showerhead (with a large number of holes with

diameter ~ 0.4 mm). Thirdly, by applying RF (radio frequency) power with a suitable

frequency (LF - low freq. 380 kHz or HF - high freq. 13.56 MHz), plasma can be

created after gases passing through the showerhead. By interacting with plasma’s

highly energetic electrons, the precursory gas mixtures are dissociated into free

molecules; and these molecules can diffuse to the sample surface and form new bonds

through chemical reactions, resulting in the film depositions.

Figure 4.2. A sketch of the plasma enhanced chemical vapor deposition system. Reprinted from

[12] with permissions.

We need to note that for each process the actual plasma impedance is adjusted

automatically by the matching units. LF generator allows for applying high energetic

plasma up to 1000 W and HF generator allows for plasma up to 300 W. In addition, the

chamber pressure and temperatures of shower head and bottom electrode also need

systematic control in the PECVD reactor. Typical pressure ranges are from a few

millitorr (mTorr) to a few hundred mTorr during the process, adjusted by the valve of

the vacuum pump, while typical deposition temperatures are kept around 250 oC or 300

oC.

Table 4.1. Optimized PECVD recipes for SiO2 and a-Si:H deposition.

Materials SiO2 a-Si:H

SiH4 flow 20 sccm 60 sccm

N2O flow 2000 sccm NA

Ar2 flow NA 270 sccm

Pressure 300 mtorr 5 mtorr

RF power 800W 10W

RF frequency 380 kHz 13.56 MHz

Platen temperature 250 oC 250

oC

Showerhead temperature 300oC 250

oC

Deposition rate ~320 nm/minute 5 nm/minute


28

The optimized recipes of a-Si:H and SiO2 PECVD deposition are given in Table

4.1, where chemical reactions SiH4 (g) → Si (s) + 2H2 (g) and SiH4 + 2N2O → SiO2 + 2

H2 + 2N2 are applied. Note that for the deposition of a-Si:H, the hydrogen quota

(provided by SiH4) should be properly chosen in order that the point defects from

unsaturated dangling bonds of silicon are properly depassivated without generating

undesired pores. The refractive indices of as deposited a-Si:H and SiO2 are around

3.545 and 1.45, respectively. The material loss of a-Si:H is around 1.5dB/cm. The

surface roughness (RMS) of a-Si:H and SiO2 measured by atomic force microcopy

(AFM) are around 8 Å and 4 Å, respectively; accuracy of deposition thickness can be

controlled within several nm [13].

4.2.2 Electron beam evaporation

Electron beam evaporation (EBE) is a form of physical vapor deposition. In our

experiments, EBE is used for coating gold, aluminum oxide, silver, titanium,

germanium, etc. Fig. 4.3 illustrates a simple sketch of the EBE system (Provac PAK

600) used in Electrum lab at KTH. During the evaporation process, the material to be

coated is firstly bombarded with energetic electron beams emitted by a charged

filament in a high vacuum chamber. Then the sample temperature increases and

transforms the material into gaseous phase. Afterwards, the vapors diffuse to the

sample surface and precipitate into solid form since the sample temperature is far below

the material’s melting point. In the EBE system, the material is filled in a crucible

placed on a holder which is water-cooled. The crucible can be rotated and there exist 7

pockets containing different materials. A shutter is automatically controlled during the

process in order to blank the vapors before e-beam stabilizes. The sample to be coated

is placed upside down on a wafer holder, which is mounted on a rotatory shaft (speed:

10 - 20 rpm) in order to achieve uniform coating. The coating thickness is dynamically

monitored by a quartz crystal. It’s noted that a very low pressure around 5×10-7

mbar

should be maintained during the process, in order to avoid undesired oxidation and

impurities. The deposition rate of EBE can be adjusted within a very wide range from 1

nm/min to 1 μm/min. In our experiments, gold and silver are deposited at a rate of 1 Å/s

and aluminum oxide at a rate of 2 Å/s. The surface roughness (RMS) of as deposited

gold measured by atomic force microcopy (AFM) is around 8 nm [Paper A].

Figure 4.3. A sketch of the electron beam evaporation system.


29

4.2.3 Electron beam lithography

After film deposition, lithography techniques are applied to transfer the user-defined

micro/nano patterns onto the sample. Standard litho methods include: conventional

photolithography (mercury lamp g-line 436 nm and i-line 365 nm), deep ultra-violet

(DUV) photolithography (excimer lasers 248 nm and 193 nm), nanoimprint

lithography (with template), electron beam lithography (EBL), focused ion beam (FIB),

etc. For our thesis work, we use primarily EBL system in Albanova Cleanroom at KTH

to define our nano structures [14-15]. The main advantage of EBL is the high resolution,

e.g. the diffraction limit of electron waves (de Broglie wavelength) accelerated by 10

kV voltage is typically ~ 10 pm. EBL is also easy to implement and very flexible.

The principle of EBL is to use a focused electron beam to scan and draw a

user-defined pattern on a sample surface which is coated with a thin layer of chemicals

(ebeam resists). Upon exposure to electrons, the resists can experience either chain

scission or cross link. Then either the exposed and unexposed areas can be selectively

dissolved when putting the sample into a developer, shaping the user-desired patterns.

Depending on the solubility of the exposed area, resists are classified into positive and

negative resists. Fig. 4.4 shows the respective exposure and development processes.

Then optical post-bake (to improve the resist hardness and adhesion) and oxygen

descum (to clean resist radicals) are performed after development, and the sample is

ready for the following liftoff, etching or ion implantation processes.

Figure 4.4. Exposure and development using positive and negative resists.

Fig. 4.5 shows a sketch of the EBL system (Raith 150 from Raith Gmbh) we used

in Albanova lab at KTH main campus. The main parts include a scanning electron

microscope (SEM), lithographic exposures related hardware and a high precision

moving stage which are all sealed in a sound-proofing container to minimize vibrations.

Other parts include a special D/A (digital-to-analog) converter (pattern generator) and a

global control computer. A simple explanation of EBL implementation process is as

follows. Firstly, electron source is generated by a gun (Gemini column) with a Schottky

field-emission filament, as shown in Fig. 4.5. The column acceleration voltage ranges

from 200 V to 30 kV, determining the beam size as well as the penetration depth. Then

the beam passes through an aperture with typical sizes of 30 μm, 10 μm, 7.5 μm etc.,

where smaller aperture means better beam convergence hence higher resolution while

lower beam current. A beam blanker is cascaded afterwards which can be switched on

and off automatically during the scanning process to avoid undesired exposure. Next,

the beam passes through a group of fine electric and magnetic coils for beam


30

adjustments including beam alignment, stigmation optimization and beam (de)focusing.

At last, the beam is scanned by a deflecting system which is controlled by signals

transferred from the user-defined patterns by a pattern generator (D/A converter). Note

that, the scanning is realized with the assistance of stage movement (XYZ directions)

which is controlled by a high precision laser interferometric system.

Figure 4.5. A sketch of the electron beam lithography system.

During EBL process, there are following issues worthy special attentions [15-17].

(1) Compensation of stitching errors. As discussed above, in EBL process, the

patterns are scanned by deflecting the beam with a group of magnetic and electric coils.

However, due to the limited deflection angle, only a small area WF (writing field,

typically 100×100 μm) can be scanned at a time. Hence, in order to expose structures

with a footprint larger than a WF, the pattern is divided into multiple WFs and

exposures take places in one WF after another, where the transitions between WFs are

realized by moving the high precision stage. In practice, because of the random errors

existing in the stage movement, there are always significant separations between

neighboring WFs also known as stitching errors. This type of error can be compensated

by several approaches. Writing field alignment is a built-in compensation method. It is

realized by adjusting the deflection system by focusing on a tiny spot (diameter ~ 50 nm)

in multiple neighboring positions. Other compensation methods include over-exposure,

introducing extra-patches, etc.

(2) Compensation of proximity effect. Proximity effect is related to the undesired

exposure of ebeam resist due to the backscattering and forward scattering of the

electron beams. Proximity effect can result in the broadening of the adjusted beam

hence changes the actual exposure area and beam density. This effect is extremely

unfavorable for sensitive ebeam resist e.g. hydrogen silsesquioxane (HSQ) since in

such cases, the scattered beam is intense enough to crosslink the chemical and form

undesired over-exposed areas. When patterning large area (e.g. microdisk) or dense

(photonic crystals) geometries, this effect is also a key role to determine the litho

qualities. Luckily, this effect can be properly compensated by designing the dose


31

distribution as well as a series of dose test.

(3) Accurate overlay of multiple layers. For complicated devices with multiple

layers, several rounds of lithography need to be performed, and the alignment accuracy

is essential. In the EBL process, together with structures, we also make alignment

markers in each round. These markers can be input into EBL system and the stage

coordinates can be adjusted accordingly. The alignment accuracy is ~ 50 nm -100nm

given sound calibration.

Table 4.2 shows a list of optimized recipes we used in our EBL experiments. Here,

the dose is defined by Dose × exposure area = beam current × exposure time/step size2.

Table 4.2. Optimized electron beam lithography recipes.

Resists ZEP 520A Ma-N 2403

Resist type Positive Negative

Spin speed ~ 5500 rpm ~ 3500 rpm

Acceleration Voltage 25 kV 25 kV

Prebake 180 oC, 10 min 90

oC, 3 min

Dose 60 μAs/cm2 110 μAs/cm

2

Developer P-xylene, 100 sec Ma-D 525S, 3 min 30 sec

4.2.4 Inductive coupled plasma -reactive ion etching

As mentioned in section 4.1, inductive coupled plasma - reactive ion etching (ICP-RIE)

is used in our experiments for anisotropic dry etchings of Si and SiO2. The machine we

use is Advanced Oxide Etcher (AOE) from Surface Technology Systems (STS) [12],

which is suitable for deep etching with vertical sidewalls and accurate dimensions. Fig.

4.6 shows a sketch of the RIE system we use. It consists of following main parts:

inductively coupled coils to generate the etching plasma with required density, a RF

biased platen to accelerate the charged ions, a vacuum chamber which is electrically

grounded, and some other supplementary components. Note that the wafer platen is

normally temperature controlled and cooled by helium flows in order to avoid resist

burning, and the chamber pressure is controlled by adjusting the valve of the central

pump. Actually, in a RIE process, there are two simultaneous processes i.e. etching and

deposition, and the etching mechanism also include two forms: physical bombardment

and chemical reaction [18]. Take Si etching as an example. Firstly, the gas mixture SF6

and C4F8 passes through the inductively coupled coils, generating plasma containing

reactive neutral radicals (F, CFx); and the plasma density is determined by the RF power

applied on the coils. Then, the plasma ions are attracted by the reversed power on platen

and bombard the sample surface. In this process, on one hand, the sample material i.e.

Si reacts with the F radicals (from SF6) and forms volatile chemicals SiF4 which can be

easily removed; on the other hand, CFx monomers (from C4F8) in the plasma results in

the deposition of a carbon-fluorine polymers. For polymers on the sample surface, they

can be sputtered away by the later highly energetic ions, hence the etching in the

horizontal direction can continue; while for the polymers on the sample sidewall, they

experiences negligible physical destruction and they can sustain and act as an etching

prohibitor (passivation) in the vertical direction. In this way, the etching can be

selective and anisotropic.


32

The net etching rate is determined by the competition between deposition and

etching. By increasing the portion of F radicals and the platen power, both physical and

chemical etching rates are enhanced hence the net etching rate is increased. Increasing

the platen power also means stronger bombardment as well as more vertical sidewall,

but normally it causes more sidewall damage and decreases the mask’s selectivity. High

pressure means denser plasma hence higher etching rate, but stronger ion-ion

interaction which decreases the plasma’s directionality and results in lower aspect ratio.

To achieve a vertical sidewall, special care is also needed to balance the deposition and

etching processes.

Figure 4.6. A sketch of an inductive coupled plasma -reactive ion etching system. Reprinted

from [12] with permissions.

Table 4.3 lists out the ICP-RIE recipes we used for Si and SiO2 etchings in our

experiments. The recipes are optimized for a high aspect ratio etching with vertical

sidewalls.

Table 4.3. Optimized ICP-RIE recipes for Si and SiO2 etchings.

Materials Si (fast) Si (slow) SiO2

C4F8 flow 40 sccm 9 sccm 10 sccm

SF6 flow 28 sccm 6 sccm NA

H2 flow NA NA 15 sccm

He flow NA NA 174 sccm

Pressure 10 mtorr 15 mtorr 15 mtorr

Platen temperature 20 °C 10 °C 10 °C

Coil power 800 W 500 W 1000 W

Platen power 20 W 20 W 200 W

Etching rate ~ 420 nm/min ~ 220 nm/min ~ 280 nm/min

4.3 Characterization methods

This section briefly introduces the methods we use for material characterization and

device characterization.


33

4.3.1 Material characterization

For the investigation of the thicknesses and dielectric constants (complex refractive

index or dielectric function) of deposited thin films, ellipsometery (Horiba UVISEL ER)

is normally used. In the process, a laser source is projected onto the sample surface with

an angle, and by detecting the change of the polarization and phase of the transmitted or

reflected light and comparing with a standard model, the relevant information can be

found. The source can range from 190 nm to 2100 nm, and the angle can be adjusted

from 55° to 90°. Mapping of up to 8 inch wafers is available.

For the investigation of the sample’s surface profile such as the surface roughness or

the step height due to etching or deposition, we have used stylus profilometer

(KLA-Tencor P-15) and atomic force microscope (AFM from Veeco/Digital

Instruments). In both cases, a fine stylus or tip is used to scan the sample surface and the

height can be translated into detectable signals. In our experiments, stylus profilometer

is normally used for measuring structures with a feature size larger than 1 μm due to

relatively large stylus size. For fine structures, we use the AFM (tip size normally < 100

nm) owing to its accuracy, but the process also consumes much longer time.

Another frequently used tool is scanning electron microscope (SEM from Zeiss) for

measuring the sample's surface topography and composition. Compared with AFM 3D

surface mapping, SEM is easy to implement and takes much shorter time. The

measurement is based on the detection of signals originating from the scattering

electrons when scanning a focused electron beam on a sample surface. The secondary

electrons generated by inelastic scattering are used for the imaging purpose; while

back-scattered electrons generated by elastic scattering are used for the spectral

analysis (also referred as energy-dispersive X-ray spectroscopy: EDS), where the

material compositions can be found.

To measure the photon emission from bandgap semiconductors, photoluminescence

spectroscopy system is used. The measurement was performed at Unit of

Semiconductor Materials at KTH. The detailed description of the system can be found

in [19].

4.3.2 Device characterization

(1) Grating couplers

Grating couplers are a versatile method to couple light from(to) a nano-scale integrated

waveguide to(from) a single mode fiber with a typical diameter of 10 μm [20-21]. The

schematic diagram of a fiber-waveguide grating coupler system is shown in Fig. 4.7,

where the fiber tilting angle is θ; the effective index of incident wave is nin; the grating’s

pitch is Λ, and the Si waveguide effective index is neff .

Figure 4.7. Schematic diagram of a fiber-waveguide grating coupler system.


34

To fulfill the phase matching between the incident wave and the propagating wave

in Si waveguide, the pitch of gratings need to satisfy Bragg equation

22 2sin( )

effinnn

m

. (5.1)

Grating couplers have the advantages of large tolerance of alignments, high

coupling efficiency, capability of wafer scale test, etc. The drawbacks are that extra

lithography and etching processes are normally needed to define the grating couplers,

and the couplers have limited bandwidth (< 100 nm) and show strong wavelength

dependence.

(2) Direct measurement

Direct measurement is performed using a home-made setup built by Nanophotonics

group at KTH [22-23]. As schematically shown in Fig. 4.8, this setup is especially

useful for measuring the propagation losses, splittings, couplings, etc. of plasmonic

waveguides (or nanowires) [24-26]. In the implementation, the sample is imaged by an

infrared charge-coupled device (CCD) camera with the assistance of a microscope

objective (100×). Illumination light is projected on the sample by two beam splitters

and a shutter is used to switch from dark field imaging to bright field imaging. A fiber

tip fastened on a translational stage is aligned in close contact with the waveguide, and

light can be evanescently coupled from the fiber mode into the waveguide mode. To

characterize the propagation loss, we move the fiber tip parallel along the waveguide

and record the dark field images at different positions by the CCD camera. Then the

intensities of scattered light at outputs and the corresponding propagation distance can

be found by the image processing. To fabricate the fiber tip from a standard single mode

fiber (SMF), we use a hybrid method i.e. flame-heated drawing assisted by wet-etching

[27-28], and the size of the tip diameter is around 1 μm or even smaller.

Figure 4.8. Schematic diagram of a fiber-tip evanescent coupling system. Reprinted from [22]

with permissions.

Compared with methods for characterizing plasmonic devices, e.g. scanning

near-field optical microscopy [29] and leakage radiation microscopy (LRM) [30], the

applied direct measurement is easy to implement and has no requirement regarding the

substrate. The drawback is that it’s not possible to characterize the overall device

performance; it’s not straight-forward to analyze the spectral response either. Note that

different from grating coupler method, direct measurement method can record multiple

outputs with a single measurement. Hence, it is preferred due to its accuracy for

measuring beam-splitting devices such as directional couplers, multimode


35

interferometers, etc. with various splitting ratios.

(3) Butt coupling

Butt coupling method is another frequently-used approach to characterize photonic

devices. Its main advantage is that it can test the device’s spectral responses in a wide

wavelength range (e.g. > 100nm), which is much larger than the bandwidth of the

grating couplers. In the implementation, light is coupled to the waveguide facet by a

lens (e.g. gradient index lens GRIN) or lensed fiber, as schematically shown in Fig.

4.9(a). The lensed fiber we use is commercially available from OZ optics, which has a

focal spot with a diameter of 2.5 ± 0.5 μm and a working distance of 14 ± 2 μm. In

practical implementations, we also use the tapered fiber for butt coupling [31-33], as

schematically shown in Fig. 4.9(b). The tapered fiber is fabricated following the

procedures discussed in previous section. By adjusting the wet-etching recipes, the tip

diameters can be decreased to several hundred nanometers which can further decrease

the size mismatch between a fiber mode and a waveguide mode. Compared with the

commercial lensed fiber, the advantages of the tapered fiber include low cost and wide

flexibility. In our experiments [paper C], we use butt coupling methods to characterize

the plasmonic resonators in a wide spectral range (> 300 nm).

Figure 4.9. Schematic diagrams of fiber-waveguide butt coupling systems by (a) lensed fibers

(b) tapered fibers.

(4) Optical pump setup

An optical pump setup is built to characterize the photoluminescence from III-V

semiconductor materials, as schematically shown in Fig. 4.10. Such schemes have been

employed for characterization of optically pumped laser cavities [34-36]. Similar as the

butt coupling setup discussed above, light can be focused on the photonic devices by

bulk optics (lens or objectives) or fibers (lensed fibers or tapered fibers). A lensed fiber

based setup is shown in Fig. 4.10, where a 980 nm continuous-wave light source is

employed as the optical pump, and a 1×2 coarse wavelength division multiplexer

(CWDM) is used for splitting and combining of the pump and signal light.


36

Figure 4.10. Schematic diagram of an optical pump system. Note that the sizes are not in real

scale. Practically, the disk has compatible diameter with the fiber end.

4.4 Device demonstrations

Based on previously presented fabrication and characterization techniques, we have

demonstrated several plasmonic components including hybrid plasmonic directional

couplers, disks, rings and donuts. Relevant results will be discussed in the subsequent

chapter.

In this section, we present the experimental results of a tunable SOI microdisk

assisted by perfect absorbers and III-V cavities.

4.4.1 Tunable SOI microdisk assisted by perfect absorbers

The schematic diagram of the demonstrated perfect absorbers assisted SOI microdisk is

shown in Fig. 4.11. The inset picture shows the SEM image of the fabricated shallow

etch grating couplers for coupling light between a standard single mode fiber and a Si

waveguide.

Figure 4.11. Schematic diagrams of a perfect absorber assisted SOI microdisk along xz and xy

planes. Inset shows the shallow-etched grating couplers for fiber-waveguide coupling.

The processes to fabricate the device are as follows:

a) 1st Ebeam Litho. ZEP 520A is used to define the microdisk pattern.

b) 1st ICP-RIE etching. SOI sample with 250 nm top Si is etched through.

c) 2nd

Ebeam Litho. Diluted ZEP 520A (by 1:2 anisole) is used to define the

patterns of grating couplers.

d) 2nd

ICP-RIE etching. Shallow etch for the grating couplers.

e) 3rd

Ebeam Litho. ZEP 520A is used to define the window for the depositions of

perfect absorbers.


37

f) Ebeam evaporation of Au-Al2O3-Au layers (EBE).

g) Following the EBE, a liftoff process is performed to get the final device.

Fig. 4.12(a) show the SEM image of the fabricated microdisk with a perfect absorber

situated in the disk center. The disk radius is ~ 7.2 μm and the absorber radius is ~ 5 μm.

The tuning mechanism is based on the temperature shift resulted from the absorption of

pump light by the Au-Al2O3-Au absorbers. Since the absorber has a smaller diameter,

the fundamental whispering gallery mode (WGM) of the Si disk is not affected.

Compared with traditional electric-thermo tuning (with heaters placed on cladding

oxide layer), the scheme features a low-power switching and a fast switching speed. Fig.

4.12(b) shows the optical microscope image of the fabricated microdisk in real colors.

The absorber exhibits a purple color owing to its unique absorption in the visible

wavelength range. Fig. 4.12(c) is the optical microscope image of a microdisk with

only a simple gold layer in the center. In Papers I and J, detailed descriptions of the

static and dynamic tuning are discussed.

Figure 4.12. (a) SEM image of the fabricated microdisk assisted by a perfect absorber. Scale bar:

10 μm. (b) and (c) are optical images in true color, (b) the fabricated device and (c) a microdisk

with a gold layer in the center.

4.4.2 III-V cavities

At KTH Materials and Nano Physics department, a novel technology for integration of

III-V on silicon by epitaxial lateral overgrowth (ELOG) has been developed using

hydride vapor phase epitaxy (HVPE) [37-38]. Aiming to demonstrate a monolithic Si

laser, we have performed the design, fabrication and characterization of III-V

quantum-well (QW) cavities. We have mainly studied the types of cavities i.e. pedestal

microdisk cavity and photonic crystal cavity.

(1) Pedestal microdisk cavities

Figure 4.13(a) and (b) are the SEM images of the fabricated pedestal microdisks in the

1st round (sample#1) and 2

nd round (sample#2). To fabricate such devices, EBL is used

to define the pattern, and ICP helps to transfer the pattern to semiconductors. At last,

selective etching is applied to make the undercuts.

For the device measurements, sample#1 is measured by the home-made setup as

described in section 4.3.2. Pump source is a continuous wave 980 nm laser with an

average power up to ~ 90 mW. Fig. 4.13(c) shows the measured photoluminescence

spectra of the semiconductor microdisks ranging from 1200 nm to 1650 nm. We can see

(a) (b)

(c)


38

that there exist small amplitude ripples which originate from the cavity resonances. The

resonance amplitude increases with the increase of pump power. However, the devices

don’t show lasing-like resonances even at a pump power of 70 mW. We think it’s

mainly due to the thermal issues which are essential when applying continuous-wave

pumping. For sample#2, longer wet-etching time is employed to create sharper pedestal

geometry, as shown in Fig. 4.13(b). Sample#2 is measured by a photoluminescence

system (HR 800 HORIBA) in Lab of Semiconductor Materials at KTH [39-41]. We can

see from Fig. 4.13(d) that sharp resonances can be achieved from sample#2 when

operating at 77 K.

Figure 4.13. (a) SEM image of 1st round pedestal microdisk (sample#1). (b) SEM image of 2

nd

round pedestal microdisk with deeper undercuts (sample#2). (c) Room temperature

photoluminescence from sample#1 measured by the home-made setup. (d) PL spectrum from

sample#2 measured by a PL system at 77 K.

(2) Photonic crystal cavities

Figure 4.14 shows the SEM images of photonic crystal (PhC) hexagon and line cavities.

The fabrication processes are similar as for microdisks (with no wet etching though).

Ebeam doses for PhCs as shown in Fig. 4.14(a) and (b) (type I) are higher than for PhCs

as shown in Fig. 4.14(c) and (d) (type II). We can see that after etching, for type I PhCs,

InP/InGaAsP/InP nano holes and pillars are partially destroyed while type II PhCs

survive. We think this is mainly due to the proximity effect i.e. the actual dose received

by a single hole is larger than the input does, due to the influence of surrounding

exposed holes. The ICP etching has a very high aspect ratio (AR) ~ 10:1. A zoomed-in

SEM image of the PhC line cavity is shown in Fig. 4.15(a), and the photonic bands

calculated by Bloch’s theorem is shown in Fig. 4.15(b).


39

Figure 4.14. SEM images of the fabricated photonic crystal cavities. (a) Hexagon cavity with

normal Ebeam dose. (b) Line cavity with normal Ebeam dose. (c) Hexagon cavity with slightly

lower Ebeam dose. (b) Line cavity with slightly lower Ebeam dose.

Figure 4.15. (a) Zoom-in SEM images of the fabricated photonic crystal line cavity. (b)

Simulated photonic bands of the photonic crystals with hexagonal lattice.

References

[1] M. Kawachi, "Recent progress in silica-based planar lightwave circuits on silicon,"

IEE Proc. Optoelectronics 143, 257-262(1996).

[2] R. Adar, C. H. Henry, C. Dragone, R. C. Kistler, and M. A.

Mildbrodt, "Broad-band array multiplexers made with silica waveguides on


40

silicon", J. Lightw. Technol., vol. 11, no. 2, pp.212 -219 (1993).

[3] D. Liang, G. Roelkens, R. Baets, and J. Bowers, “Hybrid integrated platforms for

silicon photonics,” Materials 3(3), 1782–1802 (2010).

[4] F. Kish, et. al, “Current status of large-scale InP photonic integrated circuits,”

IEEE J. Sel. Top. Quantum Electron.17, 1470–1489 (2011).

[5] Y. Barbarin, X. j. M. Leijtens, E. a. j. M. Bente, C. M. Louzao, J. R. Kooiman, and

M. K. Smit, " Extremely small AWG demultiplexer fabricated on InP by using a

double-etch process," in Optical Amplifiers and Their Applications/Integrated

Photonics Research, Technical Digest (CD) (Optical Society of America, 2004),

paper IThG4.

[6] D. Liang and J. E. Bowers, “Photonic integration: Si or InP substrates?” Electron.

Lett.45(12), 578–581 (2009).

[7] J. S. Orcutt, B. Moss, C. Sun, J. Leu, M. Georgas, J. Shainline, E. Zgraggen, H. Li,

J. Sun, M. Weaver, S. Urošević, M. Popović, R.J. Ram, and V. Stojanović, "Open

foundry platform for high-performance electronic-photonic integration," Opt.

Express 20, 12222-12232 (2012)

[8] M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat.

Photonics 4(8), 492–494 (2010).

[9] L. Wosinski, L. Liu, M. Dainese, and D. Dai, “Amorphous silicon in nanophotonic

technology”, Proceedings of the 13th European Conference on Integrated Optics,

ECIO 2007, Copenhagen, Denmark, (2007).

[10] https://snf.stanford.edu/SNF/equipment/chemical-vapor-deposition/pecvd/sts-pec

vd-tool

[11] Z. Wang, “Investigation of new concepts and solutions for silicon nanophotonics,”

doctoral thesis, ISSN 1653-7610, KTH, Sweden, (2010).

[12] SPTS Technologies Ltd [formally Surface Technology Systems (STS)]

http://www.spts.com/ .

[13] M. Dainese, “Plasma Assisted Technology for Si-based Photonic Integrated

Circuits,” PhD thesis, ISRN 0348-4467, KTH, Sweden, (2005).

[14] https://www.raith.com/?xml=solutions%7CLithography+%26+nanoengineering

%7CRAITH150-TWO

[15] http://www.nanophys.kth.se/nanophys/facilities/nfl/manual/

[16] Raith 150 Software operation manual ver. 5.

[17] A. Holmberg. “Nanofabrication of zone plate optics for compact soft X-ray

microscope,” PhD thesis, ISSN 0280-361X, KTH, Sweden, (2006).

[18] R. J. Schul and S. J. Pearton, editors. Handbook of advanced Plasma Processing

Techniques. Springer, Berlin (2000).

[19] S. Naureen, “Top-down fabrication technologies for high quality III-V

nanostructures,” ISSN 1653-7610, PhD thesis, KTH, Sweden, (2013).

[20] D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating

coupler for silicon-on-insulator waveguides”, Opt. Lett., vol. 29, pp. 2749-2751

(2004).

[21] D. Taillaert, “Grating Couplers as Interface between Optical Fibres and

Nanophotonic Waveguides”, doctoral thesis, Ghent University, Belgium (2004).

https://snf.stanford.edu/SNF/equipment/chemical-vapor-deposition/pecvd/sts-pecvd-tool

https://snf.stanford.edu/SNF/equipment/chemical-vapor-deposition/pecvd/sts-pecvd-tool

http://www.spts.com/

https://www.raith.com/?xml=solutions%7CLithography+%26+nanoengineering%7CRAITH150-TWO

https://www.raith.com/?xml=solutions%7CLithography+%26+nanoengineering%7CRAITH150-TWO

http://www.nanophys.kth.se/nanophys/facilities/nfl/manual/


41

[22] Y. Chen, “Fabrication and characterization of plasmonic nanophotonic absorbers

and waveguides,” ISSN 1653-7610, PhD thesis, KTH, Sweden, (2014).

[23] Q. Li, S. Wang, Y. Chen, M. Yan, L. Tong, and M. Qiu, “Experimental

demonstration of plasmon propagation, coupling, and splitting in silver nanowire

at 1550-nm wavelength,” IEEE J. Quantum Electron.17(4), 1107–1111 (2011).

[24] X. Guo, M. Qiu, J. M. Bao, B. J. Wiley, Q. Yang, X. N. Zhang, Y. G. Ma, K. H. Yu,

and L. M. Tong, “Direct Coupling of Plasmonic and Photonic Nanowires for

Hybrid Nanophotonic Components and Circuits,” Nano Lett. 9, 4515 (2009).

[25] Y. G. Ma, X. Y. Li, H. K. Yu, L. M. Tong, Y. Gu, and Q. H. Gong, "Direct

measurement of propagation losses in silver nanowires," Opt. Lett. 35, 1160-1162

(2010).

[26] W. Yang, Y. Ma, Y. Wang, C. Meng, X. Wu, Y. Ye, L. Dai, L. Tong, Xu Liu, and

Qing Yang, "Bending effects on lasing action of semiconductor nanowires," Opt.

Express 21, 2024-2031 (2013)

[27] L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I.

Maxwell, and E. Mazur, Nature, vol. 426, no. 4960, pp. 816–819, Dec. 2003.

[28] P. Zhao, Z. Wu, K. Chen, X. Zhang, “Hybrid fabricating of silica micro/nanofibers,”

Front. Optoelectron. China, 4(3): 338–342 (2011).

[29] Zhuo Chen, Tobias Holmgaard, Sergey I. Bozhevolnyi, Alexey V. Krasavin,

Anatoly V. Zayats, Laurent Markey, and Alain Dereux, "Wavelength-selective

directional coupling with dielectric-loaded plasmonic waveguides," Opt. Lett. 34,

310-312 (2009).

[30] A. Krishnan, C. J. Regan, L. Grave de Peralta, and A. A. Bernussi, "Resonant

coupling in dielectric loaded plasmonic waveguides," Appl. Phys. Lett. 97, 231110

(2010).

[31] Z. Zhang, “Silicon-based photonic devices: design, fabrication and

characterization,” PhD thesis, ISSN: 1653-7610, KTH, Sweden, (2008).

[32] L. Yang, D. Dai, B. Yang, Z. Sheng, and S. He, "Characteristic analysis of tapered

lens fibers for light focusing and butt-coupling to a silicon rib waveguide," Appl.

Opt. 48, 672-678 (2009).

[33] H.-M. Yang, S.-Y. Huang, C.-W. Lee, T.-S. Lay, and W.-H. Cheng,

"High-Coupling Tapered Hyperbolic Fiber Microlens and Taper Asymmetry

Effect," J. Lightwave Technol. 22, 1395- (2004)

[34] S. Kim, J. Lee, and H. Jeon, "Over 1 hour continuous-wave operation of photonic

crystal lasers," Opt. Express 19, 1-6 (2011).

[35] C. Monat, et al. "Integrated optical auto-correlator based on third-harmonic

generation in a silicon photonic crystal waveguide." Nature communications 5

(2014).

[36] Y. Park, S. Kim, C. Moon, H. Jeon, and H. J. Kim, "Butt-end fiber coupling to a

surface-emitting Gamma-point photonic crystal band edge laser," Appl. Phys.

Lett. 90, 171115 (2007).

[37] Y. Sun, “Epitaxial Lateral Overgrowth of Indium Phosphide and Its Application in

Heteroepitaxy, ” Ph.D Thesis, ISSN: 1404-0379, KTH, Sweden, (2003).

[38] C. Junesand, “High-quality InP on Si and concepts for monolithic photonic

http://link.aip.org/link/?&l_creator=getabs-normal1&l_dir=FWD&l_rel=CITES&from_key=APPLAB000099000011113302000001&from_keyType=CVIPS&from_loc=AIP&to_j=APPLAB&to_v=97&to_p=231110&to_loc=AIP&to_url=http%3A%2F%2Flink.aip.org%2Flink%2F%3FAPL%2F97%2F231110%2F1

http://link.aip.org/link/?&l_creator=getabs-normal1&l_dir=FWD&l_rel=CITES&from_key=APPLAB000099000011113302000001&from_keyType=CVIPS&from_loc=AIP&to_j=APPLAB&to_v=97&to_p=231110&to_loc=AIP&to_url=http%3A%2F%2Flink.aip.org%2Flink%2F%3FAPL%2F97%2F231110%2F1


42

integration,” PhD thesis, ISSN: 1653-7610, KTH, Sweden, (2013).

[39] S. Naureen, N. Shahid, R. Sanatinia, and S. Anand, “Top-down fabrication of high

quality III-V nanostructures by monolayer controlled sculpting and simultaneous

passivation,” Adv. Funct. Mater. 23: 1620–1627, (2012).

[40] R. Sanatinia, K. M. Awan, S. Naureen, N. Anttu, E. Ebraert, and S. Anand, "GaAs

nanopillar arrays with suppressed broadband reflectance and high optical quality

for photovoltaic applications," Opt. Mater. Express 2, 1671-1679 (2012).

[41] S. Naureen, N. Shahid, A. Dev and S. Anand, "Generation of substrate-free III–V

nanodisks from user-defined multilayer nanopillar arrays for integration on Si,"

Nanotechnology 24 (22), 225301, (2013).

43

Chapter 5

Ultracompact Plasmonic Components

This chapter presents achieved results of hybrid plasmonic functional components and

a proposal of a tightly-confined plasmonic waveguide. We choose the hybrid

plasmonic waveguide (HPWG) as our main research topic for multiple reasons: it has

a relatively low-loss and a strong light confinement; its mode can be freely tuned

between photonic-like and plasmonic-like modes by waveguide design; it’s readily

CMOS compatible, etc. The outline of this chapter is as follows. Section 5.1 is the

fabrications and evaluations of ultracompact directional couplers based on the HPWG.

Section 5.2 proposes a novel design of an ultracompact polarization beam splitter

(PBSs) based on the HPWG. Section 5.3 shows the results of experimental

demonstrations and simulations of hybrid plasmonic (HP) resonators with sub-micron

radii, including disks, rings and donuts. Section 5.4 brings up a new design of electro

optic polymer modulator based on HP resonator. Section 5.5 proposes a novel

plasmonic waveguide layered metal dielectric waveguide and studies its application as

compact resonators.

5.1 Hybrid plasmonic directional couplers

Normally, directional couplers are composed of two identical waveguides which are

placed parallel with a finite separation [1]. When light is input into one waveguide,

there will be power exchange (coupling) between the adjacent waveguides. The amount

of power transfer depends on the waveguide geometry, the waveguide separation, and

the interaction length. Directional couplers are basic components in photonic integrated

circuits and they can be used in power splitting/combining, modulation, multiplexing,

and so on. In this section we present our results of experimental demonstrations of

hybrid plasmonic directional couplers [paper A].

Fig. 5.1 shows a schematic diagram of a hybrid plasmonic waveguide (HPWG) to

compose the directional couplers. The HPWG consists of sandwiching a low-index

slot between a metal layer and a dielectric layer. To fabricate the relevant components,

we use the techniques as discussed in Chapter 4. Briefly speaking, at first, EBE is

used for the gold evaporation and PECVD is for the depositions of hydrogenated

amorphous silicon (a-Si:H) and silicon dioxide. Then the patterns are generated by

EBL with negative resist Ma-N 2403. At last, the patterns are transferred to a-Si:H by

ICP-RIE. The film thicknesses are measured by ellipsometry and profilometer as hAu

~ 100 nm, hSiO2 ~ 60 nm and hSi ~ 400 nm, respectively. The sample’s surface

roughness is measured by AFM as ~ 8 nm, which is mainly introduced by the metal

Chapter 5. Ultracompact Plasmonic Components

44

deposition. In the experiments, series of EBL dose tests are carried out to eliminate

the proximity effect which is severe for a gold substrate. Compared with previous

demonstrated hybrid plasmonic waveguides [2-5], the advantages of such HPWG

geometry are two-fold. Firstly, we can design freely the thicknesses of low-index and

high-index materials using PECVD technology, and the hybrid mode can be tuned

between plasmonic-like mode and photonic-like mode. Secondly, the fabrication is

simple and the tolerance of overlay mismatch due to multiple litho is relaxed.

Figure 5.1. Schematic diagram of the fabricated hybrid plasmonic waveguide.

Fig. 5.2(a) shows the SEM image of a fabricated straight waveguide with a

waveguide width W0 ~ 170 nm, and Fig. 5.2(b) shows the top and cross-sectional

views of a fabricated directional coupler consisted of two waveguides separated by a

gap g ~ 140 nm and an interaction length L = 1.4 μm. The length of S-bend

waveguides in the directional couplers is 6.4 µm. The sidewall angle of the etched

waveguide is found as 88o.

Figure 5.2. SEM images of fabricated hybrid plasmonic devices. (a) Straight waveguide. (b)

Directional coupler. Inset picture is the cross-sectional view of the coupling region.

Using the FEM-based COMSOL Multiphysics (as discussed in section 3.2), the

optical modes supported by the fabricated HPWG can be studied. Since the

waveguide size is small, only hybrid plasmonic quasi-TM mode is supported by such

waveguide. The effective index is 1.97 + 000195i (loss ~ 0.0687 dB/µm). The electric

field distributions are shown in Fig. 5.3(a) and 5.3(b). In order to characterize the

propagation loss, direct measurement method (see section 4.3.2) is applied, i.e. light is

coupled evanescently from a tapered fiber tip (with a diameter ~ 1 μm) to the HP

waveguide, and the output light scattering from the end facets is monitored by an

infrared CCD camera. In the implementation, the fiber tip can move parallel along the

waveguide, and the propagation distance d (from the fiber tip to waveguide end) is

changed as a result. Fig. 5.3(c) shows the bright field image of the measurement. Fig.

5.3(d)-5.3(f) correspond to the dark field images when d ~ 7.62 µm , ~12.9 µm and

~18.5 µm, respectively. Fig. 5.3(g) shows the normalized output power as a function d.


45

From the linear fitting, the propagation loss can be found to be 0.081 dB/μm,

corresponding to a propagation length of 53.6 μm.

Figure 5.3. (a) Ey field distribution of the fundamental quasi-TM mode in the hybrid

plasmonic waveguide. (b) Ey field intensity along the Y axis. (c)-(f) are images of the

measurement of the propagation loss. (g) Measured normalized output power when the

propagation distance varies.

For the fabricated hybrid plasmonic directional couplers, we classify them by the

gaps (g ~ 140 nm, 185 nm, 235 nm, and 290 nm) into four groups (the waveguide

width is fixed at ~ 170 nm). In the group of directional couplers with g ~ 140 nm, the

fabricated devices include interaction lengths L (defined as the length of coupling

region) from 0, 0.2 μm, 0.4 μm… and 4.6 μm. In the rest three groups, L vary from 0,

0.4 μm, 0.8 μm … to 8.4 μm. To measure the splitting ratios of the directional

couplers, we use a CCD camera to monitor the two outputs simultaneously, as shown

in Fig. 5.4(a). The advantage is that the output power of the through and cross ports of

the directional couplers can be recorded in a single measurement; as a result, the

splitting ratios can be accurately measured. To achieve a high coupling efficiency, we

use a butt coupling method to couple light from the fiber tip to the HP waveguide. In

addition, 1 μm wide tapers as shown in Fig. 5.2(b) are applied to decrease the mode

size mismatch. Fig. 5.4(b)-5.4(d) show three typical cases of directional couplers with

g ~ 140 nm. When L are ~ 0, 0.8 µm and 1.4 µm, the splitting ratios are ~ 0 : 100, 50 :

50 and 100 : 0, respectively. Fig. 5.4(e) shows the measured normalized output power

at through port for couplers with different gaps, and the fitting curves are given by [6]

Pt(L)'=

Pt(L)

Pt(L)+Pc(L)=cos2(

π(L-L0)

2Lc), (5.1)

describing the theoretical output power derived by coupled mode theory; L is the

interaction length, and Lc is the coupling length (defined as the interaction length for

complete power transfer).

From the fitting, we can find that the Lc are ~ 1.55 µm, 2.2 µm, 3.2 µm and 4.8

µm for g ~ 140 nm, 185 nm, 235 nm and 290 nm, respectively. We also notice that

there are certain cases (e.g., g ~ 235 nm, L ~ 4.8 µm and g ~ 185 nm, L ~ 3.2 µm, etc.)

showing actual splitting ratios which do not match the fitting curves. We think it is

mainly due to the imperfect etching facets of these waveguides.


46

Figure 5.4. (a) - (d) are measurement images of directional couplers with a gap of 140 nm. In (b),

(c) and (d), the coupler’s interaction lengths are ~ 0 µm, 0.8 µm and 1.4 µm, respectively. (e)

Measured normalized output power at through port for couplers with different gap and

interaction length.

To compare the obtained coupling lengths with theory, we use COMSOL

Multiphysics to simulate the super modes supported by the coupling regions of the

directional couplers. Fig. 5.5(a) shows the corresponding field distributions of odd

and even modes; and the propagation constants can also be obtained by the

simulations, which are denoted by βo and βe, respectively. Based on coupled mode

theory, the theoretical coupling length can be calculated by Lc = π /(βe – βo) [7]. Fig.

5.5(b) shows the measured and simulated results of the coupling length as a function

of the coupler’s gap. One can see that there’s a nice fit between the two, confirming

good accuracy of the measurements.

Figure 5.5. (a) Even and odd modes supported by the directional coupler. (b) Simulated and

measured coupling lengths as a function of the coupler’s gap.

5.2 Polarization beam splitters based on three-core directional

couplers

In high speed optical communication systems, polarization division multiplexing

(PDM) is a versatile technique to enhance the transmission capacity by transmitting

signals with both orthogonal polarizations [8]. However, current standard silicon on

insulator (SOI) wafers for fabricating photonic integrated circuits (PICs) are normally


47

with 250 nm or 220 nm thick top silicon layers, while the waveguide widths are

ranging from 400 nm to 500 nm, resulting in high birefringence [9] and polarization

dependent transmission properties [10] of the photonic components. Hence, in order

to exploit PDM technique in PICs, realizing a polarization independent circuit is

essential. One possible solution is by applying a polarization diversity scheme [11-12],

where on-chip light is firstly split into two beams with orthogonal polarizations, and

then the beams are processed separately by properly designed photonic components;

at last, two polarizations are combined at the circuit output. To demonstrate such

systems, ultracompact polarization beam splitters (PBSs) based on silicon platforms

are essential.

In this section we present a novel design of an ultra-compact and low-loss PBS based on a

dielectric - hybrid plasmonic - dielectric coupler [paper B], as schematically shown in Fig.

5.6. We assume the device is fabricated with a standard SOI wafer (250 nm thick Si), and the

width of the Si waveguides (SWGs) has a typical value of 450 nm. Differently from a

two-core SOI directional coupler, here we introduce a 200 nm wide hybrid plasmonic

waveguide (HPWG) in between to form a three-core coupler. The thickness of gold in the

HPWG is hAu = 100 nm. The SiO2 slot thickness is denoted by hd, while the coupler’s gap and

interaction length are denoted by g and Lc, respectively. Note that in our analysis, wp = 200

nm is taken as an example to prove the principle. Such dimension can also be readily

achieved using standard CMOS technology.

Figure 5.6. (a) Schematic configuration of the proposed polarization beam splitter. (b) and (c)

are Ex field distributions of x-polarized even and odd modes, respectively. (d), (e) and (f) are

Ey field distributions of 1st order symmetric, 2

nd order symmetric and anti-symmetric

supermodes.

The basic mechanism of the PBS originates from the HPWG’s high birefringence, i.e.

only quasi-TM polarized light can be guided by the HPWG. As a result, when the input light

from port #1 (as shown in Fig. 5.6) is x-polarized light, the PBS acts as an ordinary two-core

coupler with a gap of wp + 2g; however, when the input light is y-polarized, the PBS behaves

like a three-core coupler with a separation of g. As a result, the coupling length for

y-polarization is expected to be much shorter than that for x-polarization. We use the FEM

COMSOL Multiphysics to study the supermodes to confirm our assumption. Fig. 5.6(b)-(f)

show the field profiles of five supermodes guided in the coupling region when g = 100 nm

and hd = 80 nm. We can see that for TE-polarization however, there are only two supermodes

which can be supported by the coupler: even and odd modes (named as TE1 and TE2). As

discussed in Section 5.1, the coupling length for the TE polarization can be evaluated by [7]


48

0 0

1 2

22

TE

TETE TE

Lnn n

. (5.2)

On the contrary, for TM-polarization, there are in total three supermodes: two symmetric

(named as TM1 and TM2) and one anti-symmetric (named as TM3), as shown in Fig.

5.6(b)-(d). For such three-core coupler, to fully couple optical powers between adjacent

waveguides, the following phase matching condition needs to be satisfied [13],

1 2 32TM TM TMn n n , (5.3)

Here, we meet the condition by choosing proper silicon dioxide thickness. Fig. 5.7(a) plots

the effective indices of all five supermodes as functions of hd when g = 100 nm. We can see

that the effective indices of TM3, TE1 and TE2 modes remain constant when varying hd ; this

is because there are negligible light confined in HPWG for these modes as shown in Fig.

5.6(b), (c) and (f). We can also see that Eq. 5.3 can be fulfilled when hd ~ 78 nm, and in this

case, based on coupled mode theory, the coupling length of the three-core coupler is given as

[13-14]

0 0

1 32 2

TM

TMTM TM

Lnn n

. (5.4)

As seen from Fig. 5.7(a), , suggesting that the coupling length for TE

polarization is much larger than that for TM polarization. Fig. 5.7(b) shows the change of

suitable hd as the variation of the coupler’s gap, and Fig. 5.7(c) plots the corresponding

coupling lengths for TM polarization LTM and the ratios between the coupling lengths of TE

and TM polarizations LTE/LTM as functions of g. We can see that for g ranging from 75 nm to

175 nm, LTE/LTM is generally larger than 60, suggesting that the coupler is highly polarization

dependent. In our analysis, we choose a gap of g = 100 nm as a tradeoff between the device

performance and fabrication requirement, and in this case, LTM = 3.5 μm and LTE/LTM =116.6.

Figure 5.7. (a) Effective indices of the coupler’s five supermodes as functions of silicon dioxide

thickness. (b) Suitable silicon dioxide thickness to satisfy Eq. 5.3 when varying the coupler’s

gap g. (c) Coupling lengths for TM polarization and ratio between coupling lengths for TE and

TM polarizations when varying g.

Next, we use a 3D-FDTD to verify the characteristics of the designed device. Fig. 5.8(a)

and (b) show the field profiles when the input lights (at Port #1) are TE polarized and TM

polarized, respectively. The light source is a continuous wave with a wavelength of 1550 nm.


49

Fig. 5.8(c) and (d) plot the spectral responses of the proposed device, and Fig. 5.8(e) and (f)

analyze the spectral responses given a fabrication error Δh, of silicon dioxide thickness hd.

We can see that for both cases, insertion losses (ILs) are simulated as < 1.5 dB, and the

extinction ratios (ERs) are > 12 dB in the whole C-band, suggesting effectiveness of the

proposed device. A more detailed description of the device performances can be found in

[paper B].

Figure 5.8. (a) and (b) are continuous wave responses of the designed PBS when input light is

TE polarized and TM polarized, respectively. (c) and (d) are spectral responses at output ports

#2 and #3 for TE and TM inputs, respectively; silicon dioxide thickness is hd = 78 nm in both

cases. (e) and (f) are spectral responses at ports #2 and #3 for TE and TM inputs given a

fabrication error Δh of the silicon dioxide thickness.

It’s worth noticing that the device concept was also later verified experimentally by

another group in Singapore [15].

5.3 Hybrid plasmonic resonators

5.3.1 Ultrasharp 90o bends

In a practical photonic circuit, bending waveguides are basic building blocks. As

discussed in previous paragraphs, one of plasmonics’ most desirable properties is the

compact light confinement. Hence, one can expect that ultrasharp bends based on

plasmonics can have smaller radiation loss than the traditional dielectric bends. In order

to accurately investigate the losses of ultrasharp bends with radii < 2 μm, we use

3D-FDTD methods rather than FEM and FDM mode solvers which may over-estimate

the losses [16]. The properties of sub-micron ring resonators based on hybrid plasmonic

waveguide (HPWG) and Si waveguide (SiWG) are also compared [paper F].

Fig. 5.9(a) and (b) show the geometries of the studied SiWG and HPWG. The Si

core in both cases is embedded in SiO2 buffer and cladding, and the dimension is

300×300 nm2. Such SiWG can enable similar confinement for TE and TM modes,

ultra-sharp 90o bends have been studied in Ref. [17]. The gold layer thickness of

HPWG is HAu=100 nm, and the slot thickness HS is 30 nm or 60 nm. Fig. 5.9(c) and (d)

show the field distributions of the quasi-TM modes supported by SiWG and HPWG (HS


50

= 30nm), respectively. The effective index is 2.04 with an effective mode area Aeff ~

0.066 μm2 for SiWG, while 2.48 with Aeff ~ 0.023 μm

2 for HPWG, suggesting that

HPWG has a much more compact confinement than SiWG. Fig. 5.9(e) and (f) show the

schematics of 90o bends based on these two waveguides. The simulated field profiles of

the 90o bends with radii of 0.5 μm are shown in Fig. 5.9(g) and (h). One can see that

much less power irradiates out of the HPWG bend than Si bend, owing to the more

compact confinement.

Figure 5.9. (a) and (b) are cross-sectional views of a SOI waveguide (SiWG) and a hybrid

plasmonic waveguide (HPWG). (c) and (d) are the corresponding mode distributions. (e) and (f)

are the geometry of 90o bend based on SiWG and HPWG. (g) and (h) are the corresponding

field distributions.

Bending losses as functions of radii are also quantitatively studied for SiWG and

HPWG as shown in Fig. 5.10(a). One can see that for bends with sub-micron radii,

using HPWG can help to decrease the bending losses. Moreover, HPWG with a thinner

slot (Hs = 30 nm) has a lower loss than HPWG with a thicker slot (Hs = 60 nm). The

reason is that with thinner slot, hybrid mode behaves more like plasmonic mode hence

has a more compact confinement. To further analyze the influence of slot thickness Hs,

bending losses of HPWG 90o bends with R0 = 0.5 μm and R0 =1.0 μm as functions of Hs

are studied, as shown in Fig. 5.10(b). Optimal slot thicknesses exist for minimal

bending losses, due to the competition of radiation loss and absorption loss, i.e. a

thinner slot thickness enables more compact confinement hence lower radiation loss,

but at a cost of larger metal absorption loss. For R0 = 0.5 μm and R0 =1.0 μm, the

optimal thicknesses are ~ 25 nm and 45 nm, respectively. Properties of Si microring

(SiMR) and hybrid plasmonic microring (HPMR) are also investigated. Fig. 5.10(c)-(f)

show the field distributions of resonant modes of SiMR and HPMR (HS = 25 nm),

respectively. The intrinsic Q factor, mode volume V and Purcell factor F are shown in

Fig. 5.10(g) and (h). Here, the cavity’s effective mode volume V is evaluated by [18-19]

Veff =∫ 𝜀(𝑥,𝑦,𝑧)|E(x,y,z)|2𝑑𝑥𝑑𝑦𝑑𝑧

max (𝜀(𝑥,𝑦,𝑧)|E(x,y,z)|2) , (5.5)

where ε(x,y,z) is the cavity permittivity profile and E(x,y,z) is the mode electric field

distribution. Purcell factor as a figure of merit to describe the enhancement of

spontaneous emission is expressed as [18-19]


51

F = 3

4π2

Q

Veff(

λ0

n)3. (5.6)

We can also normalize Veff with the effective wavelength and obtain a dimensionless

normalized mode volume given by

V = Veff/(λ0/(2n))3. (5.7)

On the other hand, considering that the losses of a plasmonic cavity originate from two

sources i.e. radiation loss due to sharp bends and absorption loss due to metal

absorptions, intrinsic Q-factors Q are given by [20]

1/Q= 1/Qrad+1/Qabs, (5.8)

where Qrad and Qabs are radiation-related and absorption-related Q-factors, respectively.

Qabs increases exponentially with the bending radius due to decreased radiation loss,

while Qabs is mainly dependent on the waveguide geometry, hence it is insensitive to the

radius variation. Eq. 5.8 explains the tendency of Q as shown in Fig. 5.10(g). For SiMR,

Q increases exponentially as radius. For HPMR, when the bending radius is relatively

small, Qrad is the dominant contributor to Q, hence Q increases exponentially with the

radius. When the radius is relatively larger, Q is mainly determined by Qrad, and it is not

sensitive to radius variation any longer. One can also see from Fig. 5.10(g) that the

intrinsic Q factor of HPMR is much larger than that of SiMR when R0 < 1.5 µm, while

the mode volume is much smaller. From Fig. 5.10(h), one can observe that the Purcell

factor for HPMR has a maxima of ~ 300 at R0=1.055 µm, while SiMR’s maximal F is

only around 26 at R0 ~ 1.055 µm, suggesting that the light-matter interaction can be

greatly enhanced by a hybrid plasmonic cavity.

Figure 5.10. (a) Losses of 90 degree bends as functions of bending radis for SiWG as well as

HPWG with HS = 30 nm and HS = 60 nm. (b) Losses of HPWG bend as functions of slot

thickness for R0 = 0.5 μm and R0 =1.0 μm. (c)-(f) Field distributions of resonant modes in SiMR

and HPMR. (g) and (h) are the Q-factor, mode volume and Purcell factor as functions of ring

radii for SiMR and HPMR.


52

5.3.2 Hybrid plasmonic disk resonators

In this section, we discuss the experimental results of the waveguide-loaded hybrid

plasmonic disk resonators as schematically shown in Fig. 5.11(a) [paper C]. We use

similar fabrication processes as described in section 5.1 to demonstrate these devices.

Figs. 5.11(b)-(c) show the SEM images of the demonstrated disks with radii of R ~

0.525 μm and 1.05 μm, respectively. The waveguide-disk gaps in the fabricated devices

are ~ 60 nm, 100 nm and 150 nm.

Figure 5.11. (a) Sketch of a hybrid plasmonic disk resonator. (b) Top-view and tilted view SEM

images of a disk with R0 ~ 0.5 μm. (c) Top-view and tilted view SEM images of a disk with R0 ~

1 μm.

Using 3D-FDTD, the resonant modes supported by the disk cavity are firstly

analyzed. We find that along the radial direction, two types of quasi-TM modes, i.e. a

fundamental quasi-TM mode (TM1) and a higher order quasi-TM mode (TM2) are

supported. Fig. 5.12(a)-(d) show the field distributions of the respective resonant

modes along xz and yz planes. Note that in the simulations, the resonant wavelengths

are set as 1550 nm by selecting suitable bending radii. For TM1 resonance, the

azimuthal number is m = 4 and the corresponding bending radius is R1=501 nm; for

TM2 resonance, m = 6 and the bending radius is R2 = 968 nm.

Figure 5.12. Simulation results of the hybrid plasmonic microdisks. (a) and (b) are the field

profiles of TM1 mode when disk radius is R1 = 501 nm; the azimuthal number is m = 4. (c) and

(d) are field profiles of TM2 mode when R2 = 968 nm and m = 6. (e) and (f) are cavity’s Q-factor,

normalized mode volume and Purcell factor as functions of bending radii.

Furthermore, intrinsic quality factors Q, normalized mode volume V and Purcell

factor F of the cavity modes can be found by combining the FDTD simulation results

with Eq. 5.5-5.7. Figs. 5.12(e)-(f) show the relevant results for TM1 modes with

azimuthal number m from 3, 4 … to 11. TM2 mode’s Q-factor is also shown in Fig.

5.12(e) for a comparison. The smallest mode volume is 𝑉 = 0.31(𝜆0/(2 ))3 when

the radius is 399 nm and the azimuthal number is m = 3. The maximal Purcell factor is


53

F = 1357 when R ~ 885 nm and m = 8.

Next, the waveguide-loaded hybrid plasmonic disks are analyzed by 3D-FDTD. Fig.

5.13(a) and (b) show the transmission spectra of the disks with radii of 525 nm and

1050 nm, respectively. The waveguide-disk gap is denoted by g. The field distributions

under continuous-wave inputs with different wavelengths are shown as insets in Fig.

5.13(a) and (b). We can find that in the 0.5 μm-radius disk, there exist two fundamental

TM-polarized (TM1) resonances at 1415 nm and 1633 nm, corresponding to the

azimuthal numbers of 5 and 4, respectively. In the spectra of the disks with radii of 1050

nm, as shown in Fig. 5.13(b), the resonant wavelengths of 11th

, 10th

and 9th

order TM1

mode are 1438 nm, 1538 nm and 1653 nm, respectively; while the resonance at 1428

nm is 8th

order TM2 resonance (higher order mode) which is undesired for single mode

operation.

To measure the fabricated devices as shown in Fig. 5.11, we use butt coupling

between tapered waveguides and fiber tips. Super-continuum source is used to test the

wide band (>300 nm) spectral responses. Fig. 5.13(c) and (d) are the measured spectra

for disks with radii of ~ 0.5 μm and 1 μm, respectively. We see that they fit reasonably

well with the simulation results. The measured extinction ratio (ER) for the disk with a

0.5 μm radius and a gap of 60 nm is 12.8 dB at m = 4 resonant wavelength. The free

spectral range (FSR) is as large as ~ 210 nm. The ER for 1 μm radius disk at a 10th

order

resonance is 8.3 dB, and the FSR is ~ 95 nm. To find out the cavity quality factors, we

fit the resonances with Lorentz curves based on coupled mode theory [21-22]:

0

0

1 2 1 2

1 2 1 2

j( Δω / ω ) / Q / Qt

j( Δω / ω ) / Q / Q

i w

i w

, (5.9)

where t is the amplitude of transmitted field, Qi is the intrinsic Q-factor of the HP cavity,

Qw is the waveguide-coupling Q-factor, ω0 is the resonant frequency, and Δω is the

frequency detuning. The fitting results are shown by the insets in Figs. 5.13(c) and (d).

From the fittings, we deduce that the disk with a radius of 0.5 μm has an intrinsic

quality factor Qi of 90 ± 30 at around 1625 nm (4th

order resonance), and the disk with

1 μm radius has a Qi of 165 ± 40. It’s worth mentioning that for waveguide loaded-disk

with ultrasharp radius, there’s a significant phase mismatch in the coupling region,

which will result in extra coupling loss to the cavity. In addition, due to imperfect

fabrications, the demonstrated waveguides have a rough and tilted sidewall (~ 880

as

discussed above). All above reasons will contribute to the extra cavity loss, hence

deteriorating the cavity’s intrinsic Q-factor. Based on FDTD simulations, the mode

volume in the fabricated cavities can be calculated, for the disks with 0.5 μm and 1 μm

radii, normalized volume is 0.43 and 1.15, corresponding to a Purcell factor of

127 ± 42 and 87 ± 21, respectively,


54

Figure 5.13. (a) and (b) are the simulation results of the disk resonators’ spectra when R = 0.525

μm and R = 1.05 μm. The waveguide-disk gap is denoted by g. Inset pictures are the simulated

field profiles when inputting continuous wave into the disk resonators. (c) and (d) are the

measurement results of the fabricated devices’ spectra. Inset pictures are the Lorentz fittings

based on coupled mode theory. (e) Thermo tuning of the 4th order resonance of a 0.525

μm-radius disk. (f) Measured resonance variations with the change of temperature. Linear fit is

obtained by 3D-FDTD when assuming the TO coefficient of a-Si:H is ~ 2.45×10-4

/K.

We also tested the thermal tuning of the disk with a radius of 0.5 μm. The results are

shown in Fig. 5.13(e) and (f). Temperature increase of 60°C results in a resonance shift

of 5.8 nm. Because SiO2 has a relatively small thermo-optic (TO) coefficient, we think

the resonance shift is mainly due to the TO effect of a-Si:H. By 3D-FDTD simulations

and curve fittings, we deduce that the TO coefficient of the deposited a-Si:H is ~

2.45×10-4

/K.

5.3.3 Hybrid plasmonic ring and donut resonators

In this section, we present our experimental results of hybrid plasmonic ring and

donut resonators. We use similar fabrication and characterization methods as described

in previous section for the demonstrations. Fig. 5.14(a) and 5.14(d) illustrate the

configuration of the hybrid plasmonic rings and donuts, and the SEM images of the

fabricated devices are shown in Fig. 5.14(b)-(c) and 5.14(e)-(f). For ring resonators, the

waveguide width is w1 ~ 170 nm; while for donut resonators, the waveguide width is w2


55

~ 320 nm. In all cases, the access waveguide has a width of ~ 170 nm. The radii are R0

~ 0.52 μm and 1.04 μm. The gaps between the access waveguide and the resonators are

~ 50 nm, 100 nm and 150 nm.

Figure 5.14. (a) Sketch of a hybrid plasmonic ring resonator. SEM images of the rings with R0 ~

0.52 μm (b) and R0 ~ 1.04 μm (c). (d) Sketch of a hybrid plasmonic donut resonator. SEM

images of the donuts with R0 ~ 0.52 μm (e) and R0 ~ 1.04 μm (f).

Using 3D-FDTD, the Q-factors of hybrid plasmonic rings, donuts and disks are

calculated, as shown in Fig. 5.15. One can see that the Q-factors of the donuts (with a

width of 320 nm) are almost identical with the Q-factors of the disks, while the rings

(with a width of 170 nm) have significantly smaller Q.

.

Figure 5.15. 3D-FDTD simulation results of the intrinsic quality factors of the disks

(fundamental TM mode TM1 and higher order TM mode TM2), the donuts and the rings. Here,

m is the azimuthal number of the resonance.

This can be explained by looking at the mode profiles supported by these cavities, as

shown in Fig. 5.16. In all cases, the bending radii are around 800 nm and resonant

wavelengths are 1550 nm. The azimuthal numbers m of disk, donut and ring resonator

are 7, 7 and 6, respectively. One can see from Fig. 5.16(b) that for rings with w1 ~ 170


56

nm, optical modes irradiate out of the waveguide, resulting in a relatively larger

radiation loss; while for donuts with w2 ~ 320 nm, the waveguide is wide enough so that

the resonant mode is hardly influenced by the inner perimeter of the ring. As a result,

the mode has a similar profile as shown in Fig. 5.16(c) as the whispering gallery mode

in the disk resonator as shown in Fig. 5.16(a). Considering that the disk has a higher

order mode TM2 as discussed in previous section, we think a donut ring is an optimal

geometry as a tradeoff between Q-factor and single mode operation.

Figure 5.16. Simulated electrical field profiles of the resonant mode. (a) Hybrid plasmonic disk

with a radius of 791 nm and an azimuthal numbers m = 7. (b) Hybrid plasmonic ring.

Waveguide width w1 = 170 nm, R1= 795 nm and m = 6. (c) Hybrid plasmonic donut. w2 = 320

nm, R2= 811 nm and m = 7.

Using the butt coupling method, the transmission spectra of the fabricated rings and

donuts as shown in Fig. 5.14 can be characterized. Figure 5.17 shows the measured

spectra of the hybrid plasmonic rings and donuts with radii of ~ 0.52 μm and 1.04 μm

and gaps of 50 nm, 100 nm and 150 nm. The free-spectral range of the 0.5 μm

resonators are ~ 200 nm. Extinction ratios of the resonances around 1650 nm are ~ 10

dB. From curve fittings based on Eq. 5.9, intrinsic Q-factors Q of ~ 0.5 μm rings are

estimated as 75 ± 20 at ~ 1670 nm; Q of ~ 0.5 μm donuts at ~ 1530 nm are 100 ± 20.

Figure 5.17. Measured spectra. (a) and (b) are spectra of hybrid plasmonic rings with radii of ~

0.52 μm and 1.04 μm, respectively. (c) and (d) are spectra of hybrid plasmonic donuts radii of ~

0.52 μm and 1.04 μm, respectively.


57

5.4 Electro-optic polymer modulators based on HP ring

resonators

In this section, we propose and evaluate the concept of an ultracompact electro-optic

(EO) polymer modulator based on hybrid plasmonic microring resonators (with

submicron radii) [paper D]. We firstly review the state-of-the-art integrated optical

modulators, and then the proposed device is systematically evaluated. Discussion of

fabrication feasibility is carried out in the last paragraph.

5.4.1 Integrated optical modulators: an overview

Optical integrated modulators are fundamental building blocks of photonic integrated

circuits. Enabling materials for light modulation include quantum wells (based on

quantum confined Start effect) [23], graphene (based on tunable Fermi level by

electrical gating) [24], silicon (based on plasma dispersion effect) [25-26] and

electro-optic (EO) materials (based on pockels effect) [27-29]. The main drawback of

III-V quantum well modulators is that monolithic integration of III-V and Si is

challenging, while graphene modulators are only for amplitude modulations. As for Si

modulators, due to a very weak plasma effect of Si, the change of Si refractive index is

normally insignificant by modulating the carrier concentration [30], and extra material

loss is normally accompanied. Hence, silicon modulators have limited performances (in

terms of modulation speed, modulation depth, insertion loss, etc.), and the devices

normally require demanding power consumption [31]. On the other hand, electro-optic

polymers (EOPs) show great promises; recently developed EO coefficient r33 can

approach 500 pm/V while keeping negligible optical losses [32] (as a comparison: r33

of LiNbO3 is ~ 30 pm/V [33]). In addition, EO polymer has an ultra-fast phase

relaxation and in principle, modulation speed of THz is possible [34]. Demonstration of

110 Gb/s EOP modulators has been reported [35], using polymer itself as a waveguide

core. There are also intense investigations to incorporate EO polymers into compact

photonic circuits based on e.g. SOI [36-37] or plasmonics [38-39]. By confining light in

the low-index slot, hybrid plasmonic waveguide (HPWG) can also be exploited for

light modulations. Fig. 5.18 compares mode profiles and resistance-capacitance (RC)

circuits of three typical types of waveguides suitable for polymer modulators, i.e. an

Au-polymer-Si hybrid plasmonic waveguide, a silicon-polymer-silicon (Si slot)

waveguide [37] and a metal-polymer-metal (MPM) plasmonic waveguide [39]. We see

that in all cases light is highly localized in the polymer layer. Si slot waveguide has

lowest insertion loss but the RC time constant is largest, which fundamentally limits the

maximal modulation speed. MPM waveguide as shown in Fig. 5.18(c) has the ideal RC

response and maximal optical confinement in polymer, while it suffers from

intrinsically large metal absorption losses, and the coupling between MPM nad

remaining Si circuits is challenging. On the other hand, hybrid plasmonics provides a

tradeoff between these two schemes, hence it is of particular interest.


58

Figure 5.18. Electrical field distributions. (a) Optical mode profile of an Au-Polymer-Si hybrid

plasmonic waveguide. (b) Optical mode profile of a Si-polymer-Si slot waveguide. Reprinted

from [37] with permissions. (c) Mode profile of the RF signal in an Au-Polymer-Au plasmonic

waveguide. Reprinted from [39] with permissions. In all figures, equivalent

resistance-capacitance (RC) circuits are also shown.

As for the geometries for light modulations, Mach-Zehnder interferometers (MZI)

[40] and microring/disk resonators [41] are frequently used, among which cavity-based

modulators are desirable in order to decrease the modulators’ footprint, hence further

enhance the modulation performance (e.g. decreasing power consumption by

improving RC circuit). In contrary to high-Q cavities, moderate-Q cavities are more

desirable for high-speed modulations due to two reasons. Firstly, moderate-Q cavity

modulators have higher bandwidth limitations due to shorter cavity photon lifetime

[42]. As an example, a cavity with Q larger than 2000 has a limited modulation speed,

lower than 100 GHz. Secondly, moderate-Q cavities relax the tolerance to resonance

shifts due to temperature and fabrication variations, and the extra feedback models for

resonance stabilization can be eliminated [43-44]. Given above considerations, we

propose an EO polymer modulator based on hybrid plasmonic microrings, which has an

optimized RC circuit (compared with Si slot waveguide), a small insertion loss

(compared with MPM) and a moderate Q-factor. The proposed structures may find

applications in high speed modulations.

5.4.2 Performance evaluations

Figure 5.19. Sketch of an electro-optic polymer modulator based on a hybrid plasmonic

microring resonator with a dielectric access waveguide.


59

A sketch of the proposed HP ring modulator is shown in Fig. 5.19. The device is based

on standard SOI platform, light is guided in Si waveguide for low-loss propagation,

while modulation is realized by the Au-polymer-Si hybrid plasmonic microring. As

shown in Fig. 5.19, microwave signal is applied to the EO polymer to change the

refractive index, and correspondingly the cavity’s resonance can be shifted. As a result,

the transmission power of a continuous wave at a fixed wavelength λ0 can be modulated.

As discussed in section 5.3.2, based on coupled mode theory, the transmission of the

microring can be analyzed by Eq. 5.9. To pursue a maximized extinction ratios (ERs), a

critical coupling condition i.e. Qi = Qw is employed so that the transmission power of

resonant wavelength is zero. In practical device design, such condition can be achieved

by properly selecting waveguide-ring gap, access waveguide width, etc. Then the 3dB

bandwidth of the resonance can be written as Δλ3dB = λ0/ Qload = 2λ0/Qi, considering

1/Qload = 1/Qi + 1/Qw. Since the modulation power is quantified by the energy to switch

the resonance by a distance of 3dB bandwidth, we can define a figure of merit (FOM) to

quantize the modulation efficiency of switching the cavity in and out of resonance by

changing the EOP index, which can be given by

Res i

3dB EOP 0

Δλ QFOM = Γ

Δλ Δn 2λ

1 . (5.10)

Here, ΔλRes represents the resonance shift due to the polymer’s index change ΔnEOP, and

Γ is defined as the tuning efficiency written as

Res EOP/ = Δλ Δn , (5.11)

which can be re-written as effRes 0

EOP eff EOP

ΔnΔλ λΓ= =

Δn n Δn, and Γ is proportional to the ratio

of light confined in the EO polymer slot. From Eq. 5.11, one can see that to obtain a

high FOM (a low driving power), it’s essential to obtain a high intrinsic quality factor

Qi and more light confinement (hence Γ) in the EOP slot.

Using 3D-FDTD, Qi and Γ can be calculated using a stand-alone microring as shown

in Fig. 5.20(a). We firstly study a hybrid plasmonic waveguide with geometries of W =

300 nm, HSi = 400 nm and HEOP = 30 nm. The thickness of metal cap is fixed at HAg = 100

nm in all analyses. Fig. 5.20(b)-(c) show the field distributions of a 542 nm-radius

microring with a resonant wavelength of 1550 nm and an azimuthal number of m = 6.

One can see the light is highly localized in the EO polymer slot layer, and the resonant

mode of the submicron ring experiences little light radiation. To compare the

performance of the hybrid plasmonic (HP) microring and a Si slot microring, we plot

the intrinsic quality factors of both cavities as functions of the bending radius in Fig.

5.20(d). The Si slot microring used for comparison has the same waveguide width of

300 nm and Si height of 400 nm, while the 30 nm EO polymer layer is sandwiched in

the waveguide center. One can see from Fig. 5.20(d) that the HP microring has a

much higher intrinsic Q-factor (QHP) than the Si slot microring (QSlot), due to a more

compact light confinement. We also plot the ratio between QHP and QSlot in Fig.

5.20(d), one can see that the enhancement of Q-factor can be as large as 8.5 by hybrid


60

plasmonics. Next, resonance shifts with the changes of the refractive index of EO

polymer are analyzed, as shown in Fig. 5.20(e). From the slopes, the tuning

efficiencies can be determined as SlotΓ ~ 182 nm and HPΓ ~ 134 nm, respectively.

Based on Eq. 5.10, FOM of both cavities can also be calculated. The ratio between

FOMHP and FOMSlot is shown in Fig. 5.20(f). One can see that when the ring radius is

smaller than ~ 1 μm, HP microring has a larger FOM than Si slot microring,

suggesting that lower driving voltage is needed in a plasmonic modulator in

comparison to a Si slot modulator. The maximum FOM enhancement is about 6 when

the radius is around 510 nm.

Fig. 5.20. (a) Sketch of a stand-alone hybrid plasmonic microring. (b) and (c) are Ez field

profiles along xy and xz planes of a resonant mode at 1550 nm. (d) Intrinsic Q-factors of a Si

slot microring and a hybrid plasmonic (HP) microring and their ratio. (e) Resonance shifts

with polymer index changes for Si slot microring and HP microring. (f) The ratio of figure of

merits (FOM) between Si slot microring and HP microring.

We also perform systematic analysis of the influence of waveguide geometries on

the FOM of the HP microring. We find that when the thickness of electro-optic

polymer increases from 30 nm to 100 nm, FOM drops by about 40%, but we also

need to note that a higher effective EO coefficient can be achieved when the slot

thickness is larger. On the other hand, when the silicon height increases (or decreases)

from optimal thickness of 100 nm, FOM decreases by about 15%. Detailed

description can be found in [paper D].

In this paragraph, we evaluate the overall performance of the HP microring

modulator, assuming the device operates at 1549 nm and the ring radius is 542 nm

with an azimuthal number of 6. Using the results as studied in Fig. 5.20(b)-(c) and

combining them with Eq. 5.9, we can simulate the transmission spectra of the cavity

when the refractive index of the electro-optic polymer is changed from 1.65 to 1.625,

as shown in Fig. 5.21. One can see that an index change of 0.025 shifts the resonance

by ΔλRes = 3.4 nm, which is larger than the 3dB bandwidth Δλ3dB = λ0/Qload = 2.9 nm.

When the continuous wave input is at 1549 nm, the transmission is modulated from 0


61

to 0.85, corresponding to an insertion loss (IL) of 0.7dB, and an optical modulation

amplitude (OMA) of 0.85. As a matter of fact, 0.021 index change can enable a

resonance shift of 3dB bandwidth, the corresponding IL and OMA are 0.97 dB and

0.8, respectively. Assuming that the EO polymer has an EO coefficient of 80 pm/V,

according to 3

33= /(2 )EOPn n r V H , the driving voltages for 0.025 and 0.021 index

changes are calculated as 4.25 V and 3.6 V, respectively. Owing to the small footprint,

the device capacitance is very small: 02 0 82 fF EOP

ad

EOP

C R W .

H

. The RC time

constant limited modulation speed is as large as ~ 190 GHz, assuming that the device

resistance is 1500 Ω. In addition, the modulation speed limited by the cavity photon

lifetime is larger than 300 GHz in our design. When operating under a driving voltage

of 3.6 V and a modulation speed of 100 GHz, the power consumption is about 0.5

mW and the corresponding average power consumption is ~ 5 fJ/bit.

Figure 5.21. Simulated transmission spectra of the hybrid plasmonic microring modulator

when the refractive index of EO polymer is 1.65 (ΔnP = 0) and 1.625 (ΔnP = 0.025).

5.4.3 Discussion of fabrication feasibility

We discuss the fabrication feasibility of the proposed device in this paragraph. The

envisioned fabrication processes (similar to the processes in Ref. [5]) are shown in Fig.

5.22. There are mainly following steps. (a) The top Si layer of SOI sample is treated by

ion implantation; (b) the ring and waveguide patterns are defined by EBL and ICP

etching; (c) An EBL and a liftoff process help to define the bottom contact; (d) EO

polymer (dissolved in solvent) is spun on the sample and planarize the surface. The

thickness can be controlled by a combination of adjusting the spinning recipe and an

etching back process. (e) Top metal cap (also serves as a top contact) is defined by EBL

and liftoff processes. A thin layer of high-k insulator might be deposited before the top

contact deposition to further enhance the polymer’s breakdown voltage. We note that

the polymer should be poled by applying high electric field before the device functions.


62

Figure 5.22. Main steps of the envisioned fabrication processes.

5.5. Nanodisks based on layered metal-dielectric waveguide

In this section, we propose a type of plasmonic waveguides with an ultracompact light

confinement and evaluate the nanodisk cavities based on such waveguides [paper E].

Firstly, we review the strongly confined cavities. Then the guiding principle of the

proposed waveguides is explained. Whispering gallery mode cavities based on the

proposed devices are systematically studied afterwards.

5.5.1 Strongly confined cavities: an overview

Photonic cavities with high Q and small volume V are very useful for lasing, sensing,

switching and other applications [18-19]. As discussed in section 5.3, enhancement of

Purcell factor which is defined by Eq. 5.6 is of particular interest. Since conventional

dielectric cavities have mode volume generally larger than cubic effective wavelength

(λ/n)3 due to the diffraction limit, metallic cavities are promising to pursue even

stronger light-matter interactions. Among the various demonstrations,

metal-dielectric-metal (MDM) cavities have very compact mode when the slot layer is

thin [45-47]. Ref [48] shows that disk cavity radius can be shrunk down to 88 nm

which is about λ0/5n (where n is the slot index) when the slot thickness is 10 nm.

Cavities based on hyperbolic metamaterial also show very compact size due to the

extraordinary dispersion property [49-50]. Cavity size down to λ/12 [50] has been

achieved, and light-matter interaction can be enhanced using hyperbolic metamaterial

as reported in [51].

5.5.2 Guiding principle of layered metal-dielectric waveguides

Fig. 5.23(a) shows a sketch of the proposed layered metal-dielectric waveguide with

two dielectric layers (LMD2). In general, LMDN (N=1, 2 …) consists of N+1 metal

layers with N sandwiched dielectric layers. The waveguide has similar geometry as a

hyperbolic metamaterial waveguide, but the guiding principle resembles

dielectric-metal-dielectric (DMD) waveguide and MDM waveguide. For the 1D LMD2

waveguide (propagating along x+) as shown in Fig. 5.23(a), there are two fundamental

TM modes i.e. even (TM1) and odd (TM2) modes, and the field profiles are shown in

Fig. 5.23(b). One can see that Ez field is symmetric for TM1 while anti-symmetric for

TM2. Effective refractive indices of LMD2 as functions of dielectric and metal


63

thicknesses (h2 and hM) are then calculated, as shown in Fig. 5.23(c)-(d). Here, 𝑒+ and

𝑒− denote the effective indices of TM1 and TM2, respectively; 𝑒 is the effective index

of a LMD1 waveguide which is composed of two metal layers (hM thick) sandwiching a

dielectric (h2 thick) slot. One can see from Fig. 5.23(c)-(d) that 2 𝑒 = 𝑒+ + 𝑒

− .

Actually, a LMD2 can be regarded as two coupled LMD1, and the LMD1 modes that can

symmetrically or anti-symmetrically couple with each other, resulting in even and odd

modes of LMD2. One can see from Fig. 5.23(c) that when the metal layer is thin,

because more evanescent coupling between adjacent LMD1 waveguides occurs, a

larger energy splitting (i.e. the difference between 𝑒+ and 𝑒

−) appears; while when

the metal is thick enough (> 100nm), 𝑒+ and 𝑒

− are not dependent on the metal

thickness any longer, because no coupling occurs and the LMD2 degenerates into an

ordinary MDM waveguide. Fig. 5.23(d) studies the influence of dielectric thickness h2.

Effective index 𝐷 of an ordinary MDM (with 100 nm thick metal layer) is also

studied as a comparison. We see that 𝑒− and 𝑒

+ increase simultaneously when

decreasing h2, which is similar to 𝐷 of a MDM, i.e. a thinner dielectric layer

enables better confinement. Comparing with MDM, odd mode of LMD2 has a

significantly larger effective index for a given dielectric thickness, suggesting a much

stronger mode confinement.

Figure 5.23. (a) Schematic diagram of a 1D LMD2 waveguide. The propagation direction is

along x+. (b) Ez field distributions of even (TM1) and odd (TM2) modes supported by the 1D

LMD2 waveguide. (c) Effective indices as functions of metal thickness. Here, h2 = 50 nm. (d)

Effective indices as functions of dielectric thicknesses. For LMDN (N=1, 2), hM=10 nm; for

MDM waveguide, metal thickness is 100 nm.

5.5.3 Nanodisk resonator based on the proposed waveguide

In the following paragraphs, the disk cavities based on LMD2 waveguide are studied

using 3D-FDTD. Fig. 5.24(a) shows the 3D schematic diagram of the cavity. R is the

disk radius. We choose h2 = 50 nm and hM = 10 nm in the following analysis to explain

the principle. The conclusions can be extended to waveguides with different parameters.

Referring to the analysis in previous section, the disk can support two fundamental

quasi-TM modes, i.e. even (TM1) and odd (TM2) modes. Electric field profiles of a

fundamental TM1 whispering gallery mode (WGM) with an azimuthal number m = 3

are shown in Fig. 5.24(b) and (c), and the disk radius is 203 nm for a resonance at 1550

nm. Field profiles of a TM2 WGM mode are shown in Fig. 5.24(d) and (e), and the disk


64

radius is 142 nm, much smaller than the disk radius for TM1 mode, owing to its more

compact mode confinement.

Figure 5.24. (a) Sketch of a disk cavity based on LMD2 waveguide. Field distributions of a

TM1 resonant mode along ϕr (b) and zr (c) planes. (d) and (e) are field profiles of a TM2

resonant mode along ϕr and zr planes, respectively.

Then, we systematically analyze the Q-factors, mode volume V and Purcell factor F

of the LMD2 cavities as functions of disk radii. Nanodisks based on ordinary MDM

waveguide with a dielectric thickness of 2h2 = 100 nm are also investigated as a

comparison. In the following study, Drude model for silver in MDM has parameters

fitted by Johnson and Christy data (see section 2.1); while we model the 10 nm thick

silver films in LMD2 with the experimental data from [52], considering that the quality

of thin metal layer is worse than bulk material. A low temperature at 40 K is assumed

similarly as in [48], and the permittivity as function of temperature is modelled using

the methods described in [48, 53].

Table 5.1. Selected radii for 1550 ± 20 nm resonances with

an azimuthal number of m (unit: nm).

m 1 2 3 4 5 6 7

MDM NA 197 273 343 415 482 547

TM1 LMD2 86 146 203 256 309 362 NA

TM2 LMD2 61 103 142 180 218 254 NA

Table 5.1 lists out the selected disk radii for resonances at 1550 ± 20 nm with

azimuthal number m from 1 to 7. One can see that for a given m, the radius of disk based

on TM2 mode of LMD2 waveguide is the smallest, suggesting that the waveguide has

the most compact light confinement; while the MDM disk has the largest radii due to

the weakest confinement. One can also see the confinement strength from the field

profiles of the whispering gallery modes supported by MDM disk, TM1 LMD2 disk and

TM2 LMD2 disk, as shown in Fig. 5.25(a). Here, the profiles along the cross-sectional

half plane (r+) are presented and the azimuthal number is 2. Then we quantitatively

study Q, V, and F of these three disk cavities using the definitions given by Eq. 5.5-5.7.

The obtained merits as functions of azimuthal numbers are shown in Fig. 5.25(b)-(d).

We note that the intrinsic Q-factor of a metallic cavity is determined by the

radiation-related (Qrad) and absorption-related (Qabs) Q-factors together (see Eq. 5.8).

We can see from Fig. 5.25(b) and (c) that intrinsic Q-factors of MDM cavity (QMDM)

and TM1 LMD2 cavity (QN=2

TM1) increase with the azimuthal number at first, following


65

the tendency of Qrad., then maintain constant, similarly to the hybrid plasmonic

resonators previously discussed (see section 5.3). However, for the TM2 LMD2 disk,

Q almost keeps constant when m increases from 1 to 6 as shown in Fig. 5.25(c), owing

to the fact that Qrad is much larger than Qabs even for m = 1 and R = 61 nm. In Fig.

5.25(b)-(c), V as functions of m are also shown. One can see that when increasing m (as

well as R), V also increases continuously. For m = 2, 𝑉𝑁=2 1~

1

3𝑉 𝐷 and

𝑉𝑁=2 2~

1

8𝑉 𝐷 , meaning that a much more compact mode volume can be achieved in

LMD2 nanodisks. Purcell factors F of these cavities are calculated as well, as shown in

Fig. 5.25(d). Maximal F achievable by MDM cavity is ~ 3500 with m = 4 and R = 343

nm; while maximal F in TM1 LMD2 disk is ~ 3870 with m = 2 and R = 146 nm. The

largest Purcell factor in TM2 LMD2 disk is F ~ 2.3×104, when m = 1 and R = 61 nm.

LMD2 cavity achieves a five times larger Purcell factor compared to the ordinary MDM

nanodisk. We note that in principle, the performance of LMD2 cavity can be further

improved by optimizing the quality of thin metal films.

Figure 5.25. (a) Field profiles along zr cross-sectional half plane (r+) for the resonant modes

supported by MDM disk, TM1 LMD2 disk and TM2 LMD2 disk. (b) Intrinsic Q-factor Q and

normalized mode volume V of MDM disk as functions of the azimuthal number m. (c) Q and

V as functions of m for the TM1 LMD2 disk and TM2 LMD2 disk. (d) Comparison of Purcell

factors F.

We also study systematically the influence of metal and dielectric thicknesses on the

LMD2 cavities’ performances (intrinsic Q-factor, mode volume and Purcell factor);

Qrad and Qabs are also calculated. We also show that for a fixed dielectric thickness (hD =

N×hN), nanodisk based on LMDN (N = 3, 4, …) waveguide can further be shrinked. As

an example, disk radius is around 33 nm ~ λ0/(13.5n) by utilizing LMD7 waveguide,

and the corresponding mode volume is ~ 0.005(λ0/(2n))3. More details can be found in


66

[paper E]. Compared with traditional metal-dielectric-metal cavity, the proposed

scheme has advantages including: (1) significant enhancement of confinement as well

as Purcell factor at a fixed dielectric thickness, (2) convenient vertically optical

pumping due to thin metal thickness, (3) design freedoms including metal thickness and

the number of layers and (4) cascading capability. Hence, we think the presented

structures may provide an alternative to pursue ultracompact light confinement, which

may find applications in strong light-matter interaction systems.

References

[1] A. Hardy and W. Streifer, “Coupled mode theory of parallel waveguides,” J.

Lightwave Technol.3(5), 1135–1146 (1985).

[2] M. Wu, Z. Han, and V. Van, "Conductor-gap-silicon plasmonic waveguides and

passive components at subwavelength scale," Opt. Express 18, 11728-11736

(2010).

[3] I. Goykhman, B. Desiatov, and U. Levy, “Experimental demonstration of locally

oxidized hybrid silicon-plasmonic waveguide,” Appl. Phys. Lett. 97(14), 141106

(2010).

[4] S. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong, "Silicon-based horizontal

nanoplasmonic slot waveguides for on-chip integration," Opt. Express 19,

8888-8902 (2011).

[5] Z. Wang, D. Dai, Y. Shi, G. Somesfalean, P. Holmstrom, L. Thylen, S. He, and L.

Wosinski, "Experimental Realization of a Low-loss Nano-scale Si Hybrid

Plasmonic Waveguide," in Optical Fiber Communication Conference/National

Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical

Society of America, 2011), paper JThA017.

[6] Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey,

and A. Dereux, "Wavelength-selective directional coupling with dielectric-loaded

plasmonic waveguides," Opt. Lett. 34, 310-312 (2009).

[7] A. Yariv and P. Yeh., Photonics: Optical Electronics in Modern Communications,

6th ed. (Oxford University Press, New York, 2007).

[8] M. I. Hayee, M. C. Cardakli, A. B. Sahin, and A. E. Willner, "Doubling of

bandwidth utilization using two orthogonal polarizations and power unbalancing

in a polarization-division-multiplexing scheme,"IEEE Photon. Technol. Lett. 13,

881-883 (2001).

[9] D. Dai and S. He, "Analysis of the birefringence of a silicon-on-insulator rib

waveguide," Appl. Opt. 43, 1156-1161 (2004).

[10] E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, Y. A. Vlasov, "Group index and

group velocity dispersion in silicon-on-insulator photonic wires," Opt. Express. 14,

3853-3863 (2006).


67

[11] W. Bogaerts, D. Taillaert, P. Dumon, D. Van Thourhout, R. Baets, and E. Pluk, "A

polarization-diversity wavelength duplexer circuit in silicon-on-insulator photonic

wires," Opt. Express 15, 1567-1578 (2007).

[12] H. Fukuda, K. Yamada, T. Tsuchizawa, T. Watanabe, H. Shinojima, and S.-i.

Itabashi, “Silicon photonic circuit with polarization diversity,” Opt. Express, vol.

16, pp. 4872–4880 (2008).

[13] J. P. Donnelly, H. A. Haus, and N. Whitaker, “Symmetric three-guide optical

coupler with nonidentical center and outside guides,” IEEE J. Quantum Electron.

23, 401-406 (1987).

[14] K. Saitoh, Y. Sato, and M. Koshiba, "Polarization splitter in three-core photonic

crystal fibers," Opt. Express 12, 3940-3946 (2004).

[15] J. Chee, S. Zhu, and G.Q. Lo, "CMOS compatible polarization splitter using

hybrid plasmonic waveguide," Opt. Express 20, 25345-25355 (2012).

[16] Z. Sheng, D. Dai, and S. He, “Comparative Study of Losses in Ultrasharp

Silicon-on-Insulator Nanowire Bends”, Journal of selected topics in quantum

electronics 15, 1406-1412, (2009).

[17] T. Tsuchizawa,T. Watanabe, E. Tamechika, T. Shoji, K. Yamada, J. Takahashi, S.

Uchiyama, S. Itabashi and H. Morita, "Fabrication and evaluation of

submicron-square Si wire waveguides with spot-size converters", Paper TuU2

presented at LEOS Annual Meeting, p.287, Glasgow, UK (2002).

[18] T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Demonstration of ultra-high-Q

small mode volume toroid microcavities on a chip," Appl. Phys. Lett. 85,

6113-6115 (2004).

[19] K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003).

[20] T. Xu, M.S. Wheeler, H.E. Ruda, M. Mojahedi, and J.S. Aitchison, "The influence

of material absorption on the quality factor of photonic crystal cavities," Opt.

Express 17, 8343-8348 (2009).

[21] B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. -P. Laine, "Microring resonator

channel dropping filters," J. Lightwave Technol. 15, 998 (1997).

[22] W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of

non orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron.

40(10), 1511-1518 (2004).

[23] Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, J.

S. Harris, "Strong quantum-confined Stark effect in germanium quantum-well

structures on silicon," Nature 437, 1334-1336 (2005).

[24] M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang,

“A graphene-based broadband optical modulator,” Nature474(7349), 64–67

(2011).

[25] A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu,


68

M. Paniccia, “A high-speed silicon optical modulator based on a

metal-oxide-semiconductor capacitor,” Nature 427, 615-618 (2004).

[26] Q. Xu, B. Schmidt, S. Pradhan, M. Lipson, “Micrometre-scale silicon

electro-optic modulator,” Nature 435, 325-327 (2005).

[27] E. L. Wooten et al. "A review of lithium niobate modulators for fiber-optic

communications systems," IEEE J. Sel. Top. Quantum Electron. 6, 69-82 (2000).

[28] W.H. Steier, et.al, "Polymer electro-optic devices for integrated optics," Chem.

Phys., 245 (1999), pp. 487–506

[29] D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y.

Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys.

Lett. 70(25), 3335–3337 (1997).

[30] R. A. Soref and B. R. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum

Electron. 23, 123-129 (1987).

[31] G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical

modulators,” Nat. Photonics 4(8), 518–526 (2010).

[32] L. R. Dalton, B. Robinson, A. Jen, P. Ried, B. Eichinger, P. Sullivan, A. Akelaitis,

D. Bale, M. Haller, J. Luo, “Electro-optic coefficients of 500 pm/V and beyond for

organic materials,” Proc. SPIE 5935, 5935061-1, (2005).

[33] Y. Y. Lin, S. T. Lin, G. W. Chang, A. C. Chiang, Y. C. Huang, and Y. H. Chen,

"Electro-optic periodically poled lithium niobate Bragg modulator as a laser

Q-switch," Opt. Lett. 32, 545-547 (2007).

[34] L. Thylén, P. Holmström, L. Wosinski, B. Jaskorzynska, M. Naruse, T. Kawazoe,

M. Ohtsu, M. Yan, M. Fiorentino, U. Westergren, "Nanophotonics for Low-Power

Switches," in Optical Fiber Telecommunications VI (Chapter 6), Ed. Ivan

Kaminow, Tingye Li and Alan Willner, Elsevier, 2013, ISBN: 9780123969583.

[35] D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y.

Shi, “Demonstration of 110 GHz electro-optic polymer modulators,” Appl. Phys.

Lett. 70(25), 3335–3337 (1997).

[36] J.-M. Brosi, C. Koos, L.C. Andreani, M. Waldow, J. Leuthold, and W. Freude,

"High-speed low-voltage electro-optic modulator with a polymer-infiltrated

silicon photonic crystal waveguide," Opt. Express 16, 4177-4191 (2008) .

[37] L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J.

Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos,

W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon

technology,” Opt. Express 19, 11841-11851 (2011).

[38] W. Cai, J. S. White, and M. L. Brongersma, “Compact, high-speed and

power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403-4411

(2009).


69

[39] A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R.

Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M.

Sommer, C. Koos, M. Kohl, W. Freude and J. Leuthold, "High-speed plasmonic

phase modulators," Nature Photonics 8, 229–233 (2014).

[40] W. M. Green, M.J. Rooks, L. Sekaric, and Y.A. Vlasov, "Ultra-compact, low RF

power, 10 Gb/s silicon Mach-Zehnder modulator," Opt. Express 15, 17106-17113

(2007).

[41] Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s

carrier-injection-based silicon micro-ring silicon modulators," Opt. Express 15,

430-436 (2007).

[42] X. Xiao, H. Xu, X. Li, Y. Hu, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “25 Gbit/s

silicon microring modulator based on misalignment-tolerant interleaved PN

junctions,” Opt. Express 20, 2507-2515 (2012).

[43] H. M. G. Wassel, D. Dai, M. Tiwari, J. K. Valamehr, L. Theogarajan, J. Dionne, F.

T. Chong, and T. Sherwood, “Opportunities and Challenges of Using Plasmonic

Components in Nanophotonic Architectures,” IEEE Journal on Emerging and

Selected Topics in Circuits and Systems 2, 154-168 (2012).

[44] K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Dynamic

Stabilization of a Microring Modulator Under Thermal Perturbation,” Proc.

Optical Fiber Communication Conference (Optical Society of America, 2012),

paper OW4F.2.

[45] M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume

plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).

[46] H. T. Miyazaki and Y. Kurokawa, “Squeezing Visible Light Waves into a

3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96,

097401-097404 (2006).

[47] M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin,

and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384),

204–207 (2012).

[48] S.-H. Kwon, “Deep subwavelength plasmonic whispering gallery-mode cavity,”

Opt. Express 20, 24 918-924 (2012).

[49] X. Yang, J. Yao, J. Rho, X. Yin, and X. Zhang, “Experimental realization of

three-dimensional indefinite cavities at the nanoscale with anomalous scaling

laws,” Nature Photonics 6, 450 (2012).

[50] Y. He, S. He, J. Gao, and X. Yang, “Nanoscale metamaterial optical waveguides

with ultrahigh refractive indices,” J. Opt. Soc. Am. B 29(9), 2559–2566 (2012).

[51] H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M.

Menon, “Topological Transitions in Metamaterials,” Science 336(6078), 205–209

(2012).

http://josab.osa.org/abstract.cfm?&uri=josab-29-9-2559

http://josab.osa.org/abstract.cfm?&uri=josab-29-9-2559


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[52] W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin

ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt.

Express 18, 5124-5134 (2010).

[53] S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M.

Lieber, and H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor

nanodisk with silver nanopan cavity,” Nano Lett. 10(9), 3679–3683 (2010).

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Chapter 6

Conclusions and Future Work

6.1 Conclusions

In summary, this thesis presents the results on design, fabrication and characterization

of several plasmonic components based on silicon nanowire platforms.

Plasmonics has been proposed as a next-generation technology since it can

potentially bridge the size mismatch between photonic and electronic components. We

have derived plasma models including Drude model and Drude-Lorentz model to

describe the optical properties of metals, and calculated the dispersion of surface

plasmon polaritons supported by a basic metal-dielectric interface. From a comparison

with a traditional waveguide, the diffraction-free confinement in a plasmonic

waveguide is demonstrated.

In order to study sophisticated photonic/plasmonic components, two numerical

methods i.e. FDTD and FEM are implemented in the thesis. FDTD can solve lightwave

propagation behaviors. A 2D directional coupler (simplified from 3D by equivalent

index method) and a 3D photonic crystal cavity are explained as examples. FEM is

primarily used as mode solvers and solvers for multiphysics problems. Simulation of

thermo optic effect of a Si waveguide integrated with a micro heater is explained.

Fabrication and characterization techniques of the photonic/plasmonic components

are reviewed and discussed. PECVD and ebeam evaporation are optimized to deposit

a-Si:H, SiO2 and metals, providing extra flexibility of waveguide design. Ebeam

lithography is applied to obtain high-resolution patterns, and ICP-RIE transfers the

patterns from resists to substrate with high aspect ratio and vertical sidewalls. For the

device characterizations, grating couplers are easy to implement, while butt coupling

has ultra-wide bandwidth. Direct measurement is useful to characterize propagation

loss and splitting ratios with high accuracy. Optical pump system is suitable for

measuring the spontaneous emission from III-V materials.

Experimental results of a tunable silicon-on-insulator microdisk assisted by perfect

absorbers and III-V pedestal microdisks and photonic crystal cavities are firstly

presented. Then plasmonic devices are discussed in details.

Hybrid plasmonic directional couplers with various coupling gaps are

experimentally demonstrated. Splitting ratios ranging from ~ 100:0 to 50: 50 to 0:100

have been achieved. The coupling lengths for couplers with gaps of 140 nm, 185 nm,

235 nm and 290 nm are measured as 1.55 µm, 2.2 µm, 3.2 µm and 4.8 µm, respectively.

As a basic building block of photonic integrated circuit, the demonstrated directional

Chapter 6. Conclusions and Future Work

72

couples can be used for splitting, modulation, etc.

Based on a Si-hybrid-plasmonic-Si three core coupler, an ultra-compact

polarization beam splitter (PBS) has been proposed. PBS is essential component in a

polarization diversity system. The basic operational principle of the proposed device

is to utilize the hybrid plasmonic waveguide as a polarization-selective tunnel. Due to

the compactness of HP waveguide, the device size can be shrinked down to 2×5.1 μm2.

Studies of fabrication tolerance show that the device has overall insertion loss below

1.5 dB and extinction ratio above 12 dB in the entire C-band.

We also investigate ultrasharp bends and submicron-radius resonators based on

hybrid plasmonic waveguides. Compared with traditional SOI 90o bend, HP bend

features significantly decreased losses when the radius is below 1 μm, and Purcell

factor of a HP resonator is much larger, suggesting a significantly enhanced

spontaneous emission. We then experimentally demonstrate hybrid plasmonic disk,

ring and donut resonators with radii of ~ 0.5 μm and 1 μm. It’s shown that HP donut

resonator is the best solution when looking on the tradeoff between high Q factors and

single mode operation. HP disk with 0.5 micron radius has a Q-factor of 90 ± 30 at

1625 nm, and a corresponding Purcell factor of 127 ± 42. Thermal tuning of the device

is achieved, and the derived thermo optic coefficient of a-Si:H is ~ 2.45×10-4

/K.

We have proposed an ultracompact EO polymer modulator based on HP microring

resonator (radius ~ 540 nm) with a dielectric access waveguide. Comparing with Si slot

microring modulators, the proposed device has a better performance in the submicron

radius range. We show that the cavity-photon-lifetime limited modulation speed is as

large as 300 GHz, while the resistance-capacitance limited speed is above 190 GHz.

The driving voltage is 3.6V to achieve optical modulation amplitude of 0.8. The

device’s insertion loss is about 1 dB, and the power consumption is about 5 fJ/bit when

operating at a speed of 100 GHz.

At last, we propose a layered metal-dielectric (LMD) waveguide for tightly confined

system. Radii of nanodisks based on the proposed waveguide can be decreased below

60 nm. The mode volume and the corresponding Purcell factor are also analyzed.

Plasmonic active devices based on microring resonators in form of switches, routers

and modulators have been proposed by many authors as main building blocks for future

inter- and intra-chip optical communication systems that will replace present electrical

interconnects. We have shown here that the technology based on hybrid plasmonic

waveguiding allows not only to match better the size of optical components with

electronic ones, but also to get superior parameters in comparison to those based on

photonic slot waveguides. Our ring, donut and disk resonators with radii of 500 nm are

the smallest to date fabricated components of this type. We have shown that their

quality factor Q can be 8.5 times larger than Q of similar silicon slot resonator. When

comparing figures of merit characterizing modulation efficiency of modulators based

on these structures, FOM of our hybrid plasmonic microring is 6 times better than this

of corresponding silicon slot structure, both using same EO polymers as active

medium.

Chapter 6. Conclusions and Future Work

73

6.2 Future work

We propose future continuation of this work in the following areas:

(1) Optimization of the metal film quality. There are reports that by annealing the

ebeam evaporated gold layer under proper temperature, the film quality can be

improved and the propagation loss can be decreased. We think this may provide an

effective way to further decrease the waveguide propagation loss and improve the

quality-factors of the hybrid plasmonic resonators.

(2) Optimization of a-Si:H etching. We believe that the tilting angle and sidewall

roughness of the etched a-Si:H waveguide significantly deteriorate the overall device

performance. In ICP-RIE process, a series of tests of the combination of gas mixture,

RF powers, pressure need to be carried out to further optimize the etching recipes in

order to obtain vertical and smooth sidewalls.

(3) The coupling regions of the submicron resonators can be further optimized to

achieve a better phase matching condition, in order to further decrease the cavity loss.

(4) Experimental demonstration of an EO polymer hybrid plasmonic modulator.

There are on-going efforts towards this end. The challenges include efficient poling of

the electro-optic polymer, low-temperature deposition of a-Si:H, etc.

(5) Applying the hybrid plasmonic components in a light-matter interaction system

to exploit the light enhancement in the slot layer. One example is to incorporate gain

medium (e.g. quantum dots) in the slot material. Efficient gain can potentially

compensate the plasmonic loss and might result in lasing. Another example is to use

nonlinear polymers for optical nonlinear processes, such as second harmonic

generation, wavelength conversion, optical bistability, etc. It’s also interesting to use

the components in biosensors for lab-on-chip applications, considering their compact

size and enhanced light-matter interaction.

Chapter 7. Guide to Appended Papers

75

Chapter 7

Guide to Appended Papers

Paper A. Fei Lou, Zhechao Wang, Daoxin Dai, Lars Thylen, and Lech Wosinski,

“Experimental demonstration of ultra-compact directional couplers based on silicon

hybrid plasmonic waveguides,” Applied Physics Letters, 100(24), 241105 (2012).

Contribution: Design, simulation, fabrication, characterization and analysis;

major part of writing.

Paper B. Fei Lou, Daoxin Dai, and Lech Wosinski, "Ultracompact polarization beam

splitter based on a dielectric–hybrid plasmonic–dielectric coupler," Optics Letters,

37(16), 3372-3374 (2012).

Contribution: Design, simulation and analysis; major part of writing.

Paper C. Fei Lou, Lars Thylen, and Lech Wosinski, “Experimental demonstration of

silicon-based metallic whispering gallery mode disk resonators and their

thermo-tuning,” Optical Fiber Communication Conference/National Fiber Optic

Engineers Conference (OFC/NFOEC), paper Tu2E.1, (2014).

Contribution: Design, simulation, fabrication, characterization and analysis;

major part of writing.

Paper D. Fei Lou, Daoxin Dai, Lars Thylen, and Lech Wosinski, “Design and analysis

of ultra-compact E-O polymer modulators based on hybrid plasmonic microring

resonators,” Opt. Express 21, 20041-20051 (2013).


Paper E. Fei Lou, Min Yan, Lars Thylen, Min Qiu, and Lech Wosinski, “Whispering

gallery mode nanodisk resonator based on layered metal-dielectric waveguide,”

accepted by Opt. Express, (2014).


Paper F. Fei Lou, Lars Thylen, and Lech Wosinski, “Ultra-sharp bends based on hybrid

Chapter 7. Guide to Appended Papers

76

plasmonic waveguides,” manuscript, (2014).

Contribution: Design, simulation, and analysis; major part of writing.

design, fabrication and characterization of plasmonic ...reza sanatinia, maz naiini, reyhaneh...

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