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UNIVERSITY OF SOUTHAMPTON
ADVANCED BRAGG GRATING BASED INTEGRATED OPTICAL DEVICES FOR
WAVELENGTH DIVISION MULTIPLEXING SYSTEMS
By
Christos Riziotis
A Thesis submitted for the degree of Doctor of Philosophy
FACULTY OF ENGINEERING AND APPLIED SCIENCE
DEPARTMENT OF ELECTRONICS AND COMPUTER SCIENCE
OPTOELECTRONICS RESEARCH CENTRE
September 2001
ii
UNIVERSITY OF SOUTHAMPTON ABSTRACT
FACULTY OF ENGINEERING AND APPLIED SCIENCE DEPARTMENT OF ELECTRONICS
AND COMPUTER SCIENCE OPTOELECTRONICS RESEARCH CENTRE
Doctor of Philosophy
ADVANCED BRAGG GRATING BASED INTEGRATED OPTICAL DEVICES FOR
WAVELENGTH DIVISION MULTIPLEXING SYSTEMS
by Christos Riziotis This thesis presents experimental and theoretical work towards the development of advanced integrated planar optical devices for application in Wavelength Division Multiplexing (WDM) in optical communication systems. The presented work lies within a broad range of research areas, namely: design and simulation of novel Bragg grating based WDM passive devices, their performance characterization in simulated optical communication systems, fabrication and characterization of photosensitive thin films and finally device fabrication using ultraviolet induced refractive index changes. A complete model for the analysis of Bragg grating assisted devices in waveguide structures has been developed. Bragg grating based optical Add/Drop Multiplexers (OADM) have been simulated and studied by using this modelling tool. A fully optimised design for an OADM based on a null coupler and a tilted Bragg grating has been proposed. This device can exhibit optimised Add and Drop actions with suppressed backreflections and crosstalk to a level lower than –40 dB. A novel interferometric OADM configuration based on a full cycle full (100%) coupler is also proposed. This design exhibits fully optimised and symmetrical Add/Drop actions in contrast to the compromised performance of traditional interferometric configurations.
A software simulation tool has also been developed and employed for the theoretical characterization of optical filters, linking this way the proposed devices to real communication system issues related to high bit rate WDM networks. The effect of group delay ripple in WDM filters is studied for different modulation formats and a simplified figure of merit is proposed for the characterization of the effect.
For the fabrication of photosensitive thin film structures, a prototype in-house Flame Hydrolysis Deposition facility was built and it was initially characterized. Further experimental work involved detailed analysis and characterization of highly photosensitive Lead Germanate glasses grown by Pulsed Laser Deposition.
A developed direct UV-writing facility is presented and major issues around the functionality of the technique are discussed, by demonstrating solutions for the control of the optical system.
A rapid heat treatment technique is also proposed for locking the enhanced photosensitivity in deuterium loaded germanosilicate glasses and successful preliminary results are demonstrated. This method should allow finally the fabrication of complex all-UV-written devices, which has been limited to date by the degrading photosensitivity during UV writing, due to rapid deuterium outdiffusion.
iii
Table of Contents
Acknowledgements vii
List of Abbreviations viii
Introduction 1
Chapter 1: Passive Optical Devices
for Wavelength Division Multiplexing Systems 6
1.1 Introduction 6
1.2 General properties of optical filters 8
1.3 Arrayed waveguide gratings 10
1.4 Thin film filters 12
1.5 Bragg grating based filters 14
1.6 Comparison of specially designed Bragg grating filters with TFF 15
1.7 Bragg grating based OADMs 19
1.8 References 24
Chapter 2: Analysis and Modelling of Bragg Grating Assisted
Waveguide Devices 29
2.1 Introduction 29
2.2 Local normal mode analysis and step transition model 31
2.2.1 Dispersion equation for the five layer waveguide structure 32
2.2.2 Step-wise approximation of waveguide structures 33
2.3 General analysis of a non-uniform Bragg grating 36
2.4 Analysis of the composite grating-coupler structure 41
2.4.1 Excitation of the input waveguides 41
iv
2.4.2 Calculation of the response of the composite structure 42
2.5 Summary 43
2.6 References 43
Appendix 2.A: Pseudo-algorithm for the step transition model 46
Chapter 3: Null Coupler -Tilted Bragg Grating Based OADM 47
3.1 Introduction 47
3.2 Principle of operation 47
3.3 Null coupler design and optimisation 49
3.3.1 Waveguide asymmetry optimisation 50
3.3.2 Taper shape optimisation 51
3.4 Grating section 55
3.4.1 Calculation of tilted Bragg grating’s coupling coefficients 56
3.4.2 Tilted grating optimisation 57
3.5 Full spectral response of the OADM 63
3.6 Conclusions 71
3.7 References 72
Appendix 3.A: Analytical expressions for the optimum tilt angle 75
Chapter 4: Full Coupler Based Interferometric OADM 77
4.1 Introduction 77
4.2 Half-cycle coupler (HCC) based OADM 77
4.3 Full-cycle coupler (FCC) based OADM 87
4.3.1 Design procedure 88
4.4 Spectral response of the full-cycle coupler (FCC) based OADM 94
4.5 Conclusions 101
4.6 References 101
v
Chapter 5: Characterization of Optical Filters in
High Speed WDM Transmission Systems 103
5.1 Introduction 103
5.2 Simulation of an optical communication system 104
5.3 Fundamental operations in optical network’s nodes 105
5.4 Characterization of half-cycle coupler (HCC) based OADM 106
5.4.1 EOP calculations 110
5.5 Characterization of full-cycle coupler (FCC) based OADM 114
5.5.1 EOP calculations 116
5.5.2 Performance comparison of HCC and FCC OADMs 117
5.6 Effect of group delay ripple on WDM filters performance 121
5.6.1 Time delay ripple definition 121
5.6.2 EOP calculations 122
5.6.3 Time delay ripple figure of merit 126
5.7 References 129
Chapter 6: Fabrication and Characterization
of Photosensitive Thin Film Layers 131
6.1 Introduction 131
6.2 Silica-on-Silicon technology 132
6.3 Devices fabrication technology based on photosensitive films 133
6.4 Photosensitive films fabrication techniques 134
6.5 Flame Hydrolysis Deposition (FHD) technique 135
6.5.1 FHD operational principles 136
6.5.2 FHD prototype facility 142
6.6 Film fabrication considerations related to UV written devices properties 146
6.7 Characterization of photosensitive Lead Germanate optical waveguides 149
6.7.1 Growth of Lead Germanate glasses 149
6.7.2 Properties and loss characterization of the films 152
6.7.3 Photosensitivity of Lead Germanate films 158
6.8 References 161
vi
Chapter 7: Direct UV-Writing System and Applications 166
7.1 Introduction 166
7.2 Direct UV writing system 168
7.2.1 Writing spot focusing procedure 170
7.3 Photosensitivity of Germanium doped Silica glasses 173
7.4 Photosensitization of Germanium doped Silica thin films 176
7.5 Photosensitivity locking technique 179
7.6 Conclusions 183
7.7 References 184
Chapter 8: Conclusions 187
8.1 Conclusions 187
8.2 Proposed future work 190
Publications 192
vii
Acknowledgments Firstly, I would like to thank both my supervisors Dr. Peter Smith and Prof. Michalis
Zervas for their continuous support, guidance, encouragement and friendship.
Peter was a continuous source of new ideas and he passed to me some of his great
ability and talent to think and act effectively as an experimentalist. Michalis entered me
into the fascinating world of devices and optical communications. He inspired me and
formed in a great degree my attitude towards research. I am also grateful to him for
suggesting and helping me to come to Southampton and join this extremely stimulating
and international environment of work.
I am grateful also to my ex-supervisor Dr. Richard Laming for suggesting and offering
me the research project.
I would like also to thank all the people I worked with during my PhD research. I am
grateful to Prof. Rob Eason, Dr. Sakellaris Mailis, Dr. Eleanor Tarbox, Dr. Ricardo
Feced, Dr. Richard Williams, Alexander Fu and Carlos Alegria for their help and the
skills they passed to me.
I am grateful to my wife Maria for all her help, support, and encouragement during all
these years in Southampton …and for the years before.
Finally I would like to acknowledge the University of Southampton for financial
support through a research studentship.
viii
List of Abbreviations
AFM Atomic Force Microscopy
AWG Arrayed Waveguide Grating
BG Bragg Grating
CW Continuous Wave
DWDM Dense Wavelength Division Multiplexing
EDFA Erbium Doped Fibre Amplifier
EOP Eye-Opening Penalty
FCC Full-Cycle Coupler
FFT Fast Fourier Transform
FHD Flame Hydrolysis Deposition
FRED Frequency Doubled (Ar – Ion Laser)
GODC Germanium Oxygen Deficient Centres
HCC Half Cycle Coupler
IFFT Inverse Fast Fourier Transform
IM-DD Intensity Modulation – Direct Detection
LPCVD Low Pressure Chemical Vapour Deposition
LPF Low Pass Filter
MZI Mach-Zehnder Interferometer
MZM Mach-Zehnder Modulator
NRZ Non Return-to-Zero Modulation format
OADM Optical Add/Drop Multiplexer
OC Optical Circulator
OVD Outside Vapour Deposition
PLC Planar Lightwave Circuit
PLD Pulsed Laser Deposition
PRBS Pseudo Random Bit Sequence
RIE Reactive Ion Etching
RZ Return-to-Zero Modulation Format
SFC Symmetric Full Coupler
ix
TFF Thin Film Filter
UV Ultra-Violet
VAD Vapour Axial Deposition
WDM Wavelength Division Multiplexing
WGR Waveguide Grating Router
1
INTRODUCTION
Optical Communications is an extremely fast growing technology driven mainly by the
increasing need for global expansion of the Internet and multimedia communications.
Only the huge bandwidth of the optical fibre seems to be able to accommodate the
increasing amount of network traffic today and much more in the future. However, the
bandwidth of the 3rd low loss optical window (at around 1550 nm) of single mode
optical fibre is currently restricted by the availability and performance of optical
amplifiers. For low bandwidth requirements initially only the red C-Band (1540-1563
nm) was used, where the Erbium Doped Fibre Amplifier (EDFA) exhibits a quite flat
response. As the need for capacity is increased, the entire C-Band (1530-1570 nm) and
even the L-Band (1570-1610) are being used. Additional capacity is also available from
the S-band (1480-1520 nm) by using Semiconductor optical amplifiers (SOA), Thulium
doped fibre amplifiers (TDFA) or lumped Raman amplifiers.
The efficient use of this finite optical bandwidth is of imperative importance in order to
meet the future data capacity needs. The Wavelength Division Multiplexing (WDM)
technique is a very promising solution for the effective exploitation of the optical
spectrum and the successful construction of the next generation of Broadband Optical
Networks. Use of WDM technology can simply and cost effectively multiply the
capacity of the already installed fibre infrastructure by increasing the number and
spectral efficiency of the employed wavelength channels. Key components for the
development of this technology are Optical Multiplexer/Demultiplexers
(MUX/DEMUX) and Add/Drop Multiplexers (OADM), Optical Cross Connects
(OXC) and switches.
2
This thesis describes performed work within a broad range of activities towards the
understanding, design and development of passive components for use in WDM
transmission systems. Chapter 1 discusses the developing technology of passive
components and reviews the main proposed architectures and technologies. The
performance and the general characteristics of Thin Film Filters, Arrayed Waveguide
Gratings and Bragg grating based devices are discussed. The effect of the spectral
characteristics of those filters is studied in conjunction with communication systems
issues such as cascading and filter-Laser source misalignments. Various configurations
of Bragg grating based Multiplexers and Add/Drop filters are presented and their
performance, limitations and related fabrication issues are discussed. The following
Chapters of the thesis are dedicated to the underlying fabrication technology of such
Bragg grating based passive devices and also to the design, modeling and system
characterization of novel high performance Bragg grating based filters.
The choice of the material platform for the development of those devices in the long-
term target of this project is Silica-on-Silicon. The aim of the project was to transfer
device and fabrication technology of fibre-Bragg gratings into an integrated optics
implementation, which forms a more compact, and environmentally stable solution.
This implementation adds more degrees of freedom to the device design enabling thus
the development and fabrication of much more sophisticated devices with greater
density of operation over volume compared with fibre based components.
Environmental stability, compactness and device’s functional density are a major
concern in future WDM communication systems, since the number of the employed
WDM channels is continuously increased.
In 1997 a research group in the Communications Centre (COM) at University of
Denmark demonstrated low loss channel waveguides directly written by scanning a
focused UV spot on the top of a planar photosensitive germanosilicate layer. The
waveguides were fabricated by the UV induced positive refractive index change. The
direct UV writing method is ideal for the development of integrated devices combined
with the unique properties of the Bragg gratings that can also be inscripted on the same
photosensitive layer. Consequently a whole class of fibre Bragg grating devices could
be transferred in high-density planar implementation.
3
The first part of the thesis (Chapters 2 to 5) is devoted to the theoretical analysis and
characterization of Bragg grating based devices, while the second part (Chapters 6 and
7) describe the experimental part of the work.
Specifically, Chapter 2 presents the analysis and modeling of coupled waveguide
structures using the normal modes coupled mode theory. The Chapter describes also the
development of the theory for the analysis of non-uniform Bragg gratings employed
within multimode waveguide structures. The combination of the two analyses can
model successfully any Bragg grating based coupled waveguide device, and is used
within the following Chapters for the modelling of the full spectral response of Bragg
grating based filters.
Chapter 3 presents a detailed study of a non-interferometric OADM configuration,
which is based on mode conversion by using an asymmetric grating perturbation. The
Chapter discusses the general properties of a device of this kind and proposes a fully
optimized design, which predicts theoretically excellent spectral characteristics. The
proposed architecture is more robust than interferometric configurations and its
demonstrated performance is compatible with the stringent DWDM components
requirements.
Chapter 4 is devoted to the study of another class of filters, based on an interferometric
full coupler configuration. Firstly we model and calculate the spectral characteristics of
an OADM based on a half-cycle coupler (HCC). This configuration uses an
asymmetrically inscripted Bragg grating at the coupler waist and thus cannot give fully
optimized symmetrical Add and Drop characteristics, leading consequently to a
degraded non-flat amplitude spectral response. With the stringent requirements of
DWDM systems even a slightly degraded performance can lead to excessive penalties
in to the communication system performance. A novel configuration, which makes use
of a full-cycle, full coupler and with a Bragg grating symmetrically placed at the waist
of the coupler, is proposed in the second part of the chapter. This novel device can give
fully optimized Add and Drop actions. By firstly introducing universal engineering
curves of Bragg grating penetration depth versus reflectivity for specific apodisation
profiles we were able to draw general and simple design rules for these devices.
4
Chapter 5 concludes the theoretical work on Optical Add Drop Multiplexers, with
simulations of their performance characteristics when deployed in high bit rate WDM
transmission systems. A complete simulation tool has been developed during this work,
which allows the simulation of passive devices in an optical communication system.
The developed software can incorporate many system parameters, like different
modulation formats and line codes, pulse shaping through filters and Mach-Zehnder
modulators, filter- misalignments and cascades. The analysis of a communication
system and the description of the simulation tool are described initially and applied in
the characterization process of some cases of WDM filters.
Based on this tool the intra-band characteristics of the Half and Full cycle 100%
coupler based OADM –discussed in Chapter 4- are examined. Conclusions are made
about the resulting system penalty due to the spectrally degraded filter response. These
filters are compared with the counterpart non-interferometric configuration where the
Add and Drop characteristics can be fully optimized. The second part of the chapter is
devoted to the study of the dispersion characteristics of OADMs. The shape of in-band
group delay and consequently in-band dispersion are studied and conclusions are drawn
regarding the performance of traditional Bragg gratings and specially designed
dispersion-less gratings. Another important issue related to these novel-grating devices,
resulting from design compromises or fabrication imperfections, is the presence of
group delay ripples in the in-band reflection spectrum. We thoroughly study the
implications of these ripples for different input signal modulation formats and we also
firstly propose that the average time delay and not the average dispersion is the
appropriate figure of merit, describing more accurately the signal distortion effects.
Chapter 6 describes the background technology for the development of photosensitive
planar thin film layers and planar waveguides. Issues around the development of planar
structures and devices on the Silica-on-Silicon platform are also discussed. Towards the
implementation of planar integrated devices, a prototype Flame Hydrolysis Deposition
(FHD) Technique system has been constructed by the author. The system is described
and results based on its initial characterization and performance evaluation are
presented.
5
The second part of Chapter 6 is devoted to the characterization of the properties of
photosensitive Lead-Germanate glass optical waveguides grown by the Pulsed Laser
Deposition (PLD) technique. This part presents results of a collaborative research
project between the ORC and the FORTH Centre (Greece) where these optical glass
waveguides were fabricated for the first time using the PLD technique. These
waveguides characterized in the ORC and their properties –propagation loss, and
photosensitivity- were related to the PLD fabrication parameters.
In Chapter 7 the newly developed ORC prototype facility for direct UV writing is
presented. Initially, the main mechanical and optical parts of the system are described.
Major issues around the control of the UV writing optics are considered and proposed
and implemented solutions are presented. A number of the UV writing experiments
performed are discussed and the results confirm and justify the fully operational status
of the facility.
In general, the intrinsic photosensitivity of Ge-doped silicate glasses is not sufficient
for the definition of all UV written waveguides and gratings. Hydrogen or Deuterium
indiffusion into the glass matrix is a standard procedure of critical importance for
increasing the photosensitivity. A major drawback of this method is the rapid
outdiffusion of the gas from the thin film layer, which consequently leads to fabrication
problems due to continuously degraded photosensitivity during the direct UV writing.
A novel method based on a rapid heat treatment of the gas-loaded films, is proposed in
this thesis in order to overcome the problem. Experiments and initial results are
presented suggesting that this method ‘locks’ the enhanced photosensitivity for
effectively an infinite period of time. The application of this method should enable in
the future the implementation of all directly UV written devices by providing a stable
photosensitive layer for further development.
Finally Chapter 8 concludes the main results of this thesis and suggests further work
towards the development of all UV-written high performance planar integrated WDM
devices.
6
CHAPTER 1
Passive Optical Devices for Wavelength Division
Multiplexing Systems
1.1 Introduction
The continuous and global spread of multimedia communications and the Internet can
only be accommodated by the huge bandwidth that optical fibre networks can offer.
However there is a great demand for expanding the intrinsic capacity and improving
the flexibility of optical networks, and the enabling key technology is proven to be
Wavelength Division Multiplexing (WDM). This way, the capacity of the already
installed optical fibre cable network can be multiplied by the number of employed
WDM channels within the system.
WDM technology was initially applied in point-to point transmission systems (Figure
1.1a) and now is currently being employed in real photonic ring networks (Figure
1.1b). In the simplified schematic of Fig. 1.1(a) a number of channels (n) are
transmitted by monochromatic sources and they are multiplexed before they enter the
fibre link. Optical fibre amplifiers in different positions along the transmission link
keep the channels signal at a certain required level, and dispersion management
components are used for fibre dispersion compensation. At the other end of the link the
channels are de-multiplexed before they reach the optical receivers and the information
carried by the WDM channels can be recovered at the receivers and finally by the
subscribers. Along the link, there are subscriber’s serving nodes where specific WDM
channels can be added into the optical stream or dropped from it.
7
Wavelength Division Multiplexer
TX λ1
λ2
λN
Transmitters Wavelength Division
λ1
λ2
λN
Receivers
Optical Fiber including dispersion management
Optical Amplifier
(a)
λi λi Add/Drop Multiplexer (OADM)
Optical Amplifier
TX
TX RX
RX
RX
TX λ1
λ2
λN
TX
TX
OXC
OADM
OXC
OADM
OXC
OXC
OXC
Photonic Ring Network
λ1 λ2 … λi … λN
λi
λj
(b)
Figure 1.1 (a) Schematic of a typical point-to-point WDM transmission system (b) A typical WDM photonic ring network
8
In a photonic ring network (Fig. 1.1(b)) the stream of WDM channels enter the ring and
they are directed into the subscribers serving nodes by the use of Optical Cross
Connects (OXC). Within the nodes, specific channels are Dropped or Added by using
Optical Add/Drop Multiplexers (OADM) in order to serve the subscribers.
For the successful implementation of future WDM networks and systems the
performance of all these aforementioned passive and active components is of
paramount importance. The available bandwidth for today’s optical networks lies
between the 1530 - 1570 nm (EDFA C-Band) and is currently being expanded to the L-
Band (1570-1610 nm) and S-Band (1480-1520 nm) to accommodate the increasing
network traffic. For the efficient use of the total optically amplified window the optical
device specifications are getting ever more stringent. Indeed, the channel spacing in
WDM systems has evolved from 200 or 100 GHz few years ago to 50 GHz and 25
GHz. Furthermore, planned bit-rate migration towards 40 Gbit/s and higher, sets
extremely tight requirements especially on WDM components/subsystems and filters.
Filters are incorporated in optical multiplexers and demultiplexers as well as OXC and
OADMs, and are the most important passive devices used in WDM networks.
This Chapter gives a review of the state of art of different optical filter technologies.
The filters are classified into general categories and in some cases their performance is
compared using system simulations. Finally an expanded discussion is presented
around the Bragg grating based OADM architectures.
1.2 General properties of optical filters
To date there have been proposed many different architectures for optical filters and
they have been implemented in many forms. The most representatives are:
• Mach-Zehnder interferometer based filters (MZI) [1.1]
• Arrayed Waveguide Gratings (AWG) [1.2, 1.3] - also known as Waveguide Grating
Routers (WGR)
• Fourier Filters [1.4]
9
• Thin Film Filters (TFF) [1.5]
• Bragg Grating based Filters [1.6]
Based on their fundamental operational principles, these filters can be classified in
different classes, which accordingly define the general performance characteristics and
limitations of the filters.
DWDM systems, set stringent specifications on optical filters by means of in-band
characteristics (flatness, ripple, steepness of the filter edges, dispersion), out-of-band
characteristics (crosstalk, side lobes, dispersion), and insertion loss. These
characteristics depend on both the particular implementation of the filter but also on
their underlying fundamental operational principle. For example, as we will show later,
identical Bragg gratings deployed in various device architectures exhibit different
filtering characteristics although their operational principle and function is common in
all these implementations.
To accommodate densely packed WDM channels, filters with a very steep amplitude
response are needed. The in-band dispersion of these near rectangular filters needs also
to be minimum in order to accommodate high bit rate transmission through the filter. It
has been shown that the in-band dispersion is a major factor in optical filtering
performance [1.7]. The requirement for filters with flat amplitude response and with
low in-band dispersion raises a well-studied problem in the area of design of digital
filters [1.8]. Central to this problem is the concept of the Minimum Phase Filter (MPF).
In MPF’s filters there is a unique relationship between the amplitude and the phase
response while in contrast in non-MPF’s the amplitude and phase response are
uncorrelated. Obviously in the latter case the amplitude response can be tailored, by
proper design, independently from the phase response, leading to flat dispersion-less
filters [1.9]. In the following discussion the fundamental characteristics of the proposed
optical filter architectures will be identified.
1.3 Arrayed waveguide gratings
10
An Arrayed Waveguide Grating (AWG) is a very successful filtering device, especially
for applications, which require high count of WDM channels. It is implemented
exclusively in integrated planar form, known alternatively as Planar Lightwave Circuit
(PLC), on the Silica-on-Silicon platform or alternatively on semiconductor materials
(InP). The configuration of an NxN AWG multiplexer is shown in Figure 1.2.
Figure 1.2 Schematic of an NxN Arrayed Waveguide Grating
The device consists of N input/output waveguides, two focusing slab waveguides and
arrayed waveguides with a constant path length difference between neighboring
waveguides. By launching light in one of the input waveguides all the arrayed
waveguides are excited through the slab waveguide. After traveling through the arrayed
waveguides, the monochromatic light beam interferes constructively at one focal point
in the second slab. The location of the focal point and consequently the exit waveguide
depends on the wavelength. There have been fabricated and demonstrated
experimentally very high-density devices, e.g 256x256 for application in dense WDM
systems, with channel spacings as low as 25 GHz [1.10]. By employing thermo-optic
switches on the same PLC reconfigurable filters have been demonstrated based on
AWGs. [1.11]. The main disadvantages of AWG-type devices are the relatively high
insertion loss <-6dB dB, the low crosstalk performance ~ -25 dB and the round -type
spectral characteristics as illustrated in Figure 1.3.
11
AWGs have also been fabricated with improved pass-band flatness but at expense of an
increased insertion loss of about –8 dB [1.11]. A typical amplitude response for an
AWG can be seen in Figure 1.3.
Figure 1.3 Full amplitude response of an AWG with Gaussian type amplitude response (left) and flattened response for an isolated channel (right) (after [1.12, 1.13])
The round-type amplitude response of the AWG is clearly shown. This poor flatness of
the passband makes them very susceptible to cascading -which is unavoidable in a
large area network- because of the induced effective bandwidth narrowing and the
associated system penalty. Furthermore because of the transmissive mode of operation
of AWGs an individual WDM channel cannot be selectively dropped in a network node
but all the channels have to be simultaneously demultiplexed resulting thus in
accumulated distortion effects for all the channels. Another implication of the
fabrication principle of AWGs is the high cost of the device for use in a single
subscribers node. AWGs are inherently very well suited for high channel count
applications. Taking into account that the cost of a high dense PLC AWG filter is
increased drastically with the number of pigtailed fibers –for each channel- it makes it
costly inefficient when employed for filtering a single channel. Alternative filter
technologies need to be employed there, such as Bragg grating filters or TFF.
12
Theoretically, the response of an AWG filter can be expressed as a finite number of
weighted fixed delays [1.9]:
∑−
−=1
0
)()(N
njenhH ϖω (1.1)
where h(n) is the discrete impulse response and N the number of WGR arms and ω the
normalized frequency. This type of response is known in digital filter theory as Finite
Impulse Response (FIR). It has been show that theoretically this type of filter is non-
MPF and is dispersionless [1.9]. However in real devices, presence of loss in the
arrayed waveguides, random phase changes due to errors in the fabrication process,
small differences in the input and output slabs and finally losses in the slab waveguides
lead to dispersion in the AWG [1.14] and the device becomes a MPF variant. It has
been shown recently that the dispersion characteristics of AWGs cannot be considered
negligible and lead to substantial system penalties, especially at high bit rates such as
40 Gbit/s [1.14].
1.4 Thin film filters
Thin Film Filters (TFF) [1.5] have started being increasingly popular for WDM
applications mainly because of their compactness, simplicity and environmental
stability. Their structure is based on that of the Fabry-Perot (F-P) etalon, which is
composed of a cavity and mirrors and acts as a bandpass filter. The centre operational
wavelength is determined by the cavity length. A narrow-band thin film interference
filter consists of more than two F-P cavities separated by dielectric reflection layers
with a very high refractive index contrast (typically ∆n≈1). Each cavity contains a
multiple-layer structure with more than 50 layers. Typical spectra of TFF are shown in
Figure 1.4 and is obvious that the spectral shape is not inherently compatible with the
requirements of DWDM technology.
By increasing the number of the cavities (typically 3-5) the spectral response may be
squared but at the expense of added ripple in the passband, which gets worse with
increasing number of cavities. Additionally it is rather difficult to implement narrow-
band TFF for DWDM applications, mainly because of fabrication difficulties –for
13
example, fabrication of a 50 GHz filter requires typically several hundred layers of
coating-, increased assembly cost and additional insertion loss.
Figure 1.4 Spectra of multicavity TFF [1.5] & detail of spectrum [1.12] (Thick line:Transmission)
The response of the TFF can be generally expressed as that of the reflection spectrum
of a general multiple-layer structure [1.9]:
∑
∑−
−
−−
−= 1
0
1
0
1)( N
njn
Nnj
n
ea
ebH
ϖ
ϖ
ω (1.2)
where coefficients αn, bn, are derived from the reflection coefficients between the
different layers and N is the total number of layers. This type of response is known in
digital filters theory as Infinite Impulse Response (IIR) and inherently involves a
feedback mechanism, as indeed happens in TFF’s given that reflection is an inherently
feedback mechanism. In contrast to the FIR type filters described before there is no
feedback mechanism as is obviously the case in the operation of AWG’s.
It can be shown for the TFF, based on the exact transmission response expressions of
multiple cavity filters, that they are MPF’s. That additionally means that by increasing
14
the number of cavities, in order to improve their characteristics, will not only add ripple
in the passband but also increase the dispersion near the filter’s edges.
1.5 Bragg grating based filters
Bragg grating filters (BGF) operate in reflection mode and their operational principle
can be expressed generally from Equation 1.2. However there are major differences
with TFF. Firstly TFF operate, based on a feedback mechanism, in transmission mode.
Secondly the layers in photorefractive Bragg gratings involve very small index
modulations which consequently means that a BGF is built from many layers and thus
is a longer device than a TFF. Spectral characteristics of BGF are also very different
than TFF, exhibiting a very flat amplitude response. A typical spectral response of a
fiber Bragg grating is shown in Figure 1.5.
BGF have so far been implemented mostly in fibre geometry (FBG) and have the
advantage of very low insertion loss and very good spectral characteristics compared
with other waveguides based devices.
Figure 1.5 Spectral response of a fiber Bragg grating (Thick line:Reflection, Thin line: Transmission) (after [1.12])
Bragg gratings are usually fabricated by inscripting a grating structure within a
photosensitive silica fibre core or alternatively to a photosensitive planar film by UV
15
laser irradiation through a phase mask [1.15]. The period of the written Bragg grating
is typically around 0.5 µm in order to couple the forward and the backward propagating
modes and to be operated in the third telecom window (1550nm). Phase Bragg gratings
written on photosensitive waveguides are much smoother than the etched gratings
-used mainly in semiconductor materials - reducing greatly the associated loss. FBG
are very versatile devices and their characteristics can be easily tailored by adjusting
suitable fabrication parameters, such as refractive index modulation, length,
apodization profile, period chirp, tilt, and phase shift insertion. Advanced Bragg grating
writing techniques [1.16] have allowed the fabrication of sophisticated high
performance filters based on gratings with arbitrary apodization profiles and phase
shifts. Bragg gratings written in coupled waveguide structures, which offer channel
routing functions, have also been demonstrated. This class of devices is very important
for fabrication of more functional components such as Add/Drop multiplexers and will
be discussed later in this Chapter.
1.6 Comparison of specially designed Bragg grating filters with TFF The spectral properties of phase Bragg gratings can be tailored to a great extent -in
contrast with TFFs. This is primarily due to fact that TFF are transmissive devices and
therefore the dispersion performance cannot be disentangled from the transmission
profile. In addition due to causality, the more square the transmission profile, the larger
the in-band dispersion variation [1.9]. It has been proved that spatially asymmetric
Bragg gratings, working in reflective mode, are non-MPF and the dispersion spectrum
may be defined independently from the reflection spectrum [1.9]. A recently developed
inverse scattering technique has allowed efficient and physical realizable designs for
high performance Bragg gratings [1.17]. Additionally, advanced fabrication techniques
[1.16] have enabled the experimental demonstration of specially designed
dispersionless gratings with near rectangular amplitude response [1.18].
In this section the performance of high performance BG filters is demonstrated and
compared with standard TFF’s. We consider an almost dispersionless Bragg grating
(SFBG) designed using the novel inverse scattering method [1.17] and a 5-cavity TFF,
16
both with FWHM bandwidth of 0.5 nm. By using system simulations –as described in
detail in Chapter 5- the effect of cascading is examined for both filters at 10 Gbit/s
transmission speed for non-return-to-zero (NRZ) modulation format. The simulated
communication system is an Intensity Modulation/Direct Detection system (IM/DD).
Figure 1.6 gives the filter’s amplitude response.
Figure 1.6 Amplitude spectral response of TFF and specially designed SFBG
The performance of the filters is quantified by calculating the resulted Eye-Opening
penalty (EOP) after passing the signal through the cascade of the filters. Initially we
consider that all the cascaded filters are perfectly aligned to each other and also
perfectly aligned with the spectrum of the signal source. Figure 1.7 gives the EOP, as a
function of the number of cascades of the filters. Is obvious that due to elimination
effect of in-band dispersion in the Bragg grating filter and also the better square
characteristics of the amplitude response, the distortion effects to the initial signal are
negligible even after 200 cascades.
Wavelength (nm)
1549 1550 1551
Filte
r am
plitu
de
0
1
SFBG
TFF
17
Figure 1.7 Effect of perfectly aligned cascaded filtering on EOP
Figure 1.8 Effect of uniformly misaligned cascading filtering on EOP
A major issue in real WDM systems is the effect of misalignments of the filters with
the laser source. Misalignments can arise from fabrication imperfections,
laser/transmitters instabilities, temperature drifts, and due to other environmental
Cascade number
0 50 100 150 200
Eye-
Ope
ning
Pen
alty
(dB)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
FBGTFF
Cascade number
0 50 100 150 200
Eye-
Ope
ning
Pen
alty
(dB)
0.0
0.2
0.4
0.6
0.8
1.0
FBGTFF
18
parameters. The effect of these misalignments to the overall performance of these two
different types of cascaded filters is estimated here. We consider here a series of filters
with central operating wavelengths uniformly distributed within a given symmetrical
range of total misalignment. For a number of uniformly misaligned filters in the range
of [-0.1nm, 0.1nm] around the central wavelength of 1550nm the EOP is estimated as a
function of this number (Figure 1.8). After a number of 200 cascades the EOP for the
Bragg grating is only ~1 dB in contrast with TFF case where the penalty approaches
the value of 5 dB. Indicatively, Figure 1.9 shows the eye diagrams for both filters for
the cascade number of 100 (Fig. 1.9(a)) and 200 (Fig. 1.9(b)).
Figure 1.9 Indicative eye-diagrams for Bragg grating and TFF
Based on the above results, is clear the great potential of the novel specially designed
Bragg grating based filters (SBG), compared to the inherently MPF type and
dispersive TFF. With the stringent filter specifications for DWDM systems in high bit-
rate applications, the choice of SBG would be a much more favorable solution
compared to today’s competitive TFF technology.
0 10 20 30 40 50 60 700
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.1 0 10 20 30 40 50 60 70
0 0.02 0.04 0.06 0.08 0.1
0.12
0 10 20 30 40 50 60 70 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50 60 70 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
TFF
SFBG
Cascade: #200 #100
19
1.7 Bragg gratings based OADMs Four-port devices that Add and/or Drop a particular channel are of great importance for
optical networks. They can be used as simple components, which serve a single
subscriber in a node of an optical network, or as building blocks of more complex
modules such as optical cross connects and switch matrices. Simple OADM
configurations, using the unique spectral characteristics of Bragg gratings, appear to be
very promising solutions intended to find applications in DWDM systems.
A number of different four-port OADM configurations have been proposed. The
simplest one, which makes direct use of the reflection properties of a Bragg grating
written in a single mode fiber, is the well-known configuration with the two optical
circulators (OCs) [1.19] shown schematically in Figure 1.10(a). This OADM
implementation is frequently used as a benchmark in the sense that it provides excellent
crosstalk performance and negligible back reflections. In addition, the reflection and
dispersion characteristics of the OADM are identical to the ones of the grating.
However, it should be stressed that because of the circulators this OADM suffers from
relatively high insertion loss (~1dB), it is bulky and expensive and cannot be easily
integrated. It has been identified and realized that in future broadband communication
networks WDM component’s volume or alternatively ‘component’s volume per Gb/s
per WDM Channel [m3 –per- Gb/s –per- #Channel]’ becomes increasingly important
parameter in commercial dence WDM systems and thus the systematic employment of
bulky and expensive components cannot survive in the future. [1.20]
More compact grating-based OADMs, without the use of circulators, can be classified
in two main categories, namely interferometric and non-interferometric. One class of
interferometric OADMs rely on the interference between two optical signals reflected
by Bragg gratings that are incorporated into various interferometric optical
arrangements, such as Mach-Zendher interferometers (MZIs) [1.1,1.21-1.25] and full
couplers [1.26]. The other class is based on co-directional or contradirectional Bragg
grating assisted coupling in symmetrical or asymmetric couplers [1.27-1.31].
20
Figure 1.10 a) Circulator based OADM and explanation of the Add/Drop operation of a particular channel., b) Mach-Zehnder OADM configuration, (c) Symmetrical Coupler (SFC) OADM, d)Asymmetrical Coupler based OADM with Bragg grating in one waveguide only, e) Tilted Bragg grating based OADM
(a)
(b)
(c)
(d)
(e)
21
Perfectly matched MZI-based OADMs, with identical gratings in each arm, can
potentially result in an ideal performance, better than the one of OC-based OADMs,
since they show no backreflections and need no extra components, i.e. circulators or
isolators. Additionally they can provide very low insertion losses (~0.1dB) and they
can be fully integrated. However, grating mismatches and interferometer-arm
imperfections compromise the OADM performance severely, resulting in strong
backreflections and spectral distortions. In this case, careful post-processing and
trimming is required. In addition, two extra isolators are quite likely to be required at
the two input ports to avoid the deleterious effects of backreflections, making the total
extra-component count equal to the OC-based devices.
In the SFC-based OADMs, on the other hand, the grating is placed in the coupler waist
to reflect the two lowest-order eigenmodes. These modes, however, have different
propagation constants and the corresponding reflected spectra are always partially
overlapping. This results always in partial interference and produces strong
backreflections and spectral distortions and, as before, two extra isolators might be
needed. Additionally, the grating has to be placed precisely in the correct position for
optimum operation [1.26]. This OADM configuration through employing grating
assisted couplers gives the advantage compared to the MZI devices of reduced
sensitivity to fabrication imperfections and environmental changes because instead of
the far away spaced waveguide arms of the MZI we have now a simple coupler. Indeed
in the MZI configuration any imbalance of the order of one wavelength of light can
degrade drastically the performance of the device because the interference happens
between different waveguides. In the grating assisted coupler configuration the
allowable imbalance for the same degradation is much greater -of the order of the
coupling length- because the interference now is based on the beating between the
normal modes of the waist waveguide. But on the other hand this interferometric
configuration has the disadvantage that the useful bandwidth of the Add and Drop
actions is always narrower than the bandwidth of the initial employed grating, due to
grating’s intra- and out-of-band dispersion. That leads to less effective bandwidth
utilization. Ultimately, a goal for the integrated waveguide implementation of these
22
devices will be to eliminate the sensitivity to environmental factors of vibrations,
temperature changes and humidity.
The third general category of Bragg grating based OADMs includes those based on
asymmetric Bragg couplers [1.32-1.34]. In this case, a Bragg grating is used to contra-
directionally couple light between two otherwise dissimilar uncoupled waveguides. In
this geometry there are, in general, three types of interactions between the two lower
order (even and odd) modes, involving even-even (e-e), odd-odd (o-o) eigenmode self-
coupling as well as even-odd (e-o) eigenmode resonant cross-coupling. This results in
a maximum of three reflection peaks appearing in the drop- and add-port spectra, as
well as, strong backreflections in the input port. The relative strength of these peaks
can be controlled by careful grating design.
In one configuration, the grating is formed in only one of the cores of a dual dissimilar-
core fibre to minimise backreflections. The first one that was proposed and fabricated
by Dong et al. [1.32] is based on an asymmetric coupler with a Bragg grating written in
only one arm over the coupling region. Due to the strong mismatch of the cores there is
no power transfer from one to the other core forming thus a null coupler system. The
period of the grating is selected properly in order to couple efficiently at the desired
wavelength the forward propagating fundamental mode of the one core to the backward
propagating mode of the other core. This contradirectional coupling suggests the Add
or Drop operation of this OADM. The other wavelengths that don’t satisfy the Bragg
condition continue propagating along the initial input core. In order now to eliminate
the undesired back reflections in this device the two cores are well separated along the
coupling region and consequently the one core senses the grating perturbation only in
its evanescent part of the mode field [1.34]. Increasing the waveguides separation we
need stronger Bragg gratings to maintain a sufficient coupling coefficient between the
two modes. This makes necessary the use of highly photosensitive materials able to
give index modulation of ~10-2 which unfortunately is not currently the real case. To
compensate for the use of less photosensitive materials employed in real devices,
increase of the grating length is the only solution in order to achieve an adequate
grating strength. The longer grating leads to very narrow spectral characteristics
23
resulting in a tight and restrictive relation between back reflections, bandwidth and
minimum channel spacing [1.34].
Finally, another non-interferometric OADM configuration (see Figure 1.10(e)), based
on a null coupler (with zero coupling) with a tilted grating in its waist, has been
recently reported by Kewitsch et al. [1.33]. Null couplers are comprised of two
dissimilar waveguides brought gradually into close proximity and finally in contact to
form the waist. The devices are actually based on adiabatic mode transformation [1.35]
taking place along the coupler arms and their waist. A short period UV-written tilted
grating can provide resonant contra-directional coupling and add/drop function [1.6,
1.33]. A non-optimised null coupler device, however, will exhibit the same
performance limitations as the other devices of this category, namely, a maximum of
three reflection peaks at the drop- and add-port spectra, as well as, strong
backreflections at the input port. In addition to OADMs, null couplers have also been
excited with propagating flexural acoustic waves and successfully used for the
implementation of other high quality fibre components, such as frequency shifters and
switches [1.35]. With properly optimized characteristics of the null coupler and the
employed tilted grating this device can exhibit theoretically superior characteristics
[1.6] with a spectral response identical that of the employed Bragg grating, as will be
described in Chapter 3
The performance of all these Bragg grating based OADM configurations and the
requirements for optical isolators or circulators are concluded in the Table1.1 below.
Insertion Loss
Back reflections
Drop-Spectrum Peaks
Add-Spectrum
Peaks
No of Isolators
No of Circulators
Circulator Based High Negligible 1 1 - 2 Interferometric
MZI (Ideal) Low Negligible 1 1 - - MZI (Non-Ideal) Low High 1 1 2 - Symmetric Coupler Low High 1 1 2 - Frustrated Coupler Low High 1 1 2 -
Non-Interferometric (Grating-Assisted Couplers) Normal written BG Low High 3 3 2 - Tilted BG Low High 3 3 2 - Optimised Tilted BG Low Negligible 1 2 - -
24
Table 1.1 Comparison of Grating Based OADMs Performance
25
1.8 References
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narrowband wavelength-selective optical tap and combiner,” Electronics Letters, vol.
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[1.5] M. A. Scobey, D. E. Spock, “Passive DWDM components using Microplasma
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Lightwave Technology, vol. 19, no. 1, pp. 92-104, Jan. 2001.
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induced power penalty in fiber-Bragg-grating WDM filter cascades using optical
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vol. 12, no.10, pp. 1406-1408, October 2000.
[1.8] A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, Englewood
Cliffs, NJ: Prentice-Hall, 1975.
26
[1.9] G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, R. E. Slusher, “Dispersive
properties of optical filters for WDM systems,” IEEE J. Quantum Elec., vol. 34, no. 8,
pp. 1390-1402, 1998.
[1.10] Y. Hida, Y. Hibino, M. Itoh, A. Sugita, A. Himeno and Y. Ohmori, “Fabrication
of low-loss and polarization-insensitive 256-channel arrayed-waveguide grating with
25 GHz spacing using 1.5% ∆ waveguides,” Electron. Lett., vol. 36, pp. 820-821,
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[1.11] K. Okamoto, “Recent progress of integrated optics planar lightwave circuits,”
Optical and Quantum Electronics, vol. 31, pp. 107-129, 1999.
[1.12] C. R. Giles, M. Spector, “The wavelength Add/Drop multiplexers for lightwave
communication networks,” Bell Labs Technical Journal, pp. 207-229, Jan-Mar. 1999.
[1.13] Y. Hibino, “Passive optical devices for photonic networks,” IEICE Trans.
Commun., vol. E83-B, no. 10, pp. 2178-2190, Oct. 2000.
[1.14] M. E. Vieira Segatto, G. D. Maxwell, R. Kashyap, J. R. Taylor, “High-speed
transmission and dispersion characteristics of an arrayed-waveguide grating,” Optics
Communications, vol. 195, pp. 151-157, Aug. 2001.
[1.15] K. O. Hill, B. Maro, F. Bilodeau, D. C. Johnson, J. Albert, “Bragg gratings
fabricated in monomode photosensitive optical fiber by UV exposure through a phase
mask,” Appl. Phys. Lett., vol. 62, pp. 1035-1037, 1993.
[1.16] W. H. Loh, M. J. Cole, M. N. Zervas, S. Barcelos, R. I. Laming, “Complex
grating structures with uniform phase masks based on the moving fiber-scanning
technique,” Opt. Lett., vol. 20, no. 20, pp. 2051-2053, Oct. 1995.
[1.17] R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm
for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron., vol.
35, no. 8, pp. 1105-1115, Aug. 1999.
27
[1.18] M. Ibsen, P. Petropoulos, M. N. Zervas, R. Feced, “Dispersion-free fiber Bragg
gratings,” paper MC1, Optical Fiber Communication Conference, OFC’2001,
Anaheim, March 2001,
[1.19] K. P. Jones, M. S. Chadry, D. Simeonidou, N. H. Taylor, P. R. Morkel, “Optical
wavelength add-drop multiplexer in installed submarine WDM network,” Electronics
Letters, vol. 31, no. 24, pp. 2117-2118, Nov. 1995.
[1.20] Private communication with Dr. B. Garrett, Nortel Networks at PHOTON-
Project Meeting, University College London, London, April, 2001
[1.21] T. Erdogan, T. A. Strasser, M. A. Milbrodt, E. J. Laskowski, C. H. Henry, and
G. E. Kohnke, “Integrated-Optical Mach-Zehnder add-drop filter fabricated by a single
UV-induced grating exposure,” Applied Optics, vol. 36, pp. 7838-7845, 1997.
[1.22] F. Bilodeau, K. O. Hill, B. Malo, D. C. Johnson, J. Albert, “High-return-loss
narrow-band all-fibre bandpass Bragg transmission filter,” IEEE Photonics Technology
Letters, vol. 6, no. 1, pp. 80-82, Jan. 1994.
[1.23] R. Kashyap, G. D. Maxwell, and B. J. Ainslie, “Laser-Trimmed four-port
bandpass filter fabricated in single-mode photosensitive Ge-doped planar waveguide,”
IEEE Photonics Technology Letters, vol. 5, no. 2, pp. 191-194, Feb. 1993.
[1.24] F. Bilodeau, D. C. Johnson, S. Theriault, B. Malo, J. Albert, K. O. Hill, “An all-
fiber dense-wavelength-division multiplexer/demultiplexer using photoimprinted Bragg
gratings,” IEEE Photonics Technology Letters, vol. 7, no. 4, pp. 388-390, Apr. 1995.
[1.25] J. Albert, F. Bilodeau, D. C. Johnson, K. O. Hill, K. Hattori, T. Kitagawa,
Y.Hibino and M. Abe, “Low-loss planar lightwave circuit OADM with high isolation
and no polarization dependence,” IEEE Photonics Technology Letters, vol. 11, no. 3,
pp. 346-348, Mar. 1999.
28
[1.26] K. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X.
Daxhelet, F. Gonthier, “Optical add-drop multiplexer based on UV written Bragg
gratings in a fused 100% coupler,” Electronics Letters, vol. 33, no. 9, pp. 803-804, Apr.
1997.
[1.27] D. Marcuse, Theory of Dielectric Optical Waveguides, Chapter 7, Academic
Press, New York, 1991.
[1.28] R. R. A. Syms, “Optical directional coupler with a grating overlay,” Applied
Optics, vol. 24, no. 5, pp.717-726, Mar. 1985.
[1.29] J.-L. Archambault, P. St. J. Russell, S. Barcelos, P. Hua, L. Reekie, “Grating
frustrated coupler: A novel channel-dropping filter in single-mode optical fiber,”
Optics Letters, vol. 19, pp. 180-182, 1994.
[1.30] P. Yeh, H. F. Taylor, “Contradirectional frequency-selective couplers for guided
wave optics,” Applied Optics, vol. 19, no. 16, pp. 2848-2855, Aug. 1980.
[1.31] N. Imoto, “An analysis for contradirectional-coupler-type optical grating filters,”
Journal of Lightwave Technology, vol. LT-3, no. 4, pp. 895-900, 1985.
[1.32] L. Dong, P. Hua, T. A. Birks, L. Reekie, P. St. Russell, “Novel add-drop filters
for Wavelength-Division Multiplexing optical fibre systems using a Bragg grating
assisted mismatched coupler,” IEEE Photonics Technology Letters, vol. 8, no. 12, pp.
1656-1658, Dec. 1996.
[1.33] A. S. Kewitsch, G. A. Rakuljic, P. A. Willems, A. Yariv, “All fibre zero
insertion loss add drop filter for WDM,” Optics Letters, vol. 23, no. 2, pp. 106-108,
Jan. 1998.
29
[1.34] T. Erdogan, “Optical add-drop multiplexer based on asymmetric Bragg coupler,”
Optics Communications, vol. 157, pp. 249-264, Dec. 1998.
[1.35] T. A. Birks, S. G. Farwell, P. St. J. Russell, C. N. Panell. “Four-port fiber
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1966, Dec.1994.
29
CHAPTER 2
Analysis and Modelling of Bragg Grating
Assisted Waveguide Devices
2.1 Introduction
This Chapter describes the theoretical mathematical analysis and the simulation method
for arbitrarily shaped coupled waveguide structures, and develops the complete
formulation for the analysis and simulation of a non-uniform Bragg grating in a two-
mode structure. Combination of the two formulations is implemented [2.1] in order to
calculate the full spectral response of any device based on a grating based coupled
waveguide structure.
The widely established approach for the simulation of waveguide devices and grating
assisted coupled waveguide devices is probably the Coupled Mode Theory (CMT) [2.2,
2.3] which combines a deep physical and intuitive insight into the problem together
with a much greater computational simplicity compared to other methods such as Finite
Difference (FD) and Finite Element (FE) Beam Propagation Methods (BPM) [2.4,
2.5].
There are a number of different coupled-mode formulations, which have been
developed from the early 1950s until today. The choice of a particular CMT
formulation depends on the problem, the desired accuracy and the associated
computational complexity. The traditional CMT formulations are based on the ideal
modes of the individual waveguides of the structure. There are two main representative
formulations in this class, the orthogonal CMT [2.2, 2.6] and the rigorous non-
30
orthogonal CMT [2.7]. The first one is a simple intuitive approximation, which can
model quite accurately devices with weakly coupled waveguides. The later is more
complicated and can model a wider variety of problems involving dissimilar
waveguides for even the strongly coupled case [2.8-2.10]. Strong coupled mode theory
has been also applied to grating assisted filters and a discussion for the application of
this theory can be found in [2.3, 2.5]. A very strong debate developed for over a decade
during 1980s regarding these two theories. An extensive discussion and analysis about
the debate, the accuracy and the applications of the two formulations can be found in
the references [2.3] and [2.8].
A more rigorous and general coupled-mode approach uses the exact composite modes
–normal modes- of the waveguide structure instead the approximation of the
superposition of the individual waveguide modes. This approach is much more accurate
and can be applied equally effectively in the strongly coupled case since the normal
modes are calculated directly taking into account the exact shape of the structure,
without considering any approximations. The local normal mode analysis in
conjunction with the step transition model [2.11] has been applied by Burns & Milton
and Yajima [2.12, 2.13] in the problem of strongly coupled branching waveguides. The
power transfer mechanism and mode conversion between the local normal modes is
described by the step transition model giving this way a quantitative estimation of the
power propagating along the waveguide structure. The method is computationally more
intensive than the traditional CMT since for the modeling of a device is required the
solution of the dispersion equation at each step of the propagation simulation and the
calculation of modal overlap integrals. This method has been applied for the modeling
of strongly coupled tapered structures and resulted in very good agreement with the
experimental findings [2.14].
For the modeling and simulation of the waveguide devices in this thesis we use the
local normal mode analysis, since it has been proved as a very effective and general
tool for a wide variety of problems. The analysis of the Bragg grating is also based on
normal mode analysis [2.15] as it will be described later in this Chapter. The next
31
sections present the mathematical analysis and the algorithmic implementation of the
model.
2.2 Local normal mode analysis and step transition model
Figure 2.1 demonstrates the working principle of the model. An arbitrary continuous
coupler structure –with refractive indices distribution and geometrical characteristics as
described in the Figure- is divided in a number of discontinuous abrupt steps of length
dz. Each step forms a parallel, five-layer waveguide structure and the normal modes are
calculated by solving the dispersion equation of the 5-layer structure, as described in
the next section. The propagation constants of the #modes0 normal modes at step-0 and
#modes1 normal modes at step-1 are β 0 ( )i , β 1 ( )j respectively.
Figure 2.1 Schematic and parameters of the step transition model
The power transfer between the normal modes of the two successive step sections is
calculated at each interface. The amplitudes A1(j), and phases α1(j) at step-1 are
calculated as a function of the amplitudes A0(i), and phases α0(i) at step-0.
n1
n2
n3
n4
n5
z
d1
d2
S(z)=h
Step-0 Step-1
x
α0(i) A0(i)
α1(j) A1(j)
dz
modes: i=1..(modes0) propagation constants: β 0 ( )i
modes: j=1..(modes1) propagation constants:β 1 ( )j
32
All the calculations are based on a five-layer planar structure with step refractive index
profile. For channel waveguides geometry the 3D problem can be reduced to a 2D
problem through the effective index method and can be treated this way with the same
model.
2.2.1 Dispersion equation for the five layer waveguide structure
In the analysis in this Chapter we consider for simplicity only the propagation of the
Transverse Electric (TE) modes. All the waveguide structures and devices in this thesis
are modeled also for the TE case. However, it should be stressed that under the weak
guiding approximation the analysis and the results for the TE case can be applied with
very good approximation to the TM case.
The TE electric field distribution for a five-layer waveguide can be expressed as
follows:
e
E e xE e E e x dE e E e d x d hE e E e d h x d h dE e d h d x
y
k x
jk x jk x
k x k x
jk x jk x
k x
=
−∞ < <
+ < <
+ < < +
+ + < < + +
+ + < < +∞
+ − −
+ − −
+ − −
−
1
2 2 1
3 3 1 1
4 4 1 1 2
5 1 2
1
1 2
3 3
4 4
5
00
(2.1)
where
k n k i
k
i i= − =
=
β
ω µ ε
20
2
02
0 0
1 2 3 4 5( ) , , , , (2.2)
For the TE modes we have 0,0 == yz he . From the Maxwell equations we derive
also that 0,0 == xz ee and:
yx ehωµβ
−= and xeih y
z ∂
∂⋅=
ωµ
33
The boundary conditions demand that ye (and thereby automatically xh ) and xey
∂
∂(and
thereby zh ) be continuous at the boundaries x=0, d1, d1+h, d1+h+d2. By these
continuity conditions the eigenvalue equation can be obtained and is given by the
expression:
{( ) ( ) tan( )} {( ) ( ) tan( )}
exp( ){( ) ( ) tan( )}{( ) ( ) tan( )}
k k k k k k k d k k k k k k k dk h k k k k k k k d
k k k k k k k d
1 3 2 1 3 22
2 1 3 5 4 3 5 42
4 2
3 3 1 2 1 3 22
2 1
3 5 4 3 5 42
4 2
20
+ + − ⋅ + + −
− − − + + ⋅
− + + =
(2.3)
Using numerical methods this dispersion equation is solved at each step of the structure
and the propagation constants β of all the normal modes at the particular step are
calculated.
2.2.2 Step-wise approximation of waveguide structures
As described in Figure 2.1 the step transition model [2.11] can model the operation of a
coupler structure by dividing it to a series of discontinuous abrupt steps. In the model
we assume initially an excitation procedure with the waveguide modes of interest to be
incident on the first step of the structure and then calculate the transmitted mode’s
amplitudes and phases by requiring the transverse-field components to be continuous at
the step. Coupling between local normal modes takes place only at each step
discontinuity and then the modes are simply propagated along the length of each
section. It should be stressed here the difference between the local normal modes and
the true normal modes of the structure. The true normal modes are orthogonal of each
other and do not couple. The local normal modes however can couple to each other at
each step discontinuity. This mechanism is better described as mode conversion than
mode coupling. By dividing the structure into large number of small steps and
repeating this process at each step a reasonable approximation of the mode's evolution
is obtained.
34
Next we describe briefly the model for the case of propagation of transverse electric
(TE) guided modes in a multimoded coupled waveguide structure.
The guided-mode’s TE electric fields can be expressed as:
ϕββ +=⋅−Ψ= zzazajzxzEey )()),(exp(),().( (2.4)
where E(z) is the real amplitude at the position z, ),( zxβΨ the real electric field
distribution which corresponds to the propagation constant β and ϕ a phase constant
in a general case. At each step along the structure the propagation constants of the
normal modes are obtained form the solutions of the eigenvalue equation for the TE
modes. The computational core of the step transition model is based on the calculation
of mode conversion and power transfer which takes place at the interface formed
between the two successive abrupt steps 0 and 1 (Figure 2.1). The formulation which
describes the power transfer of the #modes0 normal modes at step 0 to the #modes1
normal modes at step 1 originates from the expressions of boundary conditions of
continuity for the fields xy hande .
The amplitude coefficient and phase of the j (j=1...modes1) mode - which corresponds
to propagation constant β 1 ( )j - at step-1 is given [2.3] by the expression:
∑=
−⋅⋅=0mod
1
1001 ))()(cos()(),()(es
ijaiaiAjicjA (2.5)
∑
∑
=
=
⋅⋅
⋅⋅= 0mod
100
0mod
1
00
1
))(cos()(),(
))(sin()(),())(tan( es
i
es
i
iaiAjic
iaiAjicja (2.6)
where c(i,j) is the mode-conversion coefficient between the ith mode on step 0 and the
jth mode at step 1, and equals:
35
c i ji j
j jj ii i
I i jI i i I j j
i j
i i j j
( , )( ) ( )
( ( ) ( )( ) ( )( ) ( )
( ( ), ( ))( ( ), ( )) ( ( ), ( ))`
=+
++
⋅
2 0 1
0 1
0 1
0 1
0 1
0 0 1 1
0 1
0 0 1 1
β ββ β
β ββ β
β ββ β β β
(2.7)
The overlap integrals are estimated according to the formula:
I i i x x dx c di j c d i jc d c d( ( ), ( )) ( ) ( ) , , ,( ) ( )β β β β= ⋅ ⋅ =
−∞
+∞
∫ Ψ Ψ 0 1 (2.8)
For convenience, the amplitude coefficient on the above expressions is the normalized
real amplitude A(z) of the mode, defined as the ratio of the mode amplitude in the
presence of mode conversion to that amplitude which corresponds to unity power.
After these computations at each discontinuity of the structure the ‘new’ local normal
modes at step-1 are propagated along the finite length dz of the step. The mode
propagation along the length of a waveguide structure is simulated by iterative
calculations of transmitted modes’s amplitude and phase, as described in Equations
2.5-2.7. A pseudoalgorithmic implementation of the procedure is presented in
Appendix 2.A.
This method of analysis is quite general and can model accurately any device where the
assumption that the radiation modes do not convert back into guided modes, is valid. In
this model the transmitted radiation into unguided modes is treated exactly and the
effect of this power transfer is incorporated into the model. The effect of reflected
radiation into unguided modes is considered small and is neglected.
36
2.3 General analysis of a non-uniform Bragg grating
In this section we develop and present the theory for the calculation of the spectral
response of a nonuniform–apodized Bragg grating. The treatment is very general and
accurate because it takes into account the two (even and odd) forward and the two
backward propagating normal modes of the grating and was applied for first time by
Weber [2.15] for the special case of a uniform grating.
Figure 2.2 Model for the calculation of spectral response of a Non-Uniform Grating
Initially, the non-uniform Bragg grating is divided into #n uniform step-regions
[Lk, Lk+1], where k = 0, …(n, -1). Let us assume that in the grating region, Fi (z) (i=1,2)
are the amplitudes of the two forward propagating normal modes and Gi (z) are the
amplitudes of the two backward propagating normal modes as illustrated at the
schematic model in Figure 2.2.
The electric field in the grating can be expressed as:
E F z e G z e x
F z e G z e x e
gj z j z
j z j z j t
g g
g
g g
g
= +
+ +
− +
− +
{ ( ) ( ) ) ( )
( ) ( ) ) ( )}
1 1
1 1
1 1
1
2 2
2
β ββ
β ββ
ω
Ψ
Ψ (2.9)
L0 = 0 Ln = L
GRATING
F1(0) F2(0)
G1(0) G2(0)
F1(L) F2(L)
G1(L) G2(L)
z
... Lk-1 Lk Lk+1 ...
37
where Ψβ gi are the normal modes of the refractive index-averaged waveguide, because
of the grating perturbation, which correspond to the propagation constants β gi i=1,2 at
the waist waveguide. Real grating’s fabrication capabilities [2.16] allow us to assume
always that the average refractive index of the perturbed waveguide is the same as that
of the waveguide outside the grating section, simplifying this way the problem. The
normal modes in the above equation are normalized according to the following
equation:
Ψ Ψβ βωµβ
δgi gj
x x dx i jgi
ij( ) ( ) , ,⋅ = =−∞
+∞
∫2 1 20 (2.10)
The wave equation for the electric field component is the following:
0)],()([022 =∆++∇ grrg EzxxE εεµεω (2.11)
where ε r is the relative permittivity and ∆ε r , is the perturbation of the dielectric
permittivity because of the grating presence , which is periodic in the z-direction with
zero average over a period. This perturbation can be expanded in Fourier series:
∆ ∆ Λε επ
r m
jm z
m
x z x e( , ) ( )= ⋅−
≠∑
2
0
(2.12)
where Λ is the period of the perturbation. In our analysis we retain only the
fundamental harmonic (m=1)
Substituting equations (2.9) and (2.12) in to the wave equation (2.11) we obtain the
following set of differential equations:
38
dFdz
jk G z e jk G z e
dFdz
jk G z e jk G z e
dGdz
jk F z e jk F z e
dGdz
jk F z e jk F z e
j z j z
j z j z
j z j z
j z j z
111 1
212 2
212 1 22 2
2
111 1
212 2
212 1 22 2
2
1 1 2
1 2 2
1 1 2
1 2 2
= − −
= − −
= +
= +
+
+
− − +
− + −
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( )
* * ( )
* ( ) *
∆ ∆ ∆
∆ ∆ ∆
∆ ∆ ∆
∆ ∆ ∆
β β β
β β β
β β β
β β β
(2.13)
where iβ∆ are the phase detunings from the Bragg condition:
Λ−=−=∆ /πβββigBgii K (2.14)
and ijk the three coupling coefficients:
∫
∫
∫
Ψ∆=
ΨΨ∆==
Ψ∆=
+
+
+
xb
xa
xb
xa
xb
xa
dxxxk
dxxxxkk
dxxxk
g
gg
g
)()(4
)()()(4
)()(4
21
022
10*
2112
21
011
2
21
1
β
ββ
β
εωε
εωε
εωε
(2.15)
The integration bounds xα, xb define the spatial transverse extension of the grating.
The system of differential equations can be rewritten in the form:
=
GF
zSGF
dzd )( (2.16)
where S(z) is the following 4x4 complex matrix :
39
S z
jk e jk ejk e jk e
jk e jk ejk e jk e
j z j z
j z j z
j z j z
j z j z
( )
( )
( )
* * ( )
* ( ) *
=
− −− −
+
+
− − +
− + −
0 00 0
0 00 0
112
12
12 222
112
12
12 222
1 1 2
1 2 2
1 1 2
1 2 2
∆ ∆ ∆
∆ ∆ ∆
∆ ∆ ∆
∆ ∆ ∆
β β β
β β β
β β β
β β β
(2.17)
and the vectors F, G are defined as
=
=
)()(
)()()(
)(2
1
2
1
zGzG
zGandzFzF
zF (2.18)
Generally we can relate the vectors F, G at the position z Lb= with the vectors F, G at
z La= using the transfer matrix P L La b( , ) :
⋅=
)()(
),()()(
a
aba
b
b
LGLF
LLPLGLF
(2.19)
The matrix P L La b( , ) is the solution of the system and can be calculated by numerical
integration of the differential equations system (2.16) between ba LL , . However, by
making use of the special structure of the matrix S(z) it can be proved [2.15] that the
solution matrix can be calculated analytically using the following form:
P L L S L S L L L La b b a( , ) exp( ) exp( ) ,= = −1 2∆ ∆ ∆ (2.20)
where
S
jj
jj
1
1
2
1
2
0 0 00 0 00 0 00 0 0
=−
−
∆∆
∆∆
ββ
ββ
(2.21)
40
and
S S L S
j jk e jk ej jk e jk e
jk e jk e jjk e jk e j
a
j z j z
j z j z
j z j z
j z j zz La
2 1
1 112
12
2 12 222
112
12 1
12 222
2
00
00
1 1 2
1 2 2
1 1 2
1 2 2
= − =
− − −− − −
+
+
− − +
− + −=
( )
( )
( )
* * ( )
* ( ) *
∆∆
∆∆
∆ ∆ ∆
∆ ∆ ∆
∆ ∆ ∆
∆ ∆ ∆
ββ
ββ
β β β
β β β
β β β
β β β
(2.22)
The exponential of the matrix S2 can be easily calculated by finding the equivalent third
degree polynomial and the eigenvalues of matrix S2 [2.15].
Using the above formulation we can calculate the response of a non-uniform grating by
dividing the structure into many segments and estimating the solution matrix for each
one. Then it can be proved that the total solution matrix for the whole non-uniform
grating structure can be expressed as:
P L P L L P L L P L L P L Ltotal n n n n( , ) ( , ) ( , ) ... ( , ) ( , )0 1 2 1 1 2 0 1= ⋅ ⋅ ⋅ ⋅− − − (2.23)
and finally
⋅=
)0()0(
),0()()(
GF
LPLGLF
total (2.24)
The total solution matrix can be expressed in the form:
442222
2222
)()()()(
),0(xxGGxGF
xFGxFFtotal PP
PPLP
= (2.25)
The grating spectral response can now be calculated from Equation (2.24).
In the more general case we need to estimate the grating spectral response when it is
excited from both the left and right ports simultaneously. So by considering the input
41
normal modes F(0) and G(L), we calculate the output normal modes F(L) and G(0).
From Equation (2.24) we have:
( )
⋅⋅−⋅=
⋅⋅−⋅⋅+⋅=
⇔
⋅⋅−⋅=
⋅+⋅=⇔
⋅+⋅=⋅+⋅=
−−
−−
−−
)0()()0(
)0()()0()(
)0()()0(
)0()0()()0()0()()0()0()(
11
11
11
FPPLGPGFPPLGPPFPLF
FPPLGPGGPFPLF
GPFPLGGPFPLF
GFGGGG
GFGGGGFGFF
GFGGGG
FGFF
GGGF
FGFF
which after some minor manipulations leads to the expression:
142
1
2
1
44221
221
221
221
142
1
2
1
)()()0()0(
)()()()(
)0()0()()(
x
xxGGxGFGG
xGGFGxGFGGFGFF
x LGLG
FF
PPPPPPPPP
GG
LFLF
⋅
⋅−⋅⋅⋅−
=
−−
−−
(2.26)
The phase and the amplitude information of the normal modes are contained in this
complex representation.
2.4 Analysis of the composite grating-coupler structure
The combination of the analyses for the coupled waveguide structure and the Bragg
grating section can simulate any device based on grating assisted operation in a coupled
structure. The input port of the structure is initially excited with a particular mode
profile and the excited normal modes of the structure at the input are determined. These
local normal modes are propagated along the structure exchanging power and they
enter the grating with determined phase and amplitudes. At the grating section we
estimate the forward and backward propagating normal modes and continue to
propagate them to all the ports of the device. Finally the power and the phase are
calculated at all the output ports of the device. The excitation and calculation of output
power are described in the next two sections.
42
2.4.1 Excitation of the input waveguides
When a multimode structure is excited by an input field )()( xiΨ then the excitation
amplitude pa of the pth normal mode )(xpΨ in the multimode section is given by the
overlap integral between the two modes:
2/12
)(
)(
)()(
Ψ
Ψ⋅Ψ=
∫
∫∞+
∞−
+∞
∞−
dxx
dxxxa
p
pi
p (2.27)
The fraction of incident power excited in each mode fp can be calculated as:
dxx
dxxaf
i
pp
p 2)(
2
)(
)(
∫
∫∞+
∞−
+∞
∞−
Ψ
Ψ⋅= . (2.28)
2.4.2 Calculation of the response of the composite structure
Lets consider that in the multimode structure, #N normal modes are propagating. At the
output ports #1 and #2 the relative amplitude and the phase of those modes are
Αi i i N, , , ,...,α = 1 2 . Let E x E x1 2( ), ( ) are the electric field distributions of the
fundamental modes of the individual waveguides 1 and 2 respectively.
The total electric field at the position L of the structure is:
∑=
⋅−⋅Ψ⋅=ΕN
i
ajiitot
iexAx1
)()( (2.29)
43
where Nixi ,...,2,1,)( =Ψ are the electric field distributions of the respective normal
modes.
Figure 2.3 Output waveguides of the coupler
The power Pn at the output port #n = 1,2 is given by the square of the amplitude of the
fundamental individual mode at this port:
P E x x E x x dx nn n tot n tot= = ⋅ ⋅ =−∞
+∞
∫( )| ( ) ( ) ( ) , .,Ε Ε2
2
1 2 (2.30)
2.5 Summary
A modelling method for analyzing Bragg grating assisted devices based on coupled
waveguide structures has been described. The method is based on local normal mode
analysis and is a powerful tool, which can be applied to a wide variety of problems and
structures. It doesn’t use the weak coupling approximation as the traditional coupled
mode theory do and thus this method is directly applicable to even strongly coupled
waveguides. Also the shape of the structure is taken directly into consideration through
the 5-layer waveguides formulation, and that is important when the device is
parameterized by its branch shape. The developed method here will be applied in to the
next Chapters for the analysis of Bragg grating based devices.
1
2x
zL
44
2.6 References
[2.1] C. Riziotis, M. N. Zervas, “Design considerations of optical Add-Drop filters
based on grating assisted mode conversion in null couplers,” Journal of Lightwave
Technology, vol. 19, no. 1, pp. 92-104, Jan. 2001.
[2.2] A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE Journal of
Quantum Electronics, vol. QE-9, no. 9, pp. 919-933, Sep. 1973.
[2.3] W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J.
Opt. Soc. Am. A., vol. 11, no. 3, pp. 963-983, Mar. 1994.
[2.4] K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, 1st Edition,
2000.
[2.5] R. Marz, Integrated Optics, Design and Modeling, Artech House, 1995
[2.6] R. R. A. Syms, “The digital directional coupler: improved design,” IEEE Photon.
Technol. Lett., vol. 4, no. 10, pp. 1135-1138, Oct. 1992.
[2.7] A. Hardy, W. Streifer, “Coupled mode theory of parallel waveguides,” J.
Lightwave Tech., vol. LT-3, no. 5, pp.1135-1146, Oct. 1985.
[2.8] R. G. Peall, R. R. A. Syms, “Comparison between strong coupling theory and
experiment for three-arm directional couplers in Ti:LiNbO3,” J. Lightwave Tech., vol.
7, no. 3, pp. 540-554, Mar. 1989.
[2.9] R. G. Peall, R. R. A. Syms, “Scalar strong coupled mode theory for slowly
varying waveguide arrays,” Optics Commun., pp. 421-424, 1989.
45
[2.10] S-L. Chuang, “Application of the strongly coupled-mode theory to integrated
optical devices,” IEEE J. Quantum Electronics, vol. QE-23, no. 5, pp. 499-509, May
1987.
[2.11] D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” Bell Sys.
Tech. Journal, vol. 49, pp. 273-290, 1970.
[2.12] W. K. Burns, A. F. Milton, “Mode conversion in planar-dielectric separating
waveguides,” IEEE Journal of Quantum Electronics, vol. QE-11, no. 1, pp. 32-39, Jan.
975.
[2.13] H. Yajima, “Coupled Mode Analysis of dielectric planar branching
waveguides,” IEEE Journal of Quantum Electronics, vol. QE-14, no.10, pp. 749-755,
Oct. 1978.
[2.14] H. S. Kim, R. V. Ramaswamy, “Tapered, both in dimension and in index,
velocity coupler: theory and experiment,” IEEE Journal of Quantum Electronics, vol.
29, no. 4, pp. 1158-1167, April 1993.
[2.15] J.-P. Weber, “Spectral characteristics of coupled-waveguide Bragg-reflection
tunable optical filter,” IEE Proceedings -J, vol. 140, no. 5, pp. 275-284, Oct. 1993.
[2.16] W. H. Loh, M. J. Cole, M. N. Zervas, S. Barcelos, R. I. Laming, “Complex
grating structures with uniform phase masks based on the moving fiber-scanning
technique,” Optics Letters, vol. 20, no. 20, pp. 2051-2053, Oct. 1995.
46
{excitation procedure} Initial conditions:
Propagation constants, Normalised amplitudes, Phases: b0(i), A0(i), a0(i) i=1..(modes0)
for n=1 to (n_steps) do {divide the structure to ‘n_steps’ segments and for each one do:}
begin
Solve the 5-Layer eigenvalue equation
Find the propagation constants b1(j) of the mode1 in this segment
Calculate the mode profiles Ψ(b1(j)) , j=1..(modes1)
for j=1 to (modes1) do { for each of the ‘n1_modes’ modes of the current step ‘1’ do : } begin
for i=1 to (modes0) do { for each of the ‘modes0’ modes of the previous step ‘0’ do : } begin
Calculate the overlap integrals Ii0j1 (i,j), Ij1j1 (i,j), Ii0i0(i,j)
Calculate the coupling coefficient c(i,j)
end
Calculate the new phase a1(j)
Calculate the new amplitude A1 (j)
end
{Updating for the next step} for j=1 to (modes1) do
begin
b0(j)=b1(j)
a0(j)=a1(j)+b1(j)∗dz
A0(j)=A1(j)
end
modes0=modes1 {updating end} end
Appendix 2.A
47
CHAPTER 3
Null Coupler-Tilted Bragg Grating
Based OADM
3.1 Introduction
This Chapter presents a detailed theoretical analysis of the null-coupler OADM and
investigates the conditions and design requirements for fully optimised operation. The
proposed optimisation process [3.1, 3.2] involves two main steps, namely the null-
coupler and the tilted-grating designs. In the first step, the branch V-number
asymmetry and the taper-region shape are optimised in order to obtain pure mode
transformation. In the second step, the grating tilt-angle and transverse extent are
optimised in order to maximise even-odd mode conversion and at the same time
minimise the resulting backreflections. We show finally that the proposed optimized
configuration can meet the stringent specification required for DWDM systems
3.2 Principle of operation
The schematic of the proposed OADM device is shown in Figure 3.1. As mentioned
already, null couplers are comprised of two dissimilar single-mode waveguides that are
brought gradually in close proximity to form the waist. The devices are firstly relying
on the adiabatic mode transformation that takes place along the coupler arms and waist.
Light launched in one of the ports excites predominantly only one of the waist
eigenmodes, which, in the absence of any perturbation, appears uncoupled at the output
side of the same waveguide. Actually, light from the larger V-number input waveguide
(e.g., port #1) excites only the even lowest-order (fundamental) mode at the coupler
48
waist (see Figure 3.1(a)) and proceeds uncoupled at the output of the waveguide with
the same V-number (i.e., port #3). Similarly, light from the smaller V-number input
waveguide (e.g., port #2) excites only the odd lowest-order mode at the coupler waist
(see Figure 3.1(b)) and proceeds uncoupled at the output of the waveguide with the
same V-number (i.e., port #4). Strictly speaking, under normal circumstances, the null
coupler (as the name implies) does not couple light. The mode transformation should
be kept adiabatic all along to avoid extra radiation losses and unwanted mode
excitation. In the presence, however, of an asymmetric periodic index perturbation
along the coupler waist, power from one eigenmode can be resonantly transferred into
the other one and finally appear at the opposite waveguide (see Figure 3.1(c)). The
grating parameters, such as period and tilt, determine which one of the channels
launched into port #1 will be dropped into port #2. The rest of the channels, of course,
will be transmitted at port #3. Similarly, a channel at the Bragg wavelength launched
into port #4 will be added into the transmission port #4.
Figure 3.1 Schematic of the OADM based on grating assisted mode conversion in a null coupler. a) Propagation of the even mode along the coupler, b) Propagation of the odd mode along the coupler, c) Cross-coupling of the two waist eigenmodes and demonstration of the OADM operation.
(c)
(a)
(b)
49
The performance of the OADM depends critically on a number of factors. Firstly, the
waveguide asymmetry and coupler taper region should be optimised in order to
maximise the excitation of the required eigenmode and eliminate the presence of the
unwanted forward-propagating eigenmode at the waist. Secondly, the grating tilt and
spatial extent in the coupler waist should also be optimised in order to maximise the
cross-coupling and energy transfer between forward even (odd) and backward odd
(even) modes for efficient drop and add functions. In addition, even-even and odd-odd
interactions and self-coupling should be minimised to avoid backreflections into the
input port.
3.3 Null coupler design and optimisation
The design of a high performance null coupler involves two main optimisation steps;
namely coupled-waveguide asymmetry and coupler taper shape. For the analysis of the
coupler structure we used the local normal-mode analysis and the step-transition model
as already described in Chapter 2. All the calculations are based on a general five-layer
planar structure with step refractive index profiles. This type of analysis provides a
deep physical insight into the mechanisms of mode conversion, which are important for
the
Figure 3.2 Schematic and parameters of the tilted-grating assisted null coupler
0 2500 5000 75000
5
10
15
20
1
2
3
4
d1
d2
n1 = n3 = n5 = 1.453n2 = n4 = 1.470 n1
n2
n3
n4
n5
Separation S(z) in µm
Distance along the coupler (in µm)
dg
0 2500 5000 75000
5
10
15
20
1
2
3
4
d1
d2
n1 = n3 = n5 = 1.453n2 = n4 = 1.470 n1
n2
n3
n4
n5
Separation S(z) in µm
Distance along the coupler (in µm)
dg
50
general understanding of the operation of null couplers grating-assisted filters. The
normal mode analysis takes directly into account the physical shape of the coupler
allowing us to optimise the performance of a null coupler by finding suitable branch
shapes. In this section we also briefly describe a variational procedure for determining
the optimum taper shape. The model is then used to design a fully optimised coupler.
Figure 3.2 shows the basic coupler configuration and summarizes the main geometric
and optical parameters used in the calculations.
3.3.1 Waveguide asymmetry optimisation
The coupler performance is characterized by the power crosstalk, defined as the ratio P4
/(P3+P4) where P3 and P4 are the powers at the output ports #3 and #4 respectively
when the coupler is excited from port #1. Given that the reflective grating is placed in
the null-coupler waist, in order to study the effect of waveguide asymmetry on the null
coupler performance, it is better to reduce the problem to the study of an asymmetric
Y-branch. We first consider taper regions with linearly shaped branches.
Figure 3.3 Effect of the waveguide asymmetry to the crosstalk for two different slopes
Waveguide's width (µm)
1.001.251.501.752.002.252.502.753.00
Cro
ssta
lk (d
B)
-70
-60
-50
-40
-30
-20
-10
0
Slope 0.34 degSlope 0.28 deg
Pin
P1
P2
Crosstalk: P2 / (P1+P2)
Waveguide's width (µm)
1.001.251.501.752.002.252.502.753.00
Cro
ssta
lk (d
B)
-70
-60
-50
-40
-30
-20
-10
0
Slope 0.34 degSlope 0.28 deg
Pin
P1
P2
Crosstalk: P2 / (P1+P2)
Pin
P1
P2
Crosstalk: P2 / (P1+P2)
51
Figure 3.3 shows the crosstalk P2 /(P1+P2) variation as a function of the width of one of
the waveguides, for two different slopes. Slope is defined as the angle between the two-
waveguide arms. The other waveguide has a fixed width of 3µm. In both cases, the
minimum and maximum waveguide separation is 0µm (at the point where they touch to
form the waist) and 15µm (at the input end), respectively, resulting in different branch
lengths. As input to the Y-branch is assumed the fundamental even eigenmode of the
waist waveguide. It is first shown that d2=d1=3µm results in –3dB crosstalk that
implies standard symmetric splitter. However, as the waveguide asymmetry increases,
the crosstalk becomes progressively smaller which implies lack of efficient cross
coupling (null coupler). It is shown that in order to obtain a crosstalk lower than about
-30dB, the waveguide width d2 should be smaller than 2µm, which corresponds to a V-
number asymmetry ratio (V2 / V1) smaller than about 0.67. However, it should be
stressed that V2 should be kept greater than ~1.5 to minimise bending losses. It is also
shown that, in general, a smaller branch slope results in lower crosstalk. For a slope of
0.28deg and d2=2.25µm, we observe a sharp decrease in crosstalk. This is a
wavelength-sensitive resonant effect and should be avoided if we are interested in
broadband operation.
Finally, the waveguide asymmetry and maximum separation (at the input/output ends)
determines also the efficient excitation of the null coupler. To ensure single mode
excitation at the input end, the ratio ∆β12/C12 should be quite large [3.3]. ∆β12(=β1-β2)
is the difference of the propagation constants of the isolated waveguides (proportional
to waveguide asymmetry) and C12 is the coupling constant between the two waveguide
branches at the input end (inversely proportional to their separation). We have made
sure that the asymmetries and maximum waveguide separations used in our designs
always result in efficient single mode initial excitation at the input.
3.3.2 Taper shape optimisation
In addition to waveguide asymmetry, power crosstalk is also determined by the shape
of the coupler taper [3.4]. The shape optimisation can be accomplished with a number
of different methods, such as Genetic evolution strategies combined with beam
propagation methods [3.5] and variational optimisation techniques [3.6]. The
52
variational optimisation technique is easily implemented, fast converging and is
adopted for optimising the null-coupler taper shape. In addition, it results in smoothly
varying shapes that can be easily realised by modern, flexible UV-writing techniques
[3.7]. For certain crosstalk level, complex optimised shapes, on the other hand, can
potentially result in overall shorter devices.
Variational Optimisation Technique
In this section the fundamental principles of a variational optimization technique will
be described. The general method will then be applied to the special case of reduction
the crosstalk performance of a coupler by appropriate shaping of the waveguide arms.
Lets consider the general case where the problem is to optimize the #m different states
of an abstract system. The optimization problem lies to the dynamical change of #N
specific parameters of the system in order to force the aforementioned #m states to
reach the desired target values we have set. These N parameters, which are to be,
optimised in the problem form the vector TNkkkk ],...,,[ 21=
r. The optimization
procedure starts with an initial vector kr
which is changed dynamically until the #m
states reach the desired target values. To quantify the distance between the state values
at a current optimization step and the target values, an error vector is defined as:
Tm kekekekE )](),...,(),([)( 21
rrrr= (3.1)
where mie iii ...1,)( =−= ρσ , with iσ the target value of state i and iρ its current
value for parameters vector kr
. Starting the problem with an initial non-ideal vector of
parameters kr
, we can achieve an improvement on kr
by estimating a new kr
designated as kkk newrrr
∆+= which leads to an improved error vector )(kEr
. The
incremental improvement vector kr
∆ is estimated [4.6] by the formula:
53
j
iij
TT
TT
keJ
NmkEJJJk
NmkEJJJk
∂∂α
α
=
>−=∆
<−=∆−
−
,)()(
,)()(1
1
rv
rv
(3.2)
where [J]ij is the Jacobian matrix and α is a scaling parameter used to control the
convergence rate. Equation (3.2) is repeatedly applied forming a new parameter vector iii kkkrrr
∆+=+1 at each iteration, until a satisfactory optimization is achieved or a
minimization occurs.
We apply now the above technique for the shaping of a null coupler. We set only one
target to the problem and this is the reduction of coupler crosstalk to a level of –55dB.
The shaping of the coupler is parameterized by describing its shape with a
superposition of weighted cosine terms:
S z c c iL
zii
N
( ) cos( )= +=
−
∑01
1 π (3.3)
where L is the taper length. The N coefficients ci (i=0,N-1) form the weighting
parameters of the optimisation problem which here targets to the reduction of the
crosstalk to the level we set. Equation (3.3) describes a generalised S-shape taper
region.
54
Figure 3.4 Difference between current crosstalk and target value
Number of Iterations
0 100 200 300 400 500 600
Rel
ativ
e er
ror (
dB)
0
5
10
15
20
25
55
Figure 3.5 a) Optimised separation function for the Y branch and local slope difference (inset) b) Comparison of mode evolution for the initial and the optimised null coupler.
Distance along the Y branch (µm)0 500 1000 1500 2000 2500
Nor
mal
ised
am
plitu
des
of th
e no
rmal
mod
es
0.0
0.2
0.4
0.6
0.8
1.0
Build-up of the Odd mode
Distance (µm)0 500 1000 1500 2000 2500
Am
plitu
de
0.0
0.1OptimisedInitial
Even modes evolution
Odd modes evolution
Distance along the Y- Branch (µm)0 500 1000 1500 2000 2500
Bra
nch
Sep
arat
ion
(µm
)
0
2
4
6
8
10
12
14
16Initial ShapeOptimised Shape
Local Slope Difference
Distance0 2500m
rad
-1
0
1
56
We have found that seven coefficients are enough to satisfactorily describe the taper
region. Starting with an initial set of coefficients the optimisation process adjusts them
dynamically and is completed when the target crosstalk performance has been reached.
The even eigenmode was initially excited, to the coupler and full convergence was
achieved after about 300 iterations (Figure 3.4). The convergence ratio was set to 0.1.
The initial and final S-shape coefficients ci (i=0,6) are (7.497, -7.502, 10-3, 10-3, 10-3,
10-3, 10-3) and (7.6197, -7.3788, -3.9345x10-4, -5.1494x10-2, -5.2274x10-2,-6.9656x10-2,
-6.6957x10-2) respectively.
The same crosstalk level was achieved over a bandwidth of ~40nm, centered at
1550nm. Figure 3.5(a) shows the initial and final (optimised) taper shapes. This smooth
optimised taper is described by a function which is free from discontinuities in the first
and second derivatives, a characteristic which is quite important since any
discontinuities of this kind can lead to increased bend transmission loss [3.8]. The inset
shows the difference in local slopes between the two shapes. We can notice that the
optimised taper shape exhibits higher local slopes at the initial part of the branch,
which is in agreement with the general characteristics of shaped digital optical switches
[3.4, 3.5]. Figure 3.5(b) shows the evolution of the two normal eigenmodes (their
normalized amplitudes) along the branch -when the even eigenmode at the waist was
initially excited- for the initial (un-optimised) and final (optimised) taper shapes. The
inset zooms into the amplitude evolution of the odd mode along the Y-branch. In the
un-optimised case, the odd-mode build up shows a complex pattern that finally results
in a residual excitation of the unwanted mode. The corrected local slopes of the
optimised shape, on the other hand, counteract the initial build up and result in the
target crosstalk.
3.4 Grating Section
The Bragg grating of the composite structure will be analysed and modelled
accordingly to the method developed in Chapter 2.
57
Figure 3.6 Schematic of the tilted phase grating
3.4.1 Estimation of the tilted Bragg grating’s coupling coefficients
Next we derive the basic expression which the spatial perturbation due to a tilted
grating. This will be applied to the general expressions for the estimation of the
coupling coefficients. For θ=0, we have the special case of a phase grating written
normal to the waveguide axis. The refractive index variation of the grating in Figure
3.6 is expressed in the Cartesian system (X’, Z’) by the function
∆ ∆Λ
n x z n zg
( ' , ' ) cos '= ⋅
0
2π (3.4)
By using the transformation z x z' sin cos= +ϑ ϑ between the two Cartecian systems, it
can be easily shown that the fundamental spatial harmonic of the relative dielectric
permittivity perturbation, in the (X, Z) system, can be expressed as:
∆ ∆ Λε επ
r tilted
j zx z e( , ) ( )= ⋅+
−
1
2
(3.5)
where ( )( tan )
∆ ∆ Λε επ ϑ
+ +
− ⋅= ⋅1 1
2
tilted
j xe , ∆ ∆ε ε+ = ⋅1
2o n and Λ=Λg/cosθ. The coefficient
( )∆ε +1 tilted can be used in Equations (2.15) to calculate the coupling coefficients of the
tilted grating. In the case of an apodised grating, characterized along z’ by a slowly
varying apodization function f(z’), then along the waveguide axis (z-direction) the
apodization profile is given by the projection of the original function along z-axis [3.9].
In the following analysis, the quoted apodization profiles are considered along the
waveguide axis z (or z’), given that modern UV-writing techniques [3.10] enable the
writing of the desired complex profiles along z.
z’x’
z
x
θ
θ
Λ
Λg
cladding
cladding
core
z’x’
z
x
θ
θ
Λ
Λg
cladding
cladding
core
58
3.4.2 Tilted grating optimisation
By simple inspection of Equations (2.13), it is obvious that there are three spectral
regions of resonant power exchange between the even and odd waist eigenmodes.
They are given by the relations ∆β1=0, ∆β12=∆β1+∆β2=0 and ∆β2=0 and correspond to
e-e, e-o and o-o mode interactions respectively. The relative strength of the
interactions depends on the values of the relevant coupling coefficients and the amount
of mode excitation at the null-coupler waist. The operation of the proposed OADM is
based on the grating-assisted, efficient cross coupling between the even and odd
eigenmodes (e-o interaction) at the coupler waist. This resonant power transfer takes
place at a wavelength λ o here the Λ=+ /2)()( πλβλβ oooe Bragg condition is
satisfied. In addition toλ o there are two extra wavelengthsλ 1 andλ 2 where the even-
even (e-e) and odd-odd (o-o) mode interactions take place. The wavelengthsλ 1 andλ 2
fulfill the Bragg conditions β λ πe ( ) /1 = Λ and β λ πo ( ) /2 = Λ respectively
withλ λ λ1 2> >o . In the general case, the e-e and o-o interactions result in two extra
reflection peaks, centered at λ 1 and λ 2 , respectively. These two unwanted peaks can
potentially interfere with other optical channels and severely impair the OADM
performance. Their strength depends on the degree of even and odd mode excitation at
the waist and the strength of the corresponding coupling constant (see Equation (2.15)).
Strong e-e and o-o interactions would result in significant backreflections at the high
and low V-number input waveguides, respectively. In addition to branch-asymmetry
and taper-shape optimisations, the grating tilt angle and grating extent can be also
properly chosen to eliminate the unwanted reflection peaks.
The three complex coupling coefficients κeo, κee and κoo of a tilted grating, are
calculated by Equations (2.15) and (3.5), and their moduli are plotted in Figure 3.7(a)-
(c) as a function of the tilt angle, for different coupler geometries and grating extends.
In Figures 3.7(a) and 3.7(b), on the other hand, the two waveguides are in full contact
along the waist. In Figure 3.7(c) the two dissimilar waveguides are separated by 1µm
along the null-coupler waist. In Figures 3.7(a) and (c), the grating is written in the core
areas only (only the cores are assumed photosensitive), while in Figure 3.7(b) the
59
grating is extended outside the core area (core and cladding are assumed equally
photosensitive). The amplitude of the refractive-index modulation is assumed to be
∆n=10-3.
It is shown that in the cases (a) and (b), there is always an optimum tilt-angle (θ0)
where the e-o cross coupling acquires a near-maximum value and the o-o self-coupling
is zero. This implies that when θ=θ0, launching light into port#2 (low V-number input)
of the OADM will result in maximum cross coupling, i.e. efficient drop action, without
any self-coupling, i.e. backreflections. It should be also mentioned that, when θ=θ0,
launching light into port#3, results in equally efficient cross-coupling and add OADM
function (at λ0), as well as, a sizeable e-e self-coupling and strong backreflection
(although at a different wavelength λ1) (see spectra in Figure 3.13). This
backreflection might necessitate the use of an isolator at this port. In case (c), however,
where the two photosensitive cores are separated, the tilt angle that corresponds to
maximum e-o interaction does not result simultaneously in zero o-o self-coupling.
Therefore, such OADM geometry will always suffer from strong backreflections at
both drop and add input ports. It should be mentioned that this geometry is pertinent to
a recently reported fibre-optic implementation of this OADM [3.11].
Tilted gratings, however, in addition to guided modes are known to excite cladding
[3.12], as well as, leaky and radiation [3.13] modes. Although the coupling into these
modes and the related losses are not covered here, the effect of the various parameters
on the optimum tilt angle is considered in some detail.
Figure 3.8(a) shows the variation of the optimum tilt angle (θ0) as a function of the
normalised grating width (dg/dw) for three different widths (and different V-numbers).
The refractive indices are same as in Figure 3.2. Figure 3.8(b), on the other hand,
shows the corresponding variation of the actual coupling constants κeo, κee (κoo=0 since
θ=θ0 throughout).
60
Figure 3.7 Moduli of coupling coefficients versus tilt angle a) Grating is inscripted only at the single-core waist (waveguide’s separation: h=0 µm) b) Grating is extended deeply into the equally photosensitive cladding region. c) Grating is inscripted only on the waveguide cores and the asymmetric waveguides at the waist of the coupler are separated by a distance: h=1 µm
Cou
plin
g co
effic
ient
s (µ
m-1
)
0.000
0.001
0.002
0.003
0.004e-oe-eo-o
3
2
1
4C
oupl
ing
coef
ficie
nts
(µm
-1)
0.000
0.001
0.002
0.003
0.004e-oe-eo-o
3
2
1
4
3
2
1
4C
oupl
ing
coef
ficie
nts
(µm
-1)
0.000
0.001
0.002
0.003
0.004e-oe-eo-o
3
2
1
4
Cou
plin
g co
effic
ient
s (µ
m-1
)
0.000
0.001
0.002
0.003
0.004e-oe-eo-o
3
2
1
4
3
2
1
4
3
2
1
4
Angle (degrees)0 2 4 6 8 10 12 14 16 18 20
Cou
plin
g co
effic
ient
s (µ
m-1
)
0.000
0.001
0.002
0.003e-oe-eo-o
1 3
2 4
Angle (degrees)0 2 4 6 8 10 12 14 16 18 20
Cou
plin
g co
effic
ient
s (µ
m-1
)
0.000
0.001
0.002
0.003e-oe-eo-o
1 3
2 4
1 3
2 4
1 3
2 4
61
It is shown that extending the grating into the cladding reduces significantly θ0. The
degree of grating-extent, for this reduction to take place, increases for lower V-number
waveguides because of the significant part of the mode-power spreading into the
cladding. For extents larger than this minimum-required-extent (which depends on the
V-number) the minimum θ0 and κeo, κee remain constant. This is because beyond this
value both eigenmodes overlap fully with the grating. For gratings restricted inside the
core area (dg/dw<1), θ0 is shown to increase sharply while κeo and κee decrease
significantly. Combinations of small θ0 and large κeo are obviously required in order to
achieve (for a given length) strong gratings with negligible radiation losses.
For the case of a single-core waist in step-index geometry, considered here, we can
derive analytical expressions, which relate the optimum tilt angle to the waist
parameters. These relations are given in Appendix 3.A for the gratings restricted in the
core only or extended into the infinite cladding. Figure 3.9(a) and (b) show the
variation of the optimum tilt angle (θ0) and coupling coefficients (κeo, κee),
respectively, as a function of the single-core waist V-number, for different numerical
apertures. The grating is extended infinitely into the cladding. The V-number range is
restricted to π≤V≤2π so that the waist supports only the two lowest-order eigenmodes.
It is shown that, for a fixed waist V-number, the lower the NA the smaller the optimum
tilt angle. This is due to the fact that lower NA’s result in lower mode confinement
and, therefore, smaller θ0. For V-numbers just above π, the odd mode is close to cut-
off and extends deep into the cladding. As a result the optimum tilt angles, at this
point, reduce sharply towards zero. For all NA’s, the optimum tilt angle acquires a
maximum at V≅4.5. The coupling coefficients κeo (κee) increase (decrease)
monotonically with waist V-number. Due to complete grating/mode(s) overlap, on the
other hand, both coupling coefficients are independent of the waist NA, so the e-o and
e-e coupling coefficients for the three different NAs correspond to the two single
curves in Figure 3.9(b). The inset in Figure 3.9(b) finally gives the ratio of the coupling
coefficients κeo, κee. From Figure 3.9, it is deduced that low-NA, high V-number waists
should be favoured in order to obtain strong gratings with minimum tilt angle.
However, the low-NA choice should be compromised in order to minimise bending
losses at the coupler taper region.
62
Figure 3.8 a) Relation between the optimum tilt angle and the grating’s extent for coupler waists with different V-numbers. b) Moduli of coupling coefficients at the optimum operational point, as a function of grating’s extent
Normalised grating width (dg / dw)
0 1 2 3 4 5 6 7
Opt
imum
tilt
angl
e (d
egre
es)
2
4
6
8
10dw = 6 µm (V = 5.4)dw = 5 µm (V = 4.5)dw = 4 µm (V = 3.6)
dw dg
1
2
3
4
Normalised grating width (dg / dw)
0 1 2 3 4 5 6 7
Opt
imum
tilt
angl
e (d
egre
es)
2
4
6
8
10dw = 6 µm (V = 5.4)dw = 5 µm (V = 4.5)dw = 4 µm (V = 3.6)
dw dg
1
2
3
4
dw dg
1
2
3
4
dw dg
1
2
3
4
Normalised grating width (dg / dw)0 1 2 3 4 5 6 7
Cou
plin
g co
effic
ient
s (µ
m-1
)
0.001
0.002
0.003 e-e
e-e
e-e
e-o
e-o
e-o
63
Figure 3.9 a) Effect of the V-number to the optimum tilt angle for waveguides with different numerical appertures (NA), b) Effect of the V-number to the moduli of coupling coefficients at the optimum-operational point, for waveguides with different numerical appertures (NA).
V-number at the single-core-waist waveguide 3.5 4.0 4.5 5.0 5.5 6.0
Opt
imum
tilt
angl
e (d
egre
es)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
NA = 0.22NA = 0.19NA = 0.14
3
2
1
4
V-number at the single-core-waist waveguide 3.5 4.0 4.5 5.0 5.5 6.0
Opt
imum
tilt
angl
e (d
egre
es)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
NA = 0.22NA = 0.19NA = 0.14
3
2
1
4
3
2
1
4
3
2
1
4
V-number at the single-core-waist waveguide3.5 4.0 4.5 5.0 5.5 6.0
Cou
plin
g co
effic
ient
s (µ
m-1
)
0.000
0.001
0.002
0.003
0.004
V-number4 5 6
Rat
io
0.0
0.5
1.0
e-e
e-o
Ke-o / Ke-e
64
Throughout the analysis, we have assumed that core and cladding material exhibit the
same photosensitivity and acquire the same refractive-index modulation. This is
possible by proper choice of the core and cladding co-doping materials and the UV-
writing wavelength. We have also considered the more general case where the core
and cladding regions acquire different peak index modulation. In this case, the
obtained optimum tilt angles are slightly smaller than and follow the same trends with
the ones shown in Figures 3.8 and 3.9.
3.5 Full spectral response of the OADM
In sections 3.3 and 3.4, we considered the various null-coupler and tilted-grating
optimisation steps, respectively, and discussed design criteria for the waveguide
asymmetry the taper shape and the grating tilt and extend. In this section, we take into
account the aforementioned findings and using the analysis method developed in
Chapter 2 we obtain the full spectral response of various OADM configurations.
The fundamental mode of the individual input-port waveguide is excited and then
propagated along the structure determining this way the amplitudes and phases of the
two normal modes before they enter the grating. At the waist region, where the grating
is written, we calculate the forward and backward propagating modes and continue
propagating them along the coupler to all the ports of the device. In this way, for light
launched into input port (#2), we calculate the full spectra at the drop port (#1), the
backreflected light (at the input port#1), the transmitted light (at port#4) and the cross-
coupled light at the add port (#3).
In the following analysis, we assume that the individual waveguide widths are d1=3µm,
d2=2µm and the coupler waist width is dw(=d1+d2) =5µm. The core/cladding refractive
indices are the same with the ones in Figure 1. The grating is extended deeply into the
cladding and the corresponding optimum tilt angle is 3.33o. The grating length is
considered to be 4mm and the amplitude of the refractive index modulation is 10-3.
A raised cosine apodization profile is assumed. The period of the grating is adjusted for
the different tilt angles in order to optimise the Drop and Add operations at 1550nm.
65
A. Linear-Branch Coupler – Non-Optimum Grating Tilt We first demonstrate the effect of partial optimisation on the OADM performance by
considering null couplers with linear branches. As already discussed such a coupler
design results in relatively high crosstalk for most of the waveguide branch
asymmetries (see Figure 3.3). The branch slope is 0.28o and the corresponding
crosstalk is about –30dB. The lower V-number port 2 is used as the OADM input port.
Since V2<V1, the input light excites predominantly the odd eigenmode in the waist
region. The even-mode power in the same region is ~ –30dB below the odd-mode one.
In Figures 3.10(a),(b), the calculated spectra at the drop port (#1) and output port (#4)
are shown, along with the backreflected spectra at the input port (#2) and the crosstalk
spectrum at port#3. In this case, the grating tilt angle is 5° (non-optimum) and the
corresponding coupling coefficients are κee=κoo=0.0012µm-1 and κeo=κoe=0.002µm-1
(see Figure 3.7(b)). In Figure 3.10(a), three distinct regions (A, B and C) can be seen
centered around 1545nm, 1550nm and 1555nm, respectively. The various peaks in the
drop (solid line) and backreflected (dashed line) spectra have different physical origin
and involve different coupling mechanisms. Firstly, it should be reminded that the
solid- and dashed-line responses involve the excitation backward-propagating even and
odd eigenmode, respectively, at the coupler waist. Secondly, the three aforementioned
regions correspond to odd-even (A), odd-odd (B) and even-even (C) resonant grating-
assisted (Bragg) power exchange.
(i) Region A
The solid-line peak, in region A, corresponds to resonant odd-even mode power
transfer (determined by κoe) and constitutes the main feature in the drop action. The
dashed-line peak, in the same region, corresponds to the power transfer by two
different mechanisms: Firstly because of the resonant power transfer between the
residual even mode (-30dB below the dominant odd mode) to the odd mode, which is
determined by κeo. Secondly, partial excitation of the odd mode during the backward-
propagation of the even mode to port #1 along the taper region.
66
Figure 3.10 Spectral response of the OADM with linear coupler and grating with non-optimum tilt angle (Drop action). a) Reflection spectra, b) Transmission Spectra
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0
Port 1Port 2
B A C
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0
Port 1Port 2
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0
Port 1Port 2
B A CB A C
1
2
3
4
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
Port 3Port 4
B A C
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
Port 3Port 4
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
Port 3Port 4
B A CB A C
1
2
3
4
1
2
3
4
67
(ii) Region B
The dashed-line peak, in region B, corresponds to odd-odd mode resonant (Bragg)
backreflection (determined by κoo). The solid-line peak, in the same region, is due to
the fact that the backward-propagating odd mode excites partially the even mode
during its propagation along the taper region. Since in this coupler design the taper-
induced crosstalk is –30dB, the solid-line peak B is a replica of the dashed-line peak B,
downshifted by this amount.
(iii) Region C
Finally, the solid-line peak, in region C, corresponds to the residual even-even mode
resonant (Bragg) backreflection (determined by κee). The dashed-line peak, in the same
region, is due to the fact that the backward-propagating even mode now excites
partially the odd mode during its propagation along the taper region. Again, since the
taper-induced crosstalk is –30dB for this design, the dashed-line peak C is a replica of
the solid-line peak C, downshifted by the same amount.
Figure 3.10(b) shows the transmitted (solid line) and cross-coupling (dashed line)
spectra. The two notches in the transmission spectrum correspond to the odd-even and
odd-odd resonant reflections peaks shown in Figure 3.10(a). Since κoe>κoo, the notch
in region A is deeper than the one in region B. The cross-coupled power is determined
by the taper shape. Although the Y-branches used here for the construction of the
coupler, exhibit crosstalk level better than -30 dB the resulted crosstalk level for the
coupler is ~ -27 dB. That can be explained by talking into consideration the additional
partial residual excitation of the even mode at the first half part of the coupler where
the low V-number waveguide was excited.
68
Figure 3.11 Spectral response of the OADM with linear coupler and grating with optimum tilt angle (Drop action). a) Reflection spectra, b) Transmission Spectra
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0Port 1Port 2
B A C
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0Port 1Port 2
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0Port 1Port 2
B A CB A C
1
2
3
4
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB)
-60
-40
-20
0Port 3Port 4
B A C
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB)
-60
-40
-20
0Port 3Port 4
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB)
-60
-40
-20
0Port 3Port 4
B A CB A C
1
2
3
4
1
2
3
4
69
B. Linear-Branch Coupler – Optimum Grating Tilt
Next, we consider the effect of the optimum grating tilt on the OADM performance.
The tilt angle is ~3.33°, while the coupler configuration and the rest of the parameters
are the same as in the previous case A. From Figure 3.7(b), it is deduced that in this
case the odd-odd coupling coefficient diminishes (κoo≅0), while both odd-even and
eve-even coefficients increase (κoe ≅ κee ≅ 0.0024µm-1), in comparison with the
previous case.
The most obvious spectral change is observed in region B, where, due to the
diminished κoo coefficient, the dashed-line peak is reduced below –40dB. At the same
time, the corresponding transmission notch disappears. All the other features in
spectral regions A and C (determined by κoe, κee and the taper-induced cross-coupling)
remain unchanged. Actually due to increased κoe and κee, the grating strength is
increased. This is shown by the increase in both the 3dB-bandwidth at the drop port
(Figure 3.11(a)) and the depth of the transmission notch (Figure 3.11(b)). The OADM
cross-talk (dashed line in Fig. 3.11(b)), on the other hand, remains at the same level as
in Figure 3.10(b), since the coupler design remains unchanged.
C. Fully Optimised Null-Coupler OADM – Drop Operation We now turn our attention to the performance of fully optimised OADMs. We employ
a S-shape taper region optimised to give –55dB of crosstalk. The optimum tilt angle
and the rest of the waveguide and grating parameters are the same as in the previous
case B.
Figure 3.12(a) shows the full drop (solid line) and backreflected (dashed line) OADM
spectra. Figure 3.12(b) shows the corresponding transmitted (solid line) and cross-
coupled (dashed line) spectra. Compared with the response in Figure 3.11, the solid-
line drop peak in region A and the dashed-line backreflected peak in region B are
unchanged, since they depend solely on κoe and κee, respectively, which in turn depend
on the grating tilt angle and extent. The remaining three peaks in Figure 3.12(a)
depend predominantly on the taper-induced crosstalk and are reduced to a level below
–55dB. Similar effects are observed in Figure 3.12(b).
70
71
Figure 3.12 Spectral response of the OADM with optimised null coupler and optimimum tilt angle (Drop action). a) Reflection spectra, b) Transmission Spectra
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-160
-140
-120
-100
-80
-60
-40
-20
0
Port 1Port 2
B A C1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-160
-140
-120
-100
-80
-60
-40
-20
0
Port 1Port 2
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-160
-140
-120
-100
-80
-60
-40
-20
0
Port 1Port 2
B A CB A C1
2
3
4
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB
)
-100
-80
-60
-40
-20
0Port 3Port 4
B A C
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB
)
-100
-80
-60
-40
-20
0Port 3Port 4
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB
)
-100
-80
-60
-40
-20
0Port 3Port 4
B A CB A C
1
2
3
4
1
2
3
4
72
Figure 3.13 Spectral response of the OADM with optimised null coupler and optimimum tilt angle (Add action). a) Reflection spectra, b) Transmission Spectra
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0
Port 3Port 4
B A C1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0
Port 3Port 4
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Ref
lect
ion
(dB
)
-140
-120
-100
-80
-60
-40
-20
0
Port 3Port 4
B A CB A C1
2
3
4
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB
)
-100
-80
-60
-40
-20
0
Port 1Port 2
B A C
1
2
3
4
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB
)
-100
-80
-60
-40
-20
0
Port 1Port 2
B A C
Wavelength (nm)1540 1545 1550 1555 1560
Tran
smis
sion
(dB
)
-100
-80
-60
-40
-20
0
Port 1Port 2
B A CB A C
1
2
3
4
1
2
3
4
73
Figures 3.12(a) and (b) show that a fully optimised null-coupler-based OADM provides
a single well-defined peak in drop spectrum accompanied by a single notch in the
corresponding transmission spectrum. All the other features, originating from the
grating and taper-induced crosstalk, remain well below a level that is set by the
optimised taper shape and grating tilt.
D. Fully Optimised Null-Coupler OADM – Add Operation
Finally, we consider the spectral response of the fully optimised OADM, considered in
the previous section C, under add-mode operation. In this case, light is launched into
port#3 and is expected to appear in the transmission port#1. Figure 3.13(a) shows the
full add (port#4-solid line) and backreflected (port#3-dashed line) spectra. It is shown
that due to reciprocity, the “add” spectrum is identical with the drop spectrum (see
Figure 3.12(a)). The backreflected spectrum, however, shows a very strong peak
(dashed line in region C) due to the large κee. Actually, since κee≅κeo in the present
case, the add and backreflected peaks are similar. This is further manifested by the
similar size notches in the corresponding transmission spectrum shown in Figure
3.13(b) (solid line). The strong backreflection at the “add” port#3 is out of the “Add”
band and can be further reduced by increasing the waist V-number (see Figure 3.9(b)).
Otherwise, the effect can be totally suppressed by the insertion of one optical isolator.
The dashed line in Figure 3.13(b) shows the cross-coupling into port#2, determined by
the taper shape. Since in this case the high V-number waveguide (and consequently the
even supermode of the structure) was initially excited the crosstalk level is in absolute
agreement with the performance of the optimised S-bent branch which was designed by
assuming excitation with the even waist mode. The different crosstalk level in Figure
3.12(b) (which again is below -55 B) should be attributed to the fact that the coupler
now is excited by the odd supermode.
3.6 Conclusions
We have thoroughly studied the performance of fully optimised OADMs based on null
couplers and tilted Bragg gratings. We have shown that maximisation of the device
performance involves three main optimisation steps. Firstly, the waveguide asymmetry
74
(V2/V1 ratio) should be optimised in order to minimise the extinction ratio of the
unwanted mode at the null coupler waist. Secondly, the coupler taper shape should be
optimised in order to further minimise the aforementioned extinction ratio. Thirdly, the
grating tilt angle and relative width can be also optimised to give negligible
backreflections at the input port and minimise radiation losses.
We have shown that keeping V2/V1 at ~0.67 and employing an optimised S-bend
coupler taper, the unwanted-mode extinction ratio at the coupler waist is kept at about -
55dB. Finally, a fully optimised OADM is shown to provide a drop action with cross-
talk better than -40dB. The backreflections at the input port are also kept below -40dB.
These results show that the proposed high performance OADM configuration can meet
the stringent telecom specifications. Since the relative width of the grating is great
importance, the device can be best implemented in integrated optics form. FHD planar
technology combined with UV waveguide- and grating-writing techniques can be well
suited for a the practical device implementation
It should be also stressed that, in contrast with other OADM configurations that involve
gratings in the waist of SFCs [3.14] (discussed in the introduction), the performance of
the present null-coupler OADM does not depend on the grating position. On the other
hand, since the optimised device operation relies on grating-assisted coupling, the
spectral and dispersion characteristics of the “Drop” and “Add” channels are replicas of
the grating counterparts. In that respect, the OADM characteristics can be fully
tailored by using recent advanced design algorithms [3.15].
3.7 References
[3.1] C. Riziotis and M. N. Zervas, “Optimisation of OADMs based on grating assisted
mode conversion in null couplers,” in Proc. European Conf. Optic. Communication
(ECOC’ 99), Nice, France, Sept. 21-26, 1999, paper TuD1.6.
75
[3.2] C. Riziotis, M. N. Zervas, “Design considerations of optical Add-Drop filters
based on grating assisted mode conversion in null couplers,” IEEE/OSA Journal of
Lightwave Technology, vol. 19, no. 1, pp. 92-104, Jan. 2001.
[3.3] A. F. Milton, W. K. Burns, “Tapered velocity couplers for integrated optics:
Design,” Appl. Opt., vol. 14, no. 5, pp. 1207-1212, May 1975.
[3.4] W. K. Burns, “Shaping the digital switch,” IEEE Photon. Technol. Lett., vol. 4,
no. 8, pp. 861-863, Aug. 1992.
[3.5] R. Moosburger, C. Kostrzewa, G. Fischbeck, K. Petermann, “Shaping the digital
optical switch using evolution strategies and BPM,” IEEE Photon. Technol. Lett., vol.
9, no. 11, pp. 1484-1486, Nov. 1997.
[3.6] B. E. Little, “Filter synthesis for coupled waveguides,” J. Lightwave Technol. vol.
15. no. 7, pp. 1149-1155, Jul. 1997.
[3.7] M. Svalgaard, “Direct writing of planar waveguide power splitters and directional
couplers using a focused ultraviolet laser beam,” Electron. Lett., vol. 33, no. 20, pp.
1694-1695, Sept. 1997.
[3.8] W. J. Minford, S. K. Korotky and R. C. Alferness, “Low-loss Ti:LiNbO3
waveguide bends at λ=1.3 µm,” IEEE Transac. Microwave Theory Techniq., vol.
MTT-30, no. 10, pp. 1790-1794, Oct. 1982.
[3.9] T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol., vol. 15, no. 8, pp.
1277-1294, Aug. 1997.
[3.10] W. H. Loh, M. J. Cole, M. N. Zervas, S. Barcelos, R. I. Laming, “Complex
grating structures with uniform phase masks based on the moving fiber-scanning
technique,” Opt. Lett., vol. 20, no. 20, pp. 2051-2053, Oct. 1995.
76
[3.11] A. S. Kewitsch, G. A. Rakuljic, P. A. Willems, A. Yariv, “All fibre zero
insertion loss add drop filter for WDM,” Opt. Lett., vol. 23, no. 2, pp. 106-108, Jan.
1998.
[3.12] S. J. Hewlett, J. D. Love, G. Meltz, T. J. Bailey, W. W. Morey, “Cladding-mode
coupling characteristics of Bragg gratings in depressed-cladding fiber,” Electron. Lett.,
vol. 31, no. 10, pp. 820-822, May 1995.
[3.13] T. Erdogan, J. E. Sipe, “Tilted fiber phase gratings,” J. Opt. Soc. Amer. A, vol.
13, no. 2, pp. 296-313, Feb. 1996.
[3.14] K. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X.
Daxhelet, F. Gonthier, “Optical add-drop multiplexer based on UV written Bragg
gratings in a fused 100% coupler,” Electron. Lett., vol. 33, no. 9, pp. 803-804, Apr.
1997.
[3.15] R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm
for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron.,vol. 35,
no. 8, pp. 1105-1115, Aug. 1999.
[3.16] D. L. Lee, Electromagnetic Principles of Integrated Optics. Wiley, pp. 78-
81,1986
77
Appendix 3.A: Analytical expressions for the optimum tilt angle
Figure 3.14 Symmetric 3-Layer waveguide structure
For the symmetrical 3-layer configuration (Figure 3.14) the transverse electric field for
the odd lowest-order TE-mode can be expressed as [3.16]:
ckknhknqwhere
dxdxqdh
dxdhx
dxdxqdh
xE y
/,,:
2))
2(exp()
2sin(
22)sin(
2))
2(exp()
2sin(
)(
222
221
2 ωββ =−=−=
−≤++−
≤≤−
≥−−
=
and β is the propagation constant obtained from the dispersion equation:
cot( )h d qh2
= − .
We derive here analytical expressions for the optimum tilt angle, by setting the overlap
integral -which corresponds to the coupling coefficient of the odd-odd self coupling-
equal to zero and by calculating it analytically based on the above simplified modal
field expressions.
Two distinct cases are considered, firstly when the grating is inscripted only on to the
core waveguide, and secondly when the grating is extended infinitely into the equally
photosensitive cladding:
x = + d/2
x = - d/2 d n2
n1
n1
z
x
78
I. When the grating is written in the core region only, the calculation of the zero odd-
odd shelf-coupling coefficient leads to the expression below:
[ ]{ } [ ]{ }sin( ) (cos( ) ) cos( ) (sin( ))Cd
C hd h Cd
C h hd2
2 1 82
4 02 2− + + − =
II. When the grating is extended into the infinite cladding the calculation leads to the
expression:
[ ]{ }
[ ][ ] [ ][ ]{ }sin( ) ( ) cos( )
cos( ) (cos( ) ) sin( ) (cos( ) ) sin( )
Cd
C q h hd q h q
Cd
C qh h hd q hd C q hd h hd
28 8 32
216 1 4 1 0
2 2 2 2 2 2
3
+ − + +
− − + + − − =
The parameter C =2πΛ
Θtan( ) contains in both cases the optimum tilt angle Θ .
77
CHAPTER 4
Full-Coupler Based Interferometric OADMs
4.1 Introduction
Interferometric symmetric full coupler (SFC) based OADMs have been proposed as an
alternative design to Mach-Zehnder configurations. As already discussed in Chapter 1,
despite its excellent theoretically-predicted performance, the Mach-Zehnder-type
interferometric OADM is very sensitive to any optical path imbalance of the order of
one wavelength. This limitation makes the use of the SFC type OADMs more
favourable because of their better fabricational tolerances. However in this more
compact configuration the performance is limited because of dispersion effects at the
edges of the grating reflection band, limiting consequently the efficient utilization of
the wavelength spectrum. Also the proposed implementation of the OADM in a half-
cycle coupler (HCC) [4.1], cannot give fully optimised Add and Drop actions
simultaneously.
In this chapter we analyse the operation of the half-cycle SFC OADM revealing its
limitations and we propose a novel design based on a full-cycle coupler (FCC)
configuration [4.2]. A simple and effective procedure is also proposed for the optimised
design of this novel OADM.
4.2 Half-cycle coupler (HCC) based OADM
The device is shown schematically in Figure 4.1, together with the power evolution
along the half-cycle coupler. The total length of the coupler is Lc=Zc/2 where Zc is the
78
beat length between the even and odd supermodes of the coupler. If ne and no are the
effective refractive indices of the even and odd supermodes respectively, then the
beatlength is defined as Zc=λc/( ne-no), where λc is the operating wavelength in vacuum.
Figure 4.1 Schematic of the HCC interferometric OADM. a) Power evolution along the HCC b) Asymmetric configuration for optimised Drop action, c) Symmetric grating arrangement with compromised OADM performance
In Figure 4.1, L2=Lg represents the grating length, and Lp the penetration length of the
grating at the central operating wavelength λc. Lw is the length of the coupling region
with uniform waist, and L1, L2 the distance of the left and right edges of the grating
from the left and right edges of the uniform coupling region respectively. As shown in
the figure is: L1+L2+L3=Lw.
Figure 4.1 shows a stream of WDM channels entering through Port 1, where the
channel at wavelength λ1DROP is reflected by the grating and dropped at Port 2. The
grating is placed asymmetrically within the waist so that its effective reflecting point at
M
1
Power exits at Port #4
4
Lc
Power inPort #1 Power inPort #1
1
Power exits at Port #4
4
Output λ 1 ADD , λ 2 ... λ n
Add λ 1 ADD
1
2
3
4 λ 1 ADD , λ 2 ... λ n
Add λ 1 ADD
Lp
Input λ 1 DROP , λ 2 ... λ n
Input λ 1 DROP , λ 2 ... λ n
Drop λ 1 DROP
Drop λ 1 DROP
1
2
3
4 LpL1 L3
L2=Lg Input
λ 1 DROP , λ 2 ... λ n
Drop λ 1 DROP
1
2
3
4
λ 1 DROP , λ 2 ... λ n
LpDrop λ 1 DROP
Add λ 1ADD
Add λ 1ADD
1
2
3
4 LpL1 L3
L2=Lg λ 1 ADD , λ 2 ... λ nλ 1 ADD , λ 2 ... λ nOutput
2
3 Lw
79
the wavelength of interest λ1DROP coincides with the middle-point (M) of the coupler
interaction length. At this point the two supermodes of the coupler are reflected and
their destructive interference at Port 1 guarantees that all the power at the wavelength
of interest will appear at the Drop Port 2. It should be stressed that the two modes have
different propagation constants and their corresponding reflection spectra are spectrally
displaced with respect to each other and, therefore partially overlapping. The
bandwidth of the Drop channel is determined by this overlap.
The analysis and modelling of this interferometric device can easily be performed by
decomposing the propagating fields into the even and odd supermodes of the coupler
and by calculating the interference between them. Symmetry consideration and
orthogonality guarantees that these modes do not cross-couple energy by scattering
from the grating (assuming always that the grating is written perpendicularly and
covers the entire waist cross section. However for the analysis here we applied the
more rigorous normal mode method and the step transition model, as described already
in Chapter 2. As demonstrated in Figure 4.1, in order to configure the OADM optimally
the grating has to be placed accordingly by taking into account its penetration depth -at
the central wavelength of the dropped channel.
Next, we briefly introduce the time delay and equivalent penetration depth of the
reflected light. If )(rphase=θ is the phase of the reflection coefficient r of the Bragg
grating then the time delay for reflected light is:
ocdk
ddd 1
⋅==θ
ωθτ (4.1)
where λπω 2
==oc
k and oc is the speed of light in vacuum. The equivalent
penetration depth of a particular wavelength can be estimated by considering the
length, which corresponds to half the time delay. Thus, the penetration depth is
calculated as:
80
dkd
ncdkd
nccL
o
op
θθτ ⋅⋅
=⋅⋅⋅=⋅=211
21
21
(4.2)
where c is the speed of light in the waveguide-grating region and n is the average
refractive index of the waveguide.
We consider now a typical example of a coupler structure and estimate the full
response of the OADM. The length of the coupler is ~ 20mm and the coupler’s uniform
waist length is ~ 9.6 mm. The deployed Bragg grating has a sine apodisation profile,
length 4.5 mm and refractive index modulation 10-3(p-p). The grating exhibits
reflectivity which corresponds to –45 dB transmission, and 3-dB bandwidth ~1nm. The
penetration depth at the central operating wavelength of λc =1.55µm is calculated to be
762 µm.
Figure 4.2 shows the reflection and transmission spectra of the OADM, which is
configured for optimised Drop action. The graph also shows the reflectivity spectra of
the even and odd modes Re (red line) and Ro (blue line) centred respectively at
wavelengths λe, λo. The relative spectral displacement is:
c
ocooeoe Z
nnΛ⋅⋅
=Λ⋅−⋅=−=∆λ
λλλ2
)(2 (4.3)
where Λo is the period of the grating. Increasing Zc can minimize the spectral
displacement and improve the Re, Ro overlap. Figure 4.3 shows the group time delay of
the reflection spectrum for the even and odd normal modes. They are also spectrally
displaced by λ∆ . The solid line represents the average time delay of both modes. The
equivalent penetration depth, which is related to group time delay by Equation (4.2),
varies considerably with wavelength. The time delay in transmission of symmetric
gratings is known to be identical to the one in reflection. Time delay variations in
transmission, however, correspond effectively to varying coupler length. These
dispersive effects are expected to affect considerably the spectral response in all ports
of the OADM.
81
For optimised Drop action the grating is arranged so that its effective reflection point
around the Bragg wavelength coincides with M and therefore drops efficiently around
this wavelength. Away from the Bragg wavelength, however, the time delay increases
considerably (Fig. 4.3) and the effective reflection point departs considerably from M.
As a result, the reflected light appears partially back in Port 1 (Fig. 4.2a). This
backreflection becomes more severe in the case of a stronger grating. The spectra in
Figure 4.2(b) show the transmission response in Port 4 and Port 3. Under ideal
operation conditions, no light should appear in Port 3. However, the power leaking into
this port is due to the additional grating dispersion in transmission, which results in
variation of the effective coupler length. In the case of symmetric gratings the
dispersion in transmission is identical to the one in reflection. As expected, the spectral
response of the leaking Port 3 follows closely the average time delay variation in
Figure 4.3.
It is important to stress that despite the fact that the grating response is symmetric, the
coupler based OADM response is different under Add/Drop action depending on the
relative grating position. In the first configuration (shown in Figure 4.1b) the Drop
action is optimised –Optimised (O)- by placing the grating inside the waist region
asymmetrically with respect to the mid-point M so that L1+Lp=Lwaist/2. In this case the
Add action is quite degraded –Degraded Add (D)- due the fact that the effective
reflection point on this grating side is well off the waist mid-point M. In the second
configuration (shown in Fig. 4.1c), the grating is placed symmetrically around the waist
mid-point M and the both effective reflection points are on either side of M. Due to
symmetry this configuration provides identical although compromised -Compromised
(C)- Add & Drop operation.
82
Figure 4.2 Full spectral response of Half-cycle coupler OADM (Optimised DROP)
Wavelength (nm)1548 1549 1550 1551 1552
Ref
lect
ion
(dB)
-60
-50
-40
-30
-20
-10
0Port 1DROPEven ModeOdd Mode
Wavelength (nm)
1548 1549 1550 1551 1552
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
Port 3Port 4Even ModeOdd Mode
83
Figure 4.3 Overlap of the group time delay responses of the even and odd modes. The solid line represents the average group delay of both responses.
Figures 4.4, and 4.5 give the full response for the Degraded Add and the Compromised
Add/Drop operations. By examining the graphs is clear that, firstly these two non-
optimised responses exhibit a non-zero insertion loss and for the case of the Degraded
Add is quite considerable (~ -5 dB). Secondly the non-flat amplitude responses can lead
to distortion effects in high bit rate applications introducing excess system loss. It
should be stressed here that by comparing the transmission spectra for the three
different responses ((O), (D), (C)) the spectral responses for the two exit ports are
identical. This is expected because the coupler characteristics in transmission do not
change with the relative positioning of the grating in to the coupler waist. Chapter 5
discusses in detail the performance of these non-optimum filters in WDM transmission
systems.
To illustrate the effect of the coupling length Zc on the spectral characteristics of the
OADM we consider a longer coupler with length of uniform coupler waist ~24 mm.
By deploying the same grating, its spectral characteristics for optimised Drop
arrangement are shown in Figure 4.6. As expected and predicted by equation 4.3 the
increased Re, Ro overlap results to suppression of the backrefelcted light. Indeed, the
peaks at the backreflected and the leaking light have been suppressed by almost 5 dB.
Wavelength (nm)
1549.0 1549.5 1550.0 1550.5 1551.0
Gro
up ti
me
dela
y (p
s)
5
10
15
20
25
30
35
40
TDo TDe
84
Figure 4.4 Full spectral response of Half-cycle coupler OADM (Degraded ADD)
Wavelength (nm)1548 1549 1550 1551 1552
Ref
lect
ion
(dB)
-60
-50
-40
-30
-20
-10
0Port 3Degraded ADD
Wavelength (nm)
1548 1549 1550 1551 1552
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0Port 1Port 2
85
Figure 4.5 Full spectral response of Half-cycle coupler OADM (Compromised ADD/DROP)
Wavelength (nm)1548 1549 1550 1551 1552
Ref
lect
ion
(dB)
-60
-50
-40
-30
-20
-10
0Back ReflectionADD or DROP
Wavelength (nm)
1548 1549 1550 1551 1552
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0LeakageOutput
86
Figure 4.6 Full spectral optimised Drop response of Half-cycle coupler OADM (Long Coupler)
Wavelength (nm)1548 1549 1550 1551 1552
Ref
lect
ion
(dB)
-60
-50
-40
-30
-20
-10
0Port 1DROP
Wavelength (nm)
1548 1549 1550 1551 1552
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0Port 3Port 4
87
4.3 Full-cycle coupler (FCC) based OADM
Figure 4.7 describes a novel alternative configuration of the full coupler interferometric
OADM which is based on a Full-Cycle coupler (FCC) and allows the optimal
implementation of both the Add and Drop functions. Here the coupler length is equal to
the even-odd mode beatlength Zc at the operating wavelength. If we used point
reflectors at the half-power points M1, M2 by employing a 'strong grating' extended
between these points and with 'zero' penetration depth then the device would give
optimum Add and Drop actions. In the real case where a Bragg grating is employed is
clear that this should be placed symmetrically inside the coupler and should have a
suitable length in order to make the penetration points at the Bragg wavelength
coincide with points M1 and M2.
Figure 4.7 Schematic of the full-cycle coupler (FCC) interferometric OADM. a) Power evolution along the full-cycle coupler b) Symmetric configuration for optimised Drop and Add actions
Lc
Lx
Lp Lp
L2 = Lg
Lw
M1 M2
L1 L1
Power in Port #1 Power in Port #1
Power exits Port#3
1
21
2
3
4 3
4
Input λ 1 DROP , λ 2 ... λ n
Input λ 1 DROP , λ 2 ... λ n
Drop λ 1 DROP
Drop λ 1 DROP
Add λ 1ADD
Add λ 1ADD
λ 1ADD, λ 2 ... λ nλ 1ADD, λ 2 ... λ nOutput
88
This novel design gives fully optimised Drop and Add functions with spectrally flat
Drop and Add characteristics. However, that is achieved, as is shown in the simulation
results later in this chapter, at the expense of a poorer bandwidth utilization factor of
the employed grating.
4.3.1 Design procedure
In this section, design rules are proposed for the effective optimised design of the full
cycle based OADM. The derivation is based on the geometrical characteristics of the
arrangement of the grating into the coupling region. We derive relations for the grating
penetration slope -defined as α =Lp / Lg, where Lp is the penetration depth at the design
Bragg wavelength and Lg the grating length- that eventually determine the maximum
allowed grating reflectivity. It should be stressed that the grating should be restricted
inside the uniform waist-coupling region (of length Lw). Writing the grating in the
tapered region of the coupler can severely deteriorate the OADM performance.
I. Half -Cycle Coupler (HCC) based OADM
We consider here a simplified case of grating arrangement, where at least half of the
coupler waist is used for the grating inscription (L3 = 0). We can write about the
'geometrical' relation between the grating and the coupler (see Figure 4.1):
2w
ggLaLL += (4.4)
As it has already been mentioned wg LL ≤ , which leads to:
5.0)1(2
≤⇒<−
= aLa
LL ww
g (4.5)
II. Full-Cycle Coupler (FCC) based OADM
A similar relation can be derived for this full-cycle configuration. To keep this relation
simple we can make the assumption that the length (M1M2) is equal to the half of the
waist length Lw. This is equivalent to Lw ≅ 4Lx where Lx is the length corresponding to
π/2 phase difference between the normal modes at the coupler waist. This
simplification neglects basically the effect of the contribution of the tapered waveguide
89
region to the phase evolution at the uniform waist region. We can now write (see
Figure 4.7):
2
2 wgg
LaLL +≅ (4.6)
Since wg LL ≤ , similarly, we obtain the following relation for the penetration slope,
namely:
25.0)21(2
≤⇒≤−
≅ aLa
LL w
wg (4.7)
If we consider the length Lx we can form also another exact relation now, which gives
the grating length:
L aL L LL
ag g x gx= + ⇒ =
−2 2
21 2( )
(4.8)
III. Multiple Half-Cycle Coupler based OADM
We can also generalise the derivation for the case of multiple (m) half-cycle coupler
based OADM which is illustrated in Figure 4.8.
Figure 4.8 Schematic of the optimum arrangement of a Bragg grating in a multiple half-cycle coupler (here m=5)
M1 M2
Lw
Lg
Lp Lx Lp
90
In this case, the optimum grating length can be expressed as (see Fig. 4.8):
xpg LmLL )22(2 −+= (4.9)
and taking into account that gp LL ⋅= α leads to the exact relation:
xg La
mL21
22−−
= (4.10)
which from now on will be referred as “Grating Length Equation”, because it relates
the grating length to its own characteristics (through α) as well as the coupler
characteristics (through Lx and m).
As already mentioned in the previous case of the Full-Cycle there is a finite
contribution of the tapered waveguide region to the phase and consequently to the
power evolution at the uniform waist region (Fig. 4.7). If we consider this contribution
negligible (as illustrated in Fig. 4.8) we can write for the geometrical characteristics of
the multiple-half-cycle coupler:
m
LL wx 2= (4.11)
Substituting (4.11) in to (4.9) gives:
wgwgg Lma
mLLm
maLL2)21(22
2222
−−
=⇒−
+= (4.12)
Again, imposing the limitation wg LL ≤ onto (4.12) results in:
m
ama
mLLma
mww 2
11)21(222
)21(222
≤⇒≤−−
⇒≤−− (4.13)
91
Substituting m=1,2, we recover the previous results for the half and full cycle couplers
given by Eq. (4.5) and (4.7) respectively.
We have found general engineering curves between the penetration slope and
reflectivity for three different representative cases, a uniform apodised, a sine apodised
and a raised cosine apodised grating. These general engineering curves are presented in
Figure 4.9. The significance of the ‘Grating Length Equation’ is greatly enhanced by
the fact that the penetration slope of a grating for a specified apodisation profile is
related (by ‘1-1’ relation) to its reflectivity. That allows the establishment of a
furthermore general relation between gratings spectral characteristics and grating-
coupler geometrical relation for different OADM configurations.
Figure 4.9 Engineering curves for penetration slope versus reflectivity for various apodisation profiles
One can notice at this point that the requirement for penetration slope is very tight for
the multiple-half-cycle coupler based OADM (m>1), whereas for the half-cycle (m=1)
there is no any restricting relation since always α < 0.5 (α tends to 0.5 for very weak
Absolute Reflectivity (dB)0 5 10 15 20 25 30 35 40 45 50 55 60 65 70
Pene
tratio
n Sl
ope
(cm
/cm
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
U
S
RC
Apodisation Profiles U: Uniform S: Sine RC: Raised Cosine
92
grating, and is decreasing for higher reflectivity). In contrast to the Half-Cycle, in the
Full-Cycle case the grating should exhibit penetration slope less than an upper limit.
For the theoretical obtained limit of 0.25 the grating would ‘cover’ all the coupler waist
length. Because of the effect of the taper region of the coupler the actual maximum
allowed slope is less and thus for a reasonable coupler-waist coverage from the grating
we can set a value of about α ~ 0.2.
For α = 0.2 Figure 4.9 gives minimum required (absolute) reflectivities for different
apodisation profiles. These are at 15 dB, 31dB and 60 dB for uniform, sine and raised
cosine profiles respectively. Deployment thus of more drastic apodisation profiles in
order to suppress the dispersion effects of the grating, requires stronger gratings which
in turn increase those effects, forming this way a restrictive trade off between the two
parameters. A stronger apodisation profile like Blackman [4.3] would require an
unrealistically high reflectivity in order to be accommodated in the coupler device.
The value of α can be established much more accurately if the shape of the coupling
region and the power evolution along the coupler is known. This can be measured
accurately using non-destructive coupler characterization techniques [4.4]
Design Algorithm
The results of the above discussion can be put together in the brief form of a design
algorithm, which enables the determination of the grating length with specified
apodisation profile and strength placed appropriately inside the uniform coupler waist.
We consider now the general case of the multiple (m) half-cycle coupler and we
assume that the effective refractive indices of the even and odd normal modes are ne, no
respectively. From the definition of the characteristic length Lx we have the relation:
2
2)( πλπ
=− xo
oe Lnn (4.14)
93
which leads to: )(4 oe
ox nn
L−
=λ
(4.15)
For a specific grating apodisation profile and reflectivity, the penetration slope (α) can
be estimated by the engineering curves shown in Figure 4.9. From the coupler
characteristics (Lx, m) and the estimated penetration slope, the optimum grating length
is calculated by the ‘Grating Length Equation’ Eq. 4.10. Finally the maximum
refractive index modulation is calculated for the required grating reflectivity. The
design procedure is described schematically by the following flow chart:
Figure 4.10 Grating length determination algorithm
Grating Apodisation Profile ( K(z) )
Grating Reflectivity( R )
Penetration Slope (α )
Penetration Slope vs
Reflectivity (Fig. 4.9)
Grating Length ( Lg )
Grating Length Equation (Eq. 4.10)
Refractive Index Modulation
( ∆n )
Characteristic Coupler Length ( Lx )
& Coupler Order ( m )
94
4.4 Spectral response of the full-cycle coupler (FCC) based OADM
Initially we design a full-cycle coupler in order to accommodate the Bragg grating
which was deployed in section 4.2 for the construction of the HC OADM. By using the
same grating in a properly designed coupler a symmetric and fully optimised Add/Drop
OADM will be demonstrated. Starting from the length and the penetration depth of the
grating, the required Lx parameter of the coupler is calculated by the Grating Length
Equation to be Lx=1.485 mm. Based on that we design a coupler with uniform waist of
4.540 mm, which can accommodate the Bragg grating length of 4.5 mm. Placing the
grating in to the centre of the new full cycle coupler waist, we form the OADM. In
Figure 4.11 is plotted the full response of the device which shows the simultaneously
and identical Add and Drop actions. With the red and blue lines are represented again
the overlapped reflection spectra of the even and odd supermodes.
We can notice that again the dispersion effects lead to considerable back reflections at
the input. The 3-dB bandwidth of the Drop/Add action is now 0.7 nm which implies a
lower bandwidth utilisation factor - compared with the Half-Cycle - given that the
inscripted grating had 1 nm bandwidth.
As already discussed in section 4.2 for the half-cycle coupler configuration, the average
time delay of the even and both modes determines the amount of leaking power,
because this average time delay variation leads to a varying coupler length. Figure 4.12
shows the overlap of the even/odd group time delays, together with their average (thick
solid line). As expected the average time delay curve is in agreement with the spectral
response of the leaking Port 4.
95
Figure 4.11 Full spectral response of the full-cycle coupler based OADM. The Drop/Add actions are formed by the partial overlap of the even and odd modes reflection spectra. The optimally designed and deployed Bragg grating is sine apodised with length 4.5 mm and absolute reflectivity of 45 dB.
Wavelength (nm)1548 1549 1550 1551 1552
Ref
lect
ion
(dB)
-60
-50
-40
-30
-20
-10
0Back ReflectionsDROP / ADDEven ModeOdd Mode
Wavelength (nm)
1548 1549 1550 1551 1552
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
OutputLeakageEven ModeOdd Mode
96
Figure 4.12 Overlap of the group time delay responses of the even and odd modes. The solid line represents the average group delay of the two responses.
For comparison reasons we design another full-cycle OADM device. In this example
we simply extend the original half cycle coupler forming a full cycle. The length of the
waist now is ~20.7 mm and the length Lx=5.530mm. We will optimally design and
accommodate now a Bragg grating with the same apodisation profile and the same
absolute reflectivity of 45 dB. For sine apodised Bragg grating with transmission –45
dB the penetration slope -accordingly to the engineering curves in Figure 4.9- is
α=0.17. The optimum grating length calculated by the Grating Length Equation 4.6 is
Lg=16.755 mm. The required refractive index modulation to achieve absolute
reflectivity of 45 dB can be calculated and is 2.7x10-4 (p-p). At this point all the Bragg
grating characteristics have been determined and symmetric inscription of the grating
into the centre of the coupler waist will form an optimised full-cycle coupler based
OADM. The full spectral response of the formed OADM is shown in Figure 4.13. As
expected, the spectral characteristics are very similar to that of Figure 4.11, but the
bandwidth is narrower since the employed grating now is longer with smaller refractive
index modulation.
Wavelength (nm)
1549.0 1549.5 1550.0 1550.5 1551.0
Gro
up ti
me
dela
y (p
s)
5
10
15
20
25
30
35
40
45
97
Figure 4.13 Full spectral response of the full-cycle coupler based OADM in a longer coupler. The full cycle coupler is formed by extending the half cycle used in the initial half cycle OADM.
Wavelength (nm)1549.50 1549.75 1550.00 1550.25
Ref
lect
ion
(dB)
-60
-50
-40
-30
-20
-10
0Back ReflectionDROP or ADDEven ModeOdd Mode
Wavelength (nm)
1549.50 1549.75 1550.00 1550.25
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
OutputLeakageEven ModeOdd Mode
98
As demonstrated in our proposed design algorithm, for a given full-cycle coupler
structure, there is an exact relation between the reflectivity of the deployed Bragg
grating and its physical length. Non-optimum design of the grating can lead to
degraded device performance.
Degraded performance of the OADM response due to non-optimised inscripted grating,
is demonstrated by two examples, by considering the full cycle coupler of uniform
waist 4.540mm. The optimised grating here exhibits transmission of -45 dB and length
4.5 mm.
At the first example we form the OADM device by employing a Bragg grating with
absolute value of reflectivity 45 dB and length 2.5 mm. The full spectral response is
shown in Figure 4.14. Is clear the associated loss of ~ -3dB at the Drop/Add action and
the very strong backreflections at the input port. At the second example we consider a
grating with the optimised length of 4.5 mm but with an absolute reflectivity 25 dB
(which corresponds to transmission of -25 dB). The full response of the device is
shown in Figure 4.15, where the degraded spectral characteristics are obvious again.
The Drop or Add action exhibits now a response with a much greater ‘3-dB/20-dB’
bandwidth ratio, which implies a very poor bandwidth utilisation.
The fabrication of interferometric based OADMs requires accurate control for the
optimum inscription of the grating into the uniform coupling region. The precise
characterization of the coupler is of critical importance for the successful inscription of
the grating and the implementation of the device. An effective non-destructive coupler
characterization technique applied to fibre couplers has recently proposed for this
reason [4.4]. In an early attempt to fabricate a prototype FCC OADM we found that
fabrication imperfections can severely degrade its performance [4.5]. These factors can
be the non-identical grating strength on the two waveguides at the uniform waist
region, the non-optimum grating positioning along the coupler waist, or even a slight
tilt of the grating in respect to the coupler axis. The implementation of the device in
integrated optics form could eventually give better control on these fabrication factors,
improving thus the device performance.
99
Figure 4.14 Full spectral response of a non-optimally designed FCC OADM. The employed grating exhibits the required absolute reflectivity 45 dB but the length is only 2.5 mm.
Wavelength (nm)1548 1549 1550 1551 1552
Ref
lect
ion
(dB)
-60
-50
-40
-30
-20
-10
0
Back ReflectionDROP or ADD
Wavelength (nm)1548 1549 1550 1551 1552
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
Output Leakage
100
Figure 4.15 Full spectral response of a non-optimally designed FCC OADM. The employed grating is of optimum length 4.5mm, but its absolute reflectivity is only 25 dB.
Wavelength (nm)
1549.0 1549.5 1550.0 1550.5 1551.0
Ref
lect
ion
(dB
)
-60
-50
-40
-30
-20
-10
0
Back Reflections DROP or ADD
Wavelength (nm)
1549.0 1549.5 1550.0 1550.5 1551.0
Tran
smis
sion
(dB)
-60
-50
-40
-30
-20
-10
0
OutputLeakage
101
4.5 Conclusions
In this chapter we have studied the class of interferometric full coupler based OADMs.
By modelling the traditional half-cycle based OADM we revealed its performance
characteristics and limitations due to its inherent asymmetry. A novel symmetric
OADM configuration based on a full-cycle coupler was proposed. This device gives
simultaneously optimised (with flat top-hat characteristics in the amplitude spectral
response) Add and Drop actions.
A general method was proposed also for the design of the device. The method is based
on simple mathematical expressions, which relate the grating length to the coupler
characteristics. Central to this design method are the newly proposed engineering
curves, which relate the Bragg grating’s penetration slope to its reflectivity for a
specific apodization profile.
4.6 References
[4.1] K. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X.
Daxhelet, F. Gonthier, “Optical add-drop multiplexer based on UV written Bragg
gratings in a fused 100% coupler,” Electronics Letters, vol. 33, no. 9, pp. 803-804, Apr.
1997.
[4.2] M. N. Zervas and C. Riziotis, “Novel Full Cycle Coupler –Optical Add/Drop
Multiplexer with fully optimised performance”, Patent Application.
[4.3] K. Ennser, M. N. Zervas, R. I. Laming, “Optimization of apodized linearly
chirped fiber gratings for optical communications,” IEEE J. Quantum Electron., vol.
34, no. 5, pp. 770-778, May 1998.
102
[4.4] C. Alegria, F. Ghiringhelli, M. N. Zervas, “Non-destructive characterization of
fibre couplers,” paper We.L.2.3 (invited), ECOC’ 01, Amsterdam, The Netherlands.
Sep. 30-Oct. 4, 2001.
[4.5] C. Alegria, C. Riziotis, M. N. Zervas, “Fibre grating based devices,” PIRELLI-
Project report (confidential), April 2000.
103
CHAPTER 5
Characterization of Optical Filters in
High Speed WDM Transmission Systems
5.1 Introduction
WDM optical systems are continuously migrating towards narrower channel spacing
and higher bit rates in order to use the available bandwidth most efficiently. Various
combinations of channel spacing ranging from 25GHz to 100GHz, and bit rates from
10Gb/s to 40Gb/s are currently being explored. High performance optical filters are
proving to be central to the successful deployment of high-speed optical systems. High
bandwidth efficiency sets also quite stringent requirements for WDM filter
characteristics and any imperfections in their phase and/or amplitude response becomes
critical.
The study and the understanding of the impact of those filters imperfections to
communication systems are of great importance. This Chapter studies the performance
of different types of optical filters, by using system simulations. A complete simulation
tool has been developed for this purpose and is used as the characterization test bed for
simulated custom WDM filters.
Firstly the performance of Bragg grating based filters is studied and compared, in an
Intensity-Modulation / Direct-Detection (IM/DD) communication system at 40 Gb/s
transmission speed. The effects of filter / laser source misalignments and filter’s
cascading are examined for those filters and the effects are quantified by estimating the
Eye-Opening Penalty (EOP) [5.1-5.3].
104
The second part of the chapter presents results on the effect of in-band group delay
ripple on WDM filter performance. With the continuously increasing transmission
speed the effect of dispersion becomes very critical and often is the limiting factor in
filters performance. The effect of group delay ripples is studied here at 10 and 40 Gb/s
for NRZ and RZ modulation formats [5.4].
5.2 Simulation of an optical communication system
The deployed communication system for the filter characterization is a point-to point
lightwave link based on Intensity Modulation / Direct Detection scheme [5.5, 5.6].
Starting with a pseudo-random bit sequence (PRBS) of 27 bits, the eye diagram of the
recovered signal is estimated at the other end of the link. A block diagram of the
simulated communication system is presented in Figure 5.1
Figure 5.1 Block diagram of the simulated test-bed for filter’s characterization
The initial signal represented in time domain is transformed into frequency domain by
the use of Fast Fourier Transform (FFT). The signal is shaped and filtered at different
stages of the system by multiplying its frequency domain representation with the filter
response. At the receiver, the optical signal is transformed back to frequency domain
and then is transformed to electrical signal by passing through a square law detector -
which converts the optical to electrical power. According to the SONET standards the
signal passes through an electrical filter, which is simulated as a 4-order Bessel, filter
with 3-dB bandwidth 75 % of the deployed bit rate. Converting the signal back to time
domain and overlapping slots of 3 bits duration, produces the eye diagram. If Ao, A1 are
IFFT Square Law Detector
FFT LPF
Electrical IFFT EYE Diagram
RECEIVER 10 20 30 40 50 60
PRBS Generator
Shaping Filter
FFT
TRANSMITTER Optical Filters
MZ Modulator
1 0 1 0 1 1 0 1………..
A1
A0
105
the eye opening amplitudes of the initial and the final eye diagrams, the Eye-Opening
Penalty (EOP) is defined then for an IM/DD system as:
⋅−=
0
1log10 AAEOP (5.1)
A chirp-less signal is assumed in all the simulations, by deploying a perfectly balanced
Mach-Zehnder modulator.
5.3 Fundamental operations in optical network’s nodes
In Figure 5.2 we introduce some representative Add/Drop operations for the
characterization of OADMs performance in an optical network.
Figure 5.2 a) Schematic of a single node where a channel is added in to the input optical stream or dropped from it through a switch. b) Schematic of a fundamental cascaded Add-and-Drop action in an optical network.
Figure 5.2a describes a single-channel network node where a WDM channel can either
be Added or Dropped, or can experience a cascaded Drop-and-Add action with the use
of a switch. In the node, the Dropped channel can be transmitted to the node’s final
DROP λ1
OADM
Input Output
ADD λ1
SWITCH Bar/Cros
λ 1 λ1
(a)
OADM #2
Input 2 Output 2
OADM #1
ADD λ1
Input 1 Output 1
DROP λ1
(b)
106
user (cross state of switch) or through a bypass operation (bar state of switch) can be
added again to the optical stream leading thus to a two-stage cascade in a single
OADM. In a real access network a sequence of similar optical nodes can lead to a
number of cascaded Drop-and-Add operations [5.7]. Figure 5.2(b) describes the Add-
and-Drop cascaded operation for an OADM, which can occur in different nodes of a
WDM network. The combined action of two OADMs gives the Add-and-Drop function
where a particular WDM channel is added in a node and then dropped in another node
in the network.
5.4 Characterization of half-cycle coupler (HCC) based OADM
In this section the implications of the inherently non-optimum spectral characteristics
of the half-cycle OADM are analysed using system simulations. The Add or Drop
filtering performances are examined for the main three different spectral responses this
device exhibits –depending on the grating position and the input port.
We consider here a half-cycle based OADM with 3-dB bandwidth of ~0.7 nm. The full
coupler has a total length of 20mm and a uniform waist length Lwaist=L1+L2+L3=10mm.
The deployed Bragg grating has a typical reflectivity 35 dB with length Lg=5.2 mm,
amplitude of refractive index modulation ∆n=3.65x10-4, and sine-apodisation profile.
Figure 5.3 shows the reflectivity spectra in linear scale for the Optimised (O),
Degraded (D) and compromised (C) responses of the OADM. Together is plotted the
reflection spectrum of the deployed Bragg grating (BG). The narrowing of the OADM
reflection is obvious as already discussed in Chapter 4. Figure 5.4(a) gives the intra-
band group time delay of all those responses and Figure 5.4(b) gives the corresponding
intra-band dispersion, calculated asλτ
ddD = . From Figure 5.4 it is realized that the
time delay and dispersion are almost identical for all the different modes of operation
within the bulk of the reflection band. The main difference occurs right at the edges of
the reflection bands. Figure 5.3, however, shows that the reflectivity spectra are
distinctively different for the considered modes of operation. Any differences in the
107
system response of these devices are expected to be primarily due to the particular
reflectivity spectra.
Figure 5.3 Comparison of the typical reflectivity spectra, in linear scale, for the employed Bragg grating (BG), Optimised (O), Compromised (C) and Degraded (D) actions.
We will consider also, cascaded Add/Drop actions when this type of OADM is
deployed in a WDM network. If we consider that these HCC-OADMs are deployed in a
WDM network (Figure 5.2(b)), then depending on their individual configurations and
also the relative orientation of their Ports we can get a set of different combinations and
different overall spectral responses for the two stage cascaded Add/Drop action.
Namely, ‘Optimised Drop & Degraded Add’ (O-D), 'Compromised Drop and Add' (C-
C), ‘Degraded Drop & Degraded Add’ (D-D) are some interesting combinations.
Figure 5.5 shows some of the representative transfer functions, which correspond, to
single Add or Drop actions, or to cascade Add-and-Drop actions as described above.
The transfer functions, which correspond to the reflectivity spectra in Figure 5.3, are
plotted in Figure 5.5 with the same line code for comparison.
Wavelength (nm)
1549.4 1549.6 1549.8 1550.0 1550.2 1550.4 1550.6
Ref
lect
ivity
0.0
0.2
0.4
0.6
0.8
1.0
C
O
D
BG
108
Figure 5.4 a) Comparison of the intra-band typical group time delay characteristics for the (BG), (O), (C) and (D) responses. The time delays for all the cases were normalized to zero value at the center of the filter. b) Comparison of the intra-band dispersion characteristics for the same responses.
Wavelength (nm)
1549.6 1549.8 1550.0 1550.2 1550.4
Nor
mal
ised
gro
up ti
me
dela
y (p
s)
0
10
20
30
40
50
BGOptimisedSymmetricalDegraded
BG
D
C
O
Wavelength (nm)
1549.6 1549.8 1550.0 1550.2 1550.4
Dis
perio
n (p
s/nm
)
-400
-200
0
200
400 BGOptimisedCompromisedDegraded
BG
D
C
O
109
The magnitude of the transfer function is the square root of reflectivity. Together are
plotted also the (C-C), (O-D) and (D-D) transfer functions. We can notice that despite
their different average level, which should lead to different overall insertion loss, the
shapes of the (O-D) and (C-C) responses are the same. Consequently it is expected that
they suffer from identical intra-band distortion effects. This will be confirmed later by
using system simulations, which take also the phase response of the filters into account.
Figure 5.5. Comparisons of magnitude of the reflection coefficient for single pass and cascaded Add-and-Drop actions.
The OADM performance will now be characterized for the compatible 40 Gb/s
transmission speed using NRZ modulation format. Figure 5.6 shows the reflection
spectra –in logarithmic scale- of the deployed Bragg grating together with the three
different OADM responses. The spectrum of the modulated signal is also plotted for
comparison. We examine initially the distortion effects for a single and double
cascaded operations (Fig. 5.2), as a function of misalignment between the center
frequency of the effective filter and the center frequency of the modulated signal
spectrum. The results obtained here could be transferred to any bit-rate and equivalent
employed filters, with the same filling factor (ratio of signal bandwidth and filter
Wavelength (nm)
1549.4 1549.6 1549.8 1550.0 1550.2 1550.4 1550.6
Filte
r's tr
ansf
er fu
nctio
n am
plitu
de
0.0
0.2
0.4
0.6
0.8
1.0
D-D
C-C
O-D
110
bandwidth). We concentrate our study here only on the distortion effects due to filter’s
spectral shape degradation and we neglect the additional loss associated with the non-
optimised spectral responses (Figure 5.5), which can always be compensated by use of
optical amplifiers [5.8].
Figure 5.6 Filling of the bandwidth of the different filter responses with the spectrum of NRZ 40 Gb/s PRBS signal.
5.4.1 EOP calculations
Figure 5.7 gives the EOP for a single Add or Drop action. As expected the deployed
Bragg grating is superior, given also its broader bandwidth. The optimised (O) Drop is
only slightly degraded compared to the BG case. We can notice also from the graph
that for the misalignment range of [-0.2nm to +0.2nm] the non-optimum OADM
responses leads to an EOP higher by at least 0.15dB.
Figure 5.8 shows the EOP for the Add-and-Drop operation described in Figure 6.2(b).
The ‘Optimised Drop & Degraded Add’ (O-D) and the ‘Compromised Drop and Add’
(C-C) configurations exhibit exactly the same EOP relation versus the filter
misalignment, as predicted from their spectral shape. So we can conclude that the
overall Add-and-Drop operation of a particular SFC OADM is independent of the
individual responses and consequently insensitive to the grating arrangement in the
Wavelength (nm)
1549.25 1549.50 1549.75 1550.00 1550.25 1550.50
Ref
lect
ion
(dB)
-40
-30
-20
-10
0
111
coupler waist. This is a direct consequence of the linearity and reciprocity of the
composite OADM four port device [5.9].
Figure 5.7 EOP at 40 Gb/s as a function of filter- laser source misalignment for a single Drop or Add action.
Figure 5.8. EOP at 40 Gb/s as a function of filter - laser source misalignment for a cascaded Add-and-Drop action, for representative filters combinations
Offset from the center of filter (nm)
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Eye-
Ope
ning
Pen
alty
(dB)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Employed Bragg GratingOptimised DROPCompromised ADD/DROPDegraded ADD
Offset from the centre of filter (nm)
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Eye-
Ope
ning
Pen
alty
(dB)
0
1
2
3
4
5
6
BG-BGO-OO-D or C-CD-D
112
In a large-scale network with a number of different nodes, the worst-case scenario
combination of Degraded Drop-Degraded Add (D-D) operation can occur which as
shown in Figure 5.8, suffers considerably higher EOP. By comparing Figures 5.7 and
5.8 it is clear that even a two stage cascading makes the difference between optimum
and degraded filters much more prominent especially for misalignments above ±0.05
nm. The use of degraded filters in this two-cascade operation results in a reduction of
the allowed range of filter-laser misalignments by a factor of two, in order to keep the
EOP below 1 dB.
As already discussed in Chapters 1 and 4, OADMs based on non-interferometric
configurations like the optical circulator type, or the null coupler with a tilted grating
exhibit intra-band spectral characteristics identical to those of the employed Bragg
grating. Consequently deployment of this type of filters in a WDM network should be
associated with the performance curves (in Figures 5.7 & 5.8), which represents the use
of the single Bragg-grating (BG).
Finally to determine the tolerance of the different OADM filters in cascaded operation
we estimated the EOP for all the considered different responses of the HCC OADM
device as a function of the cascade count. The filters are considered perfectly aligned
with each other and aligned also with the modulated signal spectrum. Two different
studies were performed. First we considered the actual transfer function of each filter,
which contains both the amplitude and phase response. In the second case we neglected
the phase response of the filters, concentrating thus only on the distortion effects due to
reflectivity spectral shape. The results for these two cases are summarised in Figures
5.9 and 5.10, respectively. By comparing these figures we can conclude that the
number of cascades in order to keep the EOP bellow 1dB is limited mainly by in-band
dispersion. When only the reflectivity is considered (Fig. 5.10) we can notice that for
the Optimised (O) or the Bragg Grating (BG) cases the EOP is kept well below 0.2 dB
even after 32 cascades, while in contrast, is increased almost exponentially for the non-
optimum filter responses. Consequently, deployment of specially designed,
dispersionless Bragg gratings [5.10] could greatly improve the cascadability of those
113
OADMs. The advantage, however, would be much greater for spectrally optimised
OADMs as demonstrated in Figure 5.10.
Figure 5.9 Effect of OADM cascade on EOP performance.
Figure 5.10 Effect of OADM cascade on EOP performance when only the reflectivity response of the filters is considered.
Cascade number
0 2 4 6 8 10
Eye-
Ope
ning
Pen
alty
(dB)
0
1
2
3
4
5
BGOCD
Cascade number
0 4 8 12 16 20 24 28 32
Eye
-Ope
ning
Pen
alty
(dB
)
0.0
0.2
0.4
0.6
0.8
1.0
BGOCD
114
5.5 Characterization of full-cycle coupler (FCC) based OADM
In this section, the performance of a full-cycle coupler based OADM (FCC-OADM) is
characterized at 40 Gb/s transmission speed using NRZ modulation format. As in the
case of the half cycle based OADM (section 5.4) we examine the filter performance at
40 Gb/s for a custom filter with 3-dB bandwidth of ~0.7 nm. This filter has already
been simulated in Chapter 4, and its spectral response is shown in Figure 4.11.When
the filter is optimally designed accordingly to the method proposed in Chapter 4, and
then it exhibits symmetric behavior with identical and spectrally flat (top-hat) Add and
Drop actions. The two ends of the OADM are thus identical in contrast to the optimised
half cycle based OADM. Consequently, deployment of FCC-OADM in WDM
networks (as seen in figure 5.2) is effectively described by the cascading of the filter’s
optimised Add/Drop response, and the system performance does not depend on the
relative orientation of those filters.
The performance of the FCC-OADM will be characterized and compared with the
performance of the deployed Bragg grating, in order to quantify the effect of the filter’s
response narrowing. Figure 5.11, shows the reflectivity spectra of the OADM and the
Bragg grating with 3-dB bandwidth ~0.7 and 1nm respectively.
Figure 5.11 Reflectivity spectra of the FCC-OADM response and the employed BGWavelength (nm)
1549.0 1549.5 1550.0 1550.5 1551.0
Ref
lect
ivity
0.0
0.2
0.4
0.6
0.8
1.0
BG @ FCC
FCC OADM
115
In Figure 5.12 and 5.13 are shown respectively the group time delay and the dispersion
of the FC OADM and of the employed Bragg grating.
Figure 5.12 Group time delay of the FCC-OADM and the employed grating
Figure 5.13 Group time delay of the FCC-OADM and the employed grating
Wavelength (nm)
1549.4 1549.6 1549.8 1550.0 1550.2 1550.4 1550.6
Gro
up ti
me
dela
y (p
s)
0
20
40
60
80
100
BGFCC OADM
Wavelength (nm)
1549.4 1549.6 1549.8 1550.0 1550.2 1550.4 1550.6
Dis
pers
ion
(ps/
nm)
-300
-200
-100
0
100
200
300
BGFCC OADM
116
5.5.1 EOP calculations
Is clear from graphs 5.11, 5.13 that the degradation of spectral characteristics of the
FCC OADM response, when compared to the employed grating (BG). By using again
system simulations we quantify the impact of the filter’s narrowing effect to the 40
Gb/s NRZ signal distortion. Initially, the distortion effects are estimated for a single
Drop or Add action as a function of filter and signal spectrum misalignment. The
effects are also examined for a 2-stage cascade (Add-and-Drop), and the calculated
EOP are concluded for both cases in Figure 5.14.
Figure 5.14 EOP at 40 Gb/s for one (#1) and two (#2) cascaded filter actions as a function of filter-signal spectrum misalignment.
Due to the broader bandwidth of the employed grating (BG) the exhibited EOP is lower
than that of the OADM. However for misalignments within the range of [-0.1nm,
0.1nm] the EOP curves are very flat and well bellow 0.5 dB. In this range of
misalignment, the second cascade induces an additional EOP of about 0.2 dB.
The distortion effects are examined also in the case of the cascade of perfectly aligned
filters, which are also aligned with the laser source. For the BG and the FCC-OADM
Offset from the centre of filter (nm)-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Eye-
Ope
ning
Pen
alty
(dB)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
BG (#1)FCC OADM (#1)BG (#2) FCC OADM (#2)
117
the EOP is estimated up to a number of 16-cascaded filters. The results are shown in
Figure 5.15.
Figure 5.15 EOP as a function of the number of perfectly aligned filters.
For a relatively small number off cascaded filters (less than 7) the difference in EOP
for BG and FCC-OADM cascaded filters is indistinguishable, and the EOP is kept well
below 0.5 dB. The difference becomes more prominent and is monotonically increasing
only after a number of 7 cascades.
5.5.2 Performance comparison of FCC and HCC OADMs
In this section we compare the performance of the already characterized FCC OADM
with the HCC OADM, which employs the same Bragg grating. The HCC OADM has
already been modeled in Chapter 4 and its spectral responses for the three different
operational modes are summarized in Figures 4.2, 4.4 and 4.5.
For a direct comparison, Figure 5.16 gives the reflectivity spectra for the employed BG,
the FCC OADM and the three spectral responses of the HCC OADM.
Cascade number
0 2 4 6 8 10 12 14 16 18
Eye-
Ope
ning
Pen
alty
(dB)
0.0
0.5
1.0
1.5
2.0
2.5
BGFCC OADM
118
Figure 5.16 Comparison of reflectivity spectra for FCC, HCC OADMs and of the employed Bragg grating (BG)
As has already been discussed, the FCC OADM exhibits identical and optimised Add
and Drop actions at the expense of a lower bandwidth utilization factor compared to the
HCC OADM. On the other hand the non-optimised responses of the HCC exhibit a
quite considerable insertion loss.
Figure 5.17 Insertion loss in cascaded filtering
Wavelength (nm)
1549.0 1549.5 1550.0 1550.5 1551.0
Ref
lect
ivity
0.0
0.2
0.4
0.6
0.8
1.0
BG @ FCC
FCC OADM
HCC (C)
HCC (D)
HCC (O)
Cascade number
0 2 4 6 8 10 12 14 16 18
Tota
l ins
ertio
n lo
ss (d
B)
0
5
10
15
20
25
HCC OADM (D)
HCC OADM (C)
BGFCC OADMHCC OADM (O)
119
The insertion loss in cascaded filtering operations for all the different filters has been
calculated and is shown in Figure 5.17. Optimised filter responses exhibit negligible
loss while the non-optimised HCC OADM leads to quite considerable loss.
Deployment of this type of filters can thus lead to non-uniform loss in a communication
system, which is a major problem in real systems.
We examine now the EOP for a double stage cascade as a function of filter-signal
spectrum misalignment. Figure 5.18 shows the curves of Figure 5.14, together with the
estimated EOP curves for the HCC OADM.
Figure 5.18 EOP at 40 Gb/s for two cascaded filter actions as a function of filter-signal spectrum misalignment
Despite the narrower bandwidth the FCC OADM, for the range of misalignment [-0.1
nm, 0.1 nm], exhibits performance comparable with the other much broader filters.
Offset from the centre of filter (nm)
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Eye-
Ope
ning
Pen
alty
(dB)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
BG (#2)FCC OADM (#2)HCC OADM (O-O)HCC OADM (C-C)HCC OADM (D-D)
120
The distortion effects due to cascading are examined and compared finally for the HCC
and FCC OADMs.
Figure 5.19 EOP at 40 Gb/s as a function of the number of perfectly aligned filters. Figure 5.15 is redrawn together with the EOP curves for the HCC OADM (Fig. 5.19).
The EOP relation for the optimised (O) HCC OADM follows closely that of the BG.
For number of cascades less than 7 the FCC OADM performs as the other much
broader filters.
The compromised performance HCC (C) lies between that of FCC and BG, but it
should be stressed here the existence of the associated loss to this filter response (Fig.
5.17) which tends to the value of -15 dB for a number of 16 cascades.
Cascade number
0 2 4 6 8 10 12 14 16 18
Eye-
Ope
ning
Pen
alty
(dB)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0BGFCC OADMHCC OADM (O)HCC OADM (C)HCC OADM (D)
121
5.6 Effect of group delay ripple on WDM filters performance
WDM filters based on fibre-Bragg gratings [5.10] and thin-film technologies are
known to show in-band time delay ripples due to design and manufacturing
compromises. The thorough study and understanding of the impact of time-delay ripple
period and amplitude on the transmission penalties associated with the use of these
filters is of paramount importance. In the presence of in-band time-delay noise, it is
also desirable to know which spectral components affect predominantly the filter
performance. This will help in defining design tolerances and trade-offs necessary for
the development of highly efficient filters. In-band monotonic dispersion variation is
known to limit the efficiency of grating filters [5.11]. Periodic in-band time delay
ripple has been shown to affect the performance of chirped fibre grating used as
dispersion compensators [5.12].
Here, we examine the effects of time-delay-ripple period and amplitude for WDM
filters operating at 10Gb/s and 40Gb/s with NRZ and RZ modulation formats. A very
simple expression is proposed also in order to quantify the distortion effects due to
group delay ripple. The proposed figure-of–merit is in excellent agreement with
systems simulations.
5.6.1 Time delay ripple definition
The filter in-band time delay ripple is defined as:
++−⋅=∆ θλπλλλτ
οο p
aa non
2cos)()( 2 (5.2)
where α0 and p0 are the time delay ripple amplitude and period, respectively. The
phase θ determines the relative position of the time delay peaks with respect to the
filter centre wavelength. The first term in Eq. (5.2) gives the monotonic time-delay
increase towards the band-edges observed in most of the used optical filters. Figure
5.20, shows these three representative cases with p0=100pm and θ = 0, π/2, and π. The
considered filters we use here are dispersion flattened and they can be described by a
122
dispersion order of 10 (n=5). Their in-band dispersion shape simulates closely the type
of dispersion less Bragg grating filters demonstrated in [5.10].
Figure 5.20 In-Band time-delay variation
5.6.2 EOP calculations
A. 25 GHz filter and 10 Gb/s NRZ signal
Using the simulated communication system in Figure 5.1, we estimate the eye-opening
penalty (EOP) arising from the ripple effects. A perfectly rectangular filter with
bandwidth 25GHz is employed and a signal modulated at NRZ format at 10Gb/s is
transmitted through the filter. Then the recovered signal is characterised by the EOP.
Figure 5.21 gives the EOP as a function of the ripple periodicity for two different ripple
amplitudes. The time delay pattern which corresponds to θ=±π/2 exhibits the lowest
EOP (best case), while the cases with θ=0,π give the most degraded performance
(worst case). For all the other θ’s, the EOP lies between these two extremes. For both
amplitudes, a resonance behaviour is observed with the worst-case EOP peaking for a
resonance period of ~90pm.
Wavelength (nm)1549.90 1549.95 1550.00 1550.05 1550.10
Tim
e D
elay
(ps)
-20
0
20
40
60
80
100
120
Best Case (θ=π/2)Worst Case I (θ=0)Worst Case II (θ=π)
123
For any ripple period, the EOP increases monotonically with the ripple amplitude.
Figure 5.22 shows the calculated EOPs for a ripple period of 100pm.
Figure 5.21 EOP for 10 Gb/s NRZ data and 25 GHz filter
Figure 5.22 Effect of ripple amplitude on EOP at 10Gb/s
Time delay ripple period (pm)0 100 200 300 400
Eye
-Ope
ning
Pen
alty
(dB
)
0.0
0.2
0.4
0.6
0.8
1.0 BC: 15 psWC: 15 psBC: 20 ps WC: 20 ps
Time Delay Ripple Amplitude (ps)0 5 10 15 20 25 30 35 40 45
Eye
-Ope
ning
Pen
alty
(dB
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Best case Worst case
Bit Rate: 10 Gb/sFilter BW: 25 GHzRipple Period: 100 pm
124
It is shown that for ripple amplitudes smaller that ~25ps, the worst-case EOP increases
quasi-linearly with the amplitude. For negligible additional transmission penalty
(EOP≤0.3dB), in the worst-case scenario (i.e., at resonance period ≈90pm) it is found
that the optical filter should exhibit time-delay ripple amplitude smaller than ~3ps. For
periods away from the resonance one, larger time-delay ripple amplitudes can be
tolerated.
B. 100 GHz filter and 40 Gb/s NRZ signal
We also examined the effect of the time delay ripples in the case of NRZ data
transmission at 40Gb/s through a 100GHz rectangular filter. Figure 5.23 shows the
worst and best cases for ripple amplitude of 5ps. The worst-case EOP shows the same
resonance behaviour peaking at a period of ~350pm. This resonance period is roughly
four times the corresponding value at 10Gb/s. However, we should stress that,
compared to 10Gb/s case, the same maximum worst-case EOP (~1.4dB) is achieved
with only ¼ of the ripple amplitude. Higher bit rates put much more stringent
requirements on filter characteristics.
Figure 5.23 EOP for 40 Gb/s NRZ data and 100 GHz filter
Time delay ripple period (pm)
0 500 1000 1500 2000
Eye
-Ope
ning
Pen
alty
(dB
)
0.0
0.2
0.4
0.6
0.8
1.0 Best caseWorst case
125
Ripple period (pm)
0 50 100 150 200 250 300 350 400 450 500 550 600
Eye
-Ope
ning
Pen
alty
(dB
)
0.0
0.2
0.4
0.6
0.8
Best CaseWorst Case
C. 50 GHz filter and 10 Gb/s RZ signal
The effect of the time delay ripples is examined now for a signal of 10 Gb/s and with
return-to-zero (RZ) modulation format. In this simulation the RZ pulses are shaped as
raised cosine pulses. The filter is now 50 GHz rectangular and the ripple modulation
amplitude is again 15 ps as in the case of 10 Gb/s NRZ signal.
Figure 5.24 shows the calculated EOP for the best and worst case. The EOP patterns
are now very different compared with NRZ case and the maxima EOP for the best and
worst cases occur at very different ripple periods. Is important though to notice that for
the worst-case the maximum EOP occurs at ≈90pm ripple period as in the case of 10
Gb/s NRZ signal.
Figure 5.24 EOP for 10 Gb/s RZ data and 50 GHz filter
The “best-case” penalty peaks at ≈230 pm. In this region actually “best-case” penalty
is larger than the “worst-case” one.
126
5.6.3 Time delay ripple figure of merit
In order to understand better the resonant dependence of the signal degradation
penalties on time-delay ripple period, we introduce the following parameter that gives a
measure of the average time-delay ripple size, namely:
∫
∫+
−
+
−
∆=∆
∆−∆=∆
2/
2/
2/
2/
2
)(1
)(1
BW
BWaverage
average
BW
BWripple
dBW
where
dBW
λλττ
τλλττ
(5.3)
and BW is the data bandwidth. By substituting (5.2) into (5.3), we obtain:
0
,)sin()cos(2
)2sin()2cos(121
pBWx
xx
xxaoripple πθθτ =
−
+=∆ (5.4)
Similarly is defined the average dispersion ripple:
∫
∫+
−
+
−
∆=∆
∆−∆=∆
2/
2/
2/
2/
2
)(1
)(1
BW
BWaverage
average
BW
BWripple
dDBW
Dwhere
DdDBW
D
λλ
λλ
(5.5)
By using the definition equation of dispersion: λλτλ
ddD )()( = the calculation of the
above expression leads to:
0
,)sin()sin(2
)2sin()2cos(1212
pBWx
xx
xxa
Do
oripple πθθ
ρπ
=
+
−=∆ (5.6)
127
In Figure 5.25, the average group delay ripple is plotted for the worst (θ=0,π) and best
(θ=π/2) case as a function of the ratio of ripple period over the data bandwidth
(p0/BW), assuming α0=15ps. In Figure 5.26, we plot also the average dispersion ripple
size for the worst and best cases. Interestingly, the average dispersion shows for both
cases a monotonically decreasing behaviour and cannot describe the resonance
characteristics of the transmission degradation.
Comparing the obtained curves of average group delay with the simulated EOP results
for the NRZ case, there is correlation only with the worst-case predicted curve. For the
worst case, the average time-delay ripple size exhibits a resonant peak for
(pr/BW)≈0.75 BW. For NRZ signal spectrum at 10Gb/s, the –20dB bandwidth is about
BW-20=15GHz (≡120pm) that results in a resonant period pr≈90pm. At 40Gb/s, the –
20dB data bandwidth is about BW-20=60GHz (≡480pm) that results in a resonant period
pr≈360pm.
Figure 5.25 Average group time delay ripple
Ripple Period / Data Bandwidth
0 1 2 3 4
Nor
mal
ised
ave
rage
tim
e de
lay
rippl
e
0.00
0.25
0.50
0.75
1.00
Best CaseWorst Case
128
Figure 5.26 Average dispersion due to group delay ripple (normalised to unity and shown here only the detail in the range [0.0 – 0.1])
These resonance periods are in excellent agreement with the ones obtained from the
EOP results. On the other hand for the RZ case there is complete agreement in the
exhibited patterns of EOP for the best and worst cases, with the average group delay
curves.
In conclusion, the additional EOP due to in-band periodic time delay variation of
optical filters is showing distinct resonance characteristics with the ripple period. The
worst-case resonance ripple period (pr) scales with the -20dB data bandwidth (BW-20).
Actually pr ≈ 0.75 BW-20. The ripple amplitude (α0) required to achieve certain worst-
case maximum EOP, is inversely proportional to pr (α0 ∝ 1/pr). For periods away from
pr, larger ripple amplitudes can be tolerated. Finally, in specifying the optical filter
performance, average time-delay ripple over the bandwidth data and ripple period
should be considered. Average dispersion or dispersion ripple over the filter bandwidth
seems to have no direct correlation with the observed filter-induced signal degradation.
Ripple Period / Data Bandwidth
0 1 2 3 4
Nor
mal
ised
ave
rage
dis
pers
ion
0.0
0.1
Best CaseWorst Case
129
5.7 References
[5.1] C. Riziotis M. N. Zervas, “Performance Comparison of Bragg-Grating Based
Optical Add-Drop Multiplexers in WDM Transmission Systems,” IEE Proceedings,
Circuits, Devices and Systems.
[5.2] C. Riziotis, P. G. R. Smith, M. N. Zervas, “Performance characteristics of
interferometric Bragg grating based OADMs in WDM transmission systems,” paper
BThC2, in Technical Digest of OSA International Conference in Bragg Gratings,
Photosensitivity and Poling in Glass Waveguides, BGPP 2001, Stresa, Italy, July 4-6
2001.
[5.3] C. Riziotis, M. N. Zervas, “Characterization of optical Add/Drop Multiplexers in
high bit rate WDM Networks,” in Proceedings of the 2nd IEEE International
Symposium on Communication Systems, Networks and Digital Signal Processing,
(IEEE CSNDSP 2000), Bournemouth, UK, pp.102-107.
[5.4] C. Riziotis, M. N. Zervas, “Effect of in-band group delay ripple on WDM filter
performance,” Paper Th.M.1.3, in Proceedings of ECOC 2001, Amsterdam, Sep. 30 -
Oct. 4, 2001.
[5.5] A. F Elrefaie, J. K. Townsend, M. B. Romeiser, K. S. Sanmugan, “Computer
Simulation of Digital Lightwave Links,” IEEE J. of Selec. Areas in Communications,
vol. 6, no. 1, pp. 94-105, Jan. 1998.
[5.6] G. P. Agrawal, Fiber-Optic Communication Systems, 2nd Edition, Wiley, 1997.
[5.7] A. A. M. Saleh, J. M. Simmons: “Architectural principles of optical regional and
metropolitan access networks,” Journal of Lightwave Technology, vol. 17, no.12, pp.
2431-2448, 1999.
130
[5.8] N. N. Khrais, A. F. Elrefaie, R. E. Wagner, S. Ahmed, “Performance degradation
of multiwavelength optical networks due to laser and (de)multiplexer missalignement,”
IEEE Photon. Technol. Lett., vol. 7, no.1, pp. 1348-1350, 1995.
[5.9] H. A. Haus, Waves and Fields in Optoelectronics, Englewood Cliffs, Prentice–
Hall, 1984.
[5.10] M. Ibsen, P. Petropoulos, M. N. Zervas, R. Feced, “Dispersion-free fiber Bragg
gratings,” Optical Fiber Communication Conference, OFC’2001, March 2001,
Anaheim, paper MC1.
[5.11] G. Nykolak, B. J. Eggleton, G. Lenz, T. A. Strasser, “Dispersion penalty
measurements of narrow fiber Bragg gratings at 10Gb/s,” IEEE Photon. Technol. Lett.,
vol. 10, no. 9, pp. 1319-1321, Sep. 1998.
[5.12] K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of
nonideal chirped fiber grating characteristics on dispersion cancellation,” IEEE Photon.
Technol. Lett., vol. 10, no. 10, pp. 1476-1478, Oct. 1998.
131
CHAPTER 6
Fabrication and Characterization
of Photosensitive Thin Film Layers
6.1 Introduction
The fabrication of high quality thin film layers is the first fundamental step towards the
development of integrated optics devices. Of special interest is the technology of
development of photosensitive materials and thin layers, which will allow the
fabrication of directly UV written waveguide structures and phase Bragg grating based
devices.
The Chapter discusses issues and presents results around the area of fabrication and
characterization of photosensitive thin film layers and planar optical waveguides.
Firstly is presented a brief review of materials and methods for the fabrication of
photosensitive planar films. The Flame Hydrolysis Deposition (FHD) technique is
discussed in detail and a prototype FHD facility, constructed by the author within the
ORC labs is described. Initial characterization and performance evaluation of the
facility are also presented.
The last part of the Chapter is devoted to the characterization of Lead-Germanate glass
optical waveguides, fabricated by Pulsed Laser Deposition (PLD) for the first time in
the FORTH research centre (Greece). The exhibited photosensitivity at 244nm
Ultraviolet CW radiation and propagation loss of these waveguides are studied and
then are related to the PLD fabrication parameters.
132
6.2 Silica-on-Silicon technology
The fundamental requirement for the development of planar functional devices is an
initial planar film-waveguide, where transverse structures can be defined. This research
concentrates mainly on the development of planar devices in silicate-based glasses,
which form a low cost and widely used material system. Its compatibility with the
millions of kilometers of the installed silica optical fiber cables makes it a very
promising candidate for the development of low-cost compact devices for the next
generation of WDM technology. There are some very critical advantages of the current
technology of Silica on Silicon optical integrated circuits [6.1]:
• Silicon substrates are flat, smooth, and large in area - thus allowing very long active
devices or more complicated passive devices with increased bend radius and with a
cost two orders of magnitude less than that of InP.
• Silica is used extensively in the well-established integrated circuits industry and also
for the manufacturing of optical fibers. So the silica layers are compatible with
fibres because of their very similar refractive indices, thus virtually eliminating back
reflections.
• The thermal expansion coefficients of the fiber and the silica layers are matched so
they can be fused together. Also the thermal expansion coefficient of silicon is
greater than that of doped silica, causing the film to be compressively strained and
be more stable against cracking after annealing. However there is the drawback of
strain-induced birefringence.
• Silicon also has good thermal conductivity and can be used as a laser submount
because it acts as a heat sink, making possible hybrid laser-waveguide applications
and stable thermo-optic switches.
• Finally silicon has etch stop planes that make possible the chemical etching of
precision V-grooves that are used for passive alignment of optical fibre arrays to the
integrated optical circuit (IOC).
6.3 Device’s fabrication technology based on photosensitive films
133
In Silica based glasses the structures and channel waveguides are usually defined by a
combination of Photolithography and Reactive Ion Etching (RIE) [6.1]. This procedure
is extensively used in the semiconductor technology industry and gives very good
quality structures. Functional optical devices based on this fabrication method have
already been demonstrated [6.1]. Although very good fabricational tolerances can be
achieved by this method it requires many processing steps including the deposition of
cladding layers, which are deposited in several steps with equal number of
intermediate, anneals in order to cover completely the etched waveguides.
The long-term objective of the work presented here, is to demonstrate integrated optics
devices fabricated by ultraviolet light (UV) induced refractive index changes on
photosensitive silicate glass films. Fabrication of all UV written optical waveguides
and structures with Deep Ultraviolet light has already been proposed and demonstrated
by a point-to-point direct writing technique [6.2]. The potential of inscription of
photorefractive Bragg gratings on the same photosensitive layer would give the
advantage of fabrication of very well controllable and high performance optical
devices. The advantages of this alternative fabrication method would be the easier and
more versatile way to define complicated waveguide structures combined with the
unique characteristics of photorefractive gratings.
UV processing setup
The definition of UV induced structures on to photosensitive layers can be performed
with a relatively simple setup, which does not require clean room facilities. A detailed
description of the direct UV writing facility is presented in Chapter 7. Briefly the setup
consists of three main parts:
• A frequency doubled Ar-Ion Laser operated at 244 nm with output power of
500mW.
• Three-dimensional translation system, with interferometric positioning control.
• Computerized environment for the device layout design and direct transfer to the
translation stage controller for the reproduction of the design.
134
The continuous wave (CW), frequency doubled Ar-ion laser is a preferred solution for
UV writing because of its operational stability compared with other pulsed excimer
Laser sources operating at 248nm (KrF) or 193nm (ArF). Use of 244 CW radiation has
the great advantage of producing very low loss (below 0.2 dB/cm) directly written
channel waveguides as demonstrated at the Technical University of Denmark [6.2].
Silica based waveguides exhibit an inherent degree of photosensitivity since they are
commonly fabricated by doping the silica with Ge (mainly NTT labs) or P (mainly
Lucent Technologies-Bell Labs). In the past few years’ very active research has been
initiated for the study and enhancement of the photosensitivity of silica based fibers
and waveguides. It seems that the Ge-doped silica is a much more favorable solution
for our case because of the high degree of the photosensitivity at 244 nm radiation. In
contrast, P-doped silica is sufficiently photosensitive only under 193 nm pulsed
radiation [6.3] but still remains a good candidate as dopant, since it has very good
properties as host for rare earth ions and consequently for the construction of combined
active and passive devices. Recently we have demonstrated novel phosphate based
glasses –as potential hosts for rear earth doping- doped with Europium and with a high
degree of photosensitivity at 244 nm CW ultraviolet (UV) radiation [6.4]
6.4 Photosensitive films fabrication techniques
The main techniques for fabrication of low loss photosensitive materials and
waveguides are:
• Low Pressure Chemical Vapor Deposition (LPCVD) [6.1]
• Plasma Enhanced Chemical Vapor Deposition (PECVD) [6.2, 6.5- 6.7]
• Sputtering [6.8]
• Sol-Gel [6.9]
• Flame Hydrolysis Deposition (FHD) [6.10-6.12].
135
Fabrication of photosensitive glasses has also recently been demonstrated using Pulsed
Laser Deposition Technique (PLD) [6.13-6.15], and results are presented also in this
Chapter.
The first two of the aforementioned methods are widely used in silicon-based
technology whereas FHD process is borrowed from the Fiber Fabrication Industry.
FHD is preferable for experimental use and for custom-made layers since the
deposition rate is very high ~1 µm/min/wafer in contrast with CVD with 1 µm/hour.
When large number of wafers is used, the deposition times are similar for both CVD
and FHD, because the time for FHD is proportional to the number of wafers but FHD
is much faster for depositions on small numbers of wafers. The properties of the films
produced are similar with them made by CVD, although the temperatures involved in
CVD process are lower. Compared to FHD the cost for a PECVD facility is much
higher and it requires a very long learning period to produce very controllable films in
terms of the surface uniformity and the refractive index.
6.5 Flame Hydrolysis Deposition (FHD) technique
This section presents the basic operational principles of the FHD technique and
describes a prototype FHD facility constructed by the author in the ORC labs. Only the
initially constructed setup and preliminary characterization results of it are described
here, presenting work conducted by the author while actively involved in the area.
Since then, major changes and developments have been carried out towards the
construction of a more sophisticated and more functional facility. Dr R.B Williams and
S. Watts are now responsible for the further developments and operation of the facility.
Film fabrication through the FHD technique is a two-step process; firstly the doped
silica is produced in the environment of a hot flame, as low-density soot, and then is
deposited on to the Silicon substrate. The consolidation of the deposited soot produces
the glass film. The FHD technique is a modified process of the fiber fabrication
136
techniques: Vapour Axial Deposition (VAD) [6.16, 6.17] and Outside Vapour
Deposition (OVD) [6.18], in order to meet the planar waveguide fabrication needs.
FHD is well suited for the fabrication of very low loss waveguides (losses as low as
0.01dB/cm) [6.10, 6.19] and also for rare earth doping (such as Er/Yb and Nd) by using
either aerosol doping or solution doping [6.20]. The typical performance of the FHD
technique is very good and can produce films, which are compatible with the needs of
advanced device fabrication. Index uniformity can be controlled to better than 10-4.
Thickness variation and surface roughness better than 0.1 µm and 0.1 nm respectively
are achievable thanks to the post fabrication step of consolidation of the low-density
soot. During consolidation at a typical temperature of 1300o C there is a macroscopic
flow of the material which gives rise to self planarization of the layer.
Due to its very good performance FHD technique is widely used in Photonics industry
for the production of planar waveguides and PLC type of devices. Companies such as
NTT (Japan), BT (UK), KYMATA (UK), PIRI, FURUKAWA, use this technique for
the production of commercial high dense AWG devices.
6.5.1 FHD operational principles
A normal experimental setup is shown in Figure 6.1. It consists of the following parts:
• The halide precursors (SiCl4, GeCl4, POCl3, BCl3) with relatively high vapour
pressure.
• The bubblers where these halide materials are stored
• The mass flow controllers (MFC), which control, through the carrier gas flow rate,
the amount of the gaseous halides directed to the burner.
• The transmission pipelines system for the carrier gas and the halides.
• A burner where all the mixture of the halides and the carrier gasses are directed.
Fuel gas (methane or preferably hydrogen) is used for the production of the flame
where the chemical reaction and the production of the doped soot take place.
Additionally, with this setup it is possible to carry out rare earth doping of the
waveguides by using the aerosol doping technique [6.19]. What is needed is just an
137
atomizer for the atomization of the initial rare earth precursors into droplets, and an
additional MFC to control the amount of the carrier gas through the atomizer and
consequently the amount of the rare earth doped materials directed to the burner.
The target substrate is attached to a holder, which in turn has attached a heating system
in order to control the temperature of the wafer at a specified value during the
deposition process. To obtain uniform coverage of the wafer with doped soot it is
necessary to have an accurate transverse system, which can move the wafer or either
the wafer and burner. The usual arrangement for the wafer holder is a rotating turntable
with the wafers resting on it and the burner is mounted pointing downwards to the table
at an angle. NTT for example uses a similar setup for massive production of even 50
wafers at a time. In our setup however we are using a novel scheme where the burner
and the wafer are in vertical arrangement (as seen in Fig. 6.1).
Based on the above-described experimental setup we give a short description of the
basic operational principles:
I. Silica soot production
Silica is synthesized in the oxygen-hydrogen flame into which gaseous silicon
tetrachloride is injected with the carrier gas. The flame gases are usually oxygen and
hydrogen, while the carrier gas for the halides is usually oxygen or nitrogen. The two
main chemical reactions, which take place in the flame for the production of the doped
silica soot, are oxidation and hydrolysis.
Oxidation takes place in oxygen rich flames and at relatively high temperatures above
1200oC. So, oxidation is the dominant reaction along the central axis of the flame
where temperature can be as high as 2000oC [6.21].
Oxidation: SiCl4 (v) + O2 → SiO2 (v) + 2Cl2 (v)
GeCl4 (v) + O2 → GeO2 (v) + 2Cl2 (v)
The formed Cl2 is converted to HCl through reaction with water.
138
Hydrolysis can occur at room temperature, and is the dominant reaction for
temperatures below 1200oC. The production of silica and dopant oxides through
hydrolysis is described by the following chemical equations:
Hydrolysis: SiCl4 (v) + 2 H2O → SiO2 (s) + 4HCl(v)
2POCl3 (v) + 3 H2O → P2O5 (s) + 6HCl(v)
4BCl3 (v) + 6 H2O → 2B2O3 (s) + 12HCl(v)
The hydrolysis and oxidation processes can be transformed between each other through
changes of the temperature distribution across the flame.
II. Doped silica soot deposition on the substrate
The gas phase silica produced in the flame rapidly condenses into solid primary
particles –with dimensions of order of magnitude 0.1 µm in diameter- which then grow
by collision and coalescence to become aggregates of approximately 0.2 µm in
diameter [6.22]. The formation of particles from the oxide vapour is assumed to be
almost instantaneous for SiO2, P2O5, and B2O3 in contrast to GeO2, which is formed on
the substrate surface [6.23, 6.24]. This is due to the fact that the saturated vapour
pressure of GeO2, at high temperatures of about 1200 o - 1500o C, is several orders of
magnitude larger than the value for silica.
The produced soot in the flame -which can be doped by proper control of the amount of
the other halides injected into the flame- is directed towards the target wafer. The major
mechanism that controls the rate of deposition is the thermophoretic effect. This effect,
which arises because of differential gaseous momentum fluxes to the particle, induces a
drift velocity in small particles towards regions of lower temperature. Since the
deposition target is relatively cold with respect to the flame product gases, the particles
develop a large drift velocity in the thermal boundary layer near the target.
139
The thermophoretic velocity is approximated by
MFC
O2 / N2
Bypass
N2
O2
H2
Burner
Si Substrate
MFC N2
Atomizer
Aerosol Doping
Sub-system
MFC
SiCl4
MFC
GeCl4
MFC
POCl3
MFC
BBr3
Figure 6.1 FHD typical experimental setup (shown with optional aerosol delivery system)
140
∇⋅⋅−=
TTKu TT
rr ν (6.1)
where T is the local temperature , ν [m2/sec] is the kinematic viscosity of the flame
gases, and KT is the thermophoretic coefficient.
The temperature of the substrate has a profound effect on the rate of deposition of all
oxide materials, but also has an effect on the nature of the material deposited for some
of the dopants. It is well known [6.24] that the properties and the amount of the
deposited dopants (GeO2, B2O3) are highly dependent on the target -wafer temperature.
Since GeO2 is deposited directly on to the substrate from the vapour phase, it is
possible for either crystalline or amorphous structures to be deposited. The relative
concentration of the deposited germania and also the form of its deposited structure are
given in Figure 6.2. For substrate temperatures below 400oC is deposited with
crystalline (hexagonal) structure, where on the other hand, assumes a noncrystalline
form dissolved into SiO2 glass networks for temperatures above 500oC. The hexagonal
GeO2 concentration decreases with increasing substrate temperature and the dissolved
GeO2 concentration increases with increasing substrate temperature from 500o C to
800o C.
GeO2
Concentration
(Arbit. scale)
200 400 600 800
Crystalline form
Non-crystalline form
Substrate Temperature
Figure 6.2 Substrate temperature dependence of GeO2 concentration in SiO2 - GeO2
141
Figure 6.3 illustrates schematically possible particle structures for the SiO2-GeO2
system suggested by Edahiro et. al [6.23]. It is clear that a noncrystalline phase of SiO2
- GeO2 composite glass matrix is absolutely critical for a high quality low loss and
photosensitive optical glass. Firstly, because any crystallization causes excess optical
loss due to scattering and secondly because the photosensitivity of Ge doped silica
is based on the germanium related oxygen deficient centers (GODC’s) [6.25] which
are formed in the germanosilicate glass matrix. To form this glass matrix is necessary
to dissolve the GeO2 into the SiO2 glass matrix as happens in the case of the non-
crystalline deposition of the GeO2.
III. Soot consolidation
The next step of the fabrication process with the FHD technique is the suitable
processing of the soot in order to produce low loss and highly uniform glass layers. The
two post-processing steps of the soot are namely: dehydration and consolidation.
Dehydration is the process of removing the OH- -groups and is necessary because of
the strong absorption of these groups in the infrared band [6.26]. The hydroxyl groups
are produced because of the water, which is present in the flame. The dehydration of
the low-density soot with high porosity is based on the treatment with SOCl2 or Cl2 at
above 500o C with He or O2 as carrier gases:
Si-OH + SOCl2 → SO-Cl + SO2 + HCl
Figure 6.3 Particle structure models for SiO2 - GeO2 products
TS < 400 O C TS > 500 O C
SiO2 noncrystalline
SiO2 - GeO2 non-crystalline
GeO2 crystalline
142
After the dehydration treatment the OH- - free soot is heated continuously at a higher
temperature - depending on the doping of the soot- to fuse the glass particles until we
make a pore free transparent glass [6.27]. The relative densities of the soot bodies are
typically one-tenth that of the resulted solid glass. The consolidation process is very
important for obtaining highly transparent glass, which is free from scattering defects
such as bubbles caused by closed pores. Generally, sintering is performed in mixed
He/O2 atmosphere. Oxygen removes any remaining OH-groups and He - with its large
diffusivity - closes any existed bubbles in the final stages of the sintering process, when
the pores are almost closed.
6.5.2 FHD prototype facility
Our prototype FHD setup follows the scheme of Figure 6.1. One specific characteristic
of the setup is the vertical arrangement of the burner and the wafer holder. The target
substrate is attached to a holder, which is above the burner.
The central part of a FHD facility is the burner for the production of the soot. The type
and the design of the burner set the range of the fabrication parameters that can be
varied in the deposition process. There are two general categories of burners [6.21,
6.22, 6.28] used in the FHD technique.
The first is a burner where the halides and the flame gases are premixed, and thus
there is no much independent control on the flame characteristics or the injection of the
halides into the flame.
The second is the concentric multi-ring type burner, which produces diffusion
flames, and exhibits much better operational control and stability. A typical concentric
burner is formed by a number of independent rings as seen in Figure 6.4.
Generally the central ring delivers the halides together with the carrier gas while the
other rings are used for the flame gasses or for the shield gas (e.g. nitrogen) in order to
control the flame characteristics.
143
Figure 6.4 Six rings prototype concentric burner
Our prototype burner consists of six concentric rings as seen in Figure 6.4. Each tube
is connected to a separate input pipeline, which is connected to a mass flow controller,
or to a gas flow controller to determine the gas flow rates delivered to the tube. The
halide materials for the silica production and doping are fed through the tube #1,
together with the carrier gas (oxygen). Hydrogen is fed through tube #5, and oxygen
through tube #3. Nitrogen is used as shield gas, in this kind of burner in order to
controllably reduce the initial silica formation rate sufficiently and avoid this way
burner clogging when gaseous SiCl4 is delivered through the central tube in the
deposition process. In our case additional care has also been taken for the shielding
purposes. So, nitrogen is fed through tubes #2, #6 and #4. Nitrogen in tube #4 plays
the standard role, isolating the hydrogen from the oxygen and controls thus the flame
characteristics (e.g. high, temperature distribution). The second tube gives an additional
protection of the central halide’s line from the flame, and the sixth tube isolates the
inner gaseous flame from the surrounding space avoiding this way any potential
contamination.
# 2, 4, 6 N2
#1 SiCl4 GeCl4 & O2
#3 O2
#5 H2
144
The burner was made from commercially available 316-stainless steel tubes -a special
alloy which is chemical inert with the halides – based approximately on burner
designs by Bautista [6.22] and Lee [6.28]. The tubes are glued using epoxy on a
supporting rigid stainless steel base where there are drilled the gas inputs. The
performance of the burner was exceptionally good with very stable operation. Burner’s
tip clogging with soot has successfully avoided as expected from the burner design.
The only drawback was of the stainless steel burner is the difficulty to keep it clean,
due to erosion between depositions. Continuous purging with nitrogen of burners tubes
with nitrogen can minimize the problem. To overcome the erosion problem we also
attempted to construct an all glass multi-ring Burner by drilling tubes in a solid
cylindrical piece of silica glass using the Ultrasonic Mill Facility. But because of the
fragility of glass, the applied stress and the non-perfect alignment of the drills it was
very difficult to demonstrate finally a finished functional burner.
For this stainless steel multi-ring burner we identified proper operational conditions, in
terms mainly of flame stability and silica production rate, which for the case of
fabrication of planar thin films should be kept low enough in order to be able to
fabricate layers with an accuracy in thickness better than 1 micrometer. The flow rates
of all the gases for the stable operation of the burner as well as the geometrical
characteristics of the burner are concluded in table 6.1.
With these typical conditions the burner can produce a stable flame and the silica
production rate is about 1 µm / minute on a stationary wafer at a distance of 8cm above
the tip of the burner. This distance has again been chosen in order to avoid turbulent
effects and maintain thus a uniform deposition at a small area of the wafer when the
burner and the sample are relatively stationary.
The initial set of deposition experiments -performed by the author- for the
characterization and evaluation of the burner (Table 6.1) were performed on a
stationary wafer without moving relatively the burner. Furthermore, there was no
heating element on the wafer holder restricting thus the range of possible depositions.
145
Tube & Gas
Flow Rate
Tube Inner Diameter
(mm)
Tube Outer Diameter
(mm) Tube 1: O2 through the SiCl4 Bubbler (*) 60 sccm 2.3 3.2
Tube 2: N2 0.6 lpm 4.3 4.7
Tube 3: O2 1.2 lpm 5.2 6.3
Tube 4: N2 1.6 lpm 6.9 7.9
Tube 5: H2 1.2 lpm 8.5 9.5
Tube 6: N2 6.0 lpm 10.7 12.6
Table 6.1 Burner’s Geometrical characteristics and gas typical flow rates for stable operation (Values are given for bubbler temperature 21.5oC)
However, the obtained optimum flow rate values and separation between the burner
and wafer were estimated quite successfully and are in excellent agreement with a more
recent characterization by other co-workers [6.29], despite the fact of the use there of a
heating element for the wafer.
In our initial experiments we attempted also to consolidate a few samples with
deposited doped soot. Silica heavily doped with Ge was fabricated by using flow rates
ratio for GeCl4 and SiCl4 equal to 90/10. The consolidation process was performed in a
furnace with maximum achievable temperature 1200oC. The soot sample was resting in
a long silica cylindrical tube, with a constant flow of oxygen during the consolidation
procedure. The heating was gradual with a ramp of 25oC /min. The sample left at
1200oC for 4 hours, and cooled down at room temperature using a ramp gradient of –
25oC/hour. This procedure produced a clear glassy germanosilicate film.
The presented prototype FHD setup has been further improved by others members of
the research group, and better results have been demonstrated [6.29]. To date the
facility can produce layers doped with Ge, B, P, and with quite good uniformity
characteristics. The smoothness of the produced glass films can be controlled to less
than 100 nm variations over a distance of 100 µm across the wafer. The thickness
variation is less than 5% of the thickness of the deposited layer.
146
6.6 Film fabrication considerations related to UV written devices
properties The technology of the UV written devices bring to light many new issues closely
related to the planar thin films fabrication.
A. Birefringence
There are two causes of birefringence in UV written devices in silica-on-silicon. Firstly
the stress induced because of the different thermal expansion coefficients of silica and
silicon, is the more significant and is about B= nTE-nTM =2x10-4. Several methods have
been demonstrated for birefringence elimination. For our case, there are enough
methods that could be applied:
The use of quartz substrate [6.30] instead of silicon substrate, the use of half wave plate
of polyimide [6.31] the use of a thin layer of silicon nitride underneath the waveguide
[6.32] or depositing an amorphous silicon film on the top surface of the waveguide
[6.10]. The simplest seems to be the first one with demonstrated performance, of only
0.1 Angstrom polarization dependent splitting. Use of silica substrate modifies also the
recipe of the planar waveguide structure. For example in PIRI (NTT Labs) when quartz
is used as substrate only one buffer layer of 20 µm is used instead of two in silicon
substrates in order to isolate the core from the high refractive index substrate. Recently
another method has been proposed for the elimination of the stress-induced
birefringence. Is based on tailoring the thermal expansion coefficient of the
overcladding by appropriate doping [6.33]. Furthermore the fabrication of these special
overcladdings has been demonstrated by using FHD.
The other cause of birefringence, intrinsic with UV written waveguides, is due to
waveguide geometry, which is not azimuthally symmetric because of the different
refractive index profiles in vertical and horizontal directions (Figure 6.5). To overcome
this problem we need to have index matched layers which means that ideally the core
should be photosensitive (Ge doped) but with the same refractive index layers as
surrounding claddings. That could be achieved by codoping the core with Boron, which
147
Silicon
Air
SiO2
Ge / SiO2
SiO2
(∆n)h
(∆n)v
UV
lowers the refractive index. If the core index is matched to cladding index, then the UV
induced channel will exhibit identical refractive index contrast in the horizontal and
vertical directions: vh nn ∆=∆ .
Figure 6.5 Origin of birefringence in a waveguide with non-matched layers
B. Fibre - Waveguide Coupling Loss
The coupling loss between a fibre and a channel waveguide is determined
predominantly by the degree of their mode matching. Assuming Gaussian mode
profiles this loss is given by the expression [6.34]:
( ) ( )na a b
a b a bspoth y
h y
= ⋅⋅ ⋅ ⋅
+ ⋅ +
104 2
2 2 2 2log [dB] (6.2)
where ah ,ay are the FWHM mode widths of the waveguide intensity distribution in the
horizontal and vertical direction and b the fiber mode width respectively. It is
reasonable to assume that optimum matching to the fiber mode happens when the
horizontal and vertical widths are equal. For ah=ay the value of the function above is
minimized for ah=ay=b. To obtain equal horizontal and vertical widths index matched
layers sould be employed in the fabrication of the planar structure as described above.
148
C. Cladding layers
Finally another issue that should be taken into account is the buffer and cladding layer
thickness. An adequate thickness is required for both layers in order to isolate the
guided mode from the silicon wafer and air and reduce the transverse elongated
asymmetricity of the mode profile. FHD layers thicker than 15 µm can be easily
grown and they offer sufficient isolation of the guided mode from both silicon and air
layers.
It has been realised that backreflection of the UV light from the silicon interface can
create severe problems while fabricating fine structures like gratings. These
backreflections can reduce the contrast of the inscripted grating or even erase
completely the grating structure. One potential solution that should be taken into
account in to the design process of photosensitive multipe-layer structures is the
fabrication of an adequate thick and absorbant buffer layer which could eliminate the
backreflected light from the silicon substrate.
The total thickness of the silica and the doped silica glass determines also the required
time time for the hydrogen loading photosensitization treatments. A detailed discussion
on this procedure is presented in Chapter 7. Experiments conducted and presented in
Chapter 7, suggests also that 2-layer structures, in contrast with 3-layer structures
exhibit much lower damage threshold for the same UV writing power. This fact
suggests additionally the need for thick overcladding layers.
6.7 Characterization of photosensitive Lead Germanate
149
optical waveguides
This part of the Chapter discusses the characterization of photosensitive lead germanate
glass waveguides [6.14, 6.15]. These glasses were fabricated for the first time at
FORTH Centre (Crete, Greece) by using the Pulsed Laser Deposition technique. This
research was collaborative in nature. The glasses were characterised in the ORC and
important results were found regarding their propagation loss and photosensitivity
characteristics. These characteristics were related to the PLD fabrication parameters.
Pulsed laser deposition (PLD) is a comparatively fast, easy, and flexible technique for
growing thin films of a wide range of materials [6.13]. Amorphous, polycrystalline, and
single crystal layers are routinely grown, depending on experimental parameters that
include target composition, substrate temperature, target-substrate distance, and the
presence of an ambient gas, often oxygen, at moderately low partial pressures. Glasses,
however, have proved more difficult to grow using PLD. Several early attempts to
grow both silicate and phosphate glasses resulted in films which were opaque and
diffuse in character, and under scanning microscopic examination, revealed their
structure to be composed of ~few µm sized particles only: no smooth, continuous and
transparent films could be grown. The underlying reasons for this are likely due to the
extremely non-equilibrium nature of PLD, when compared to other existing methods
for glass fabrication. Additionally, the choice of ablation laser wavelength has a
distinct role to play: it has been found that phosphate glasses do not grow at all well
using 248 nm (KrF laser), whereas 193 nm (ArF) produces very smooth, transparent
films.
6.7.1 Growth of Lead Germanate glasses
I. Target Composition
The target glass composition in mole% is 55GeO2 - 20PbO- 10BaO- 10ZnO - 5K2O,
with some glasses having a partial substitution of Al3+ for Zn2+. The bulk glasses were
prepared from anhydrous oxide powders for Ge, Al, Zn, Pb, and anhydrous carbonate
powders for Ba, and K. All chemicals were of common analytical grade except for
GeO2, which was of electronic grade (99.999% purity, Aldrich Chemicals). Glass
150
batches in quantities of 150-200g of powder were mixed for at least half an hour, in a
clean glass container, mounted on a rotating lathe. Batches were then melted in a
platinum crucible, placed in an electrically heated furnace, containing an air
atmosphere, at temperatures between 1000o C, and 1250o C, depending on the glass.
The melts were kept well stirred, with a silica rod to achieve homogeneous mixing, and
later refined to remove bubbles. The refined glass-melts were removed from the
furnace at 1150o C, and cast into a prewarmed stainless steel mould, before being
annealed in a muffle furnace at ~500o C.
II. Deposition parameters
Films were grown by PLD using bulk undoped, and 1wt% Nd:doped lead germanate
glass targets, in a background oxygen gas ambient atmosphere. The growth was
performed using a typical PLD system, which includes a vacuum chamber capable of
maintaining a base pressure of ~10-6 mbar, and an excimer laser operating at either 248
nm (KrF), or 193 nm (ArF). Background oxygen was admitted into the chamber, once
the working pressure of ~10-5 mbar had been reached, and the turbo pump was then
switched off. The range of background (molecular) oxygen pressures investigated was
varied between 5.0 x 10-3 mbar and 1.0 x 10-1 mbar. These values span those typically
used when growing films in a background gas, and were chosen based on previous
experience. The excimer laser was a Lambda Physik LPX 200, operating with either
KrF or ArF gas mixtures. All other deposition parameters of interest are listed in Table
6.2.
Both target and substrate were asynchronously rotated, in order to achieve a degree of
radial uniformity. At the 8cm target-substrate distance used, the films produced showed
pronounced interference ring patterns, indicating that film thickness peaked at the
centre of the substrate. Film thicknesses were measured using profilometers (Tallystep,
Alphastep), across a step region introduced at the edge of each film. Although the
deposition times, and all other conditions were nominally identical for each growth run
(apart from varying oxygen pressures for example), the resultant film thicknesses
obtained varied between 1.8µm and 2.7µm. For equal deposition times, thicker films
151
were produced at lower ambient oxygen pressures, which is to be expected due to the
reduced plasma emission range at higher background pressure.
Parameter
KrF depositions
ArF depositions
Laser pulse energy
160 mJ
190 mJ
Spot size on target
2.5mm x 8.5 mm
2 mm x 6 mm
Laser energy density
0.75 J cm-2
1.6 J cm-2
Target-substrate distance
8 cm
8 cm
Pulse repetition rate
20Hz
8 Hz
Substrate temperature
Room temperature
Room temperature
Background pressure
3.5 x 10-5 mbar
3.5 x 10-5 mbar
Oxygen ambient pressure
5.0 x 10-3 - 1.0 x 10-1 mbar
1.5 x 10-2 - 5.0 x 10-2 mbar
Oxygen flow rate
Not recorded
0.6 - 3.1 sccm
Number of pulses
24000
21600- 63000
Film thickness produced
1.8 µm - 2.7 µm.
1.2µm - 12 µm.
Table 6.2 PLD deposition parameters for Germanosilicate glasses
The substrates used were cleaned microscope slides and fused silica discs. The larger
microscope slides (76 mm x 25 mm) enabled a study of the optical properties as a
function of radial distance to be carried out. PLD typically produces films with
stoichiometry that varies by only a small degree over ~ mm dimensions, but over larger
~cm distances variations in absorption, quality, or in the case of the films here, defect
concentration, can be readily observed. At critical values of oxygen pressure, films
were grown that showed a brown-clear-yellow colour trend on a single substrate.
152
Although growth on substrates held at temperatures greater than room temperature is
routinely performed for crystalline film growth, no temperature other than room
temperature was used here. For multicomponent targets, (such as the glass here),
stoichiometry variations between target and film can be exacerbated due to deposition
at elevated temperatures.
6.7.2 Properties and loss characterization of the films
The films obtained show distinct colour variations, depending on the ambient oxygen
pressure used during growth. For low oxygen pressures, (~10-3 mbar), the films were
brown in colour. At higher pressures, (~10-2 mbar), uncoloured films were produced,
while for the highest pressures, (~10-1 mbar), pale yellow to deeper yellow films were
grown. All films showed good adhesion to the substrates, apart from those grown at the
very highest oxygen pressure, which were opaque and flakey in character. Figure 6.6(a)
shows spectrophotometer traces of a set of films grown using 248 nm excimer laser
deposition, within the oxygen pressure range of 1.5 x 10-2 mbar to 4 x 10-2 mbar. These
films varied in colour from clear, to pale yellow. The short wavelength absorption edge
is seen to shift to progressively higher wavelengths as the oxygen pressure increases.
Figure 6.6(b) shows the value of absorption coefficient, evaluated at a wavelength of
400 nm, as a function of oxygen pressure. This value of wavelength was chosen as it
falls conveniently between the absorption edge, and region of high transparency. The
data points in figure 6.6(b) have been obtained by normalising the spectrophotometer
traces to the film thickness, at film centre. Figure 6.7(a) and 6.7(b) show similar results
for the 193 nm excimer laser grown films. While the trend is similar, the transmission
losses of the 193 nm grown films are systematically lower than those grown using 248
nm excimer deposition.
There is a systematic difference in material appearance, as evidenced through atomic
force microscopy (AFM) surface topographic scans, which depends on the excimer
laser wavelength used for the PLD growth. Using 248 nm excimer deposition, films
which were composed of macroscopic sized particles (few µm to tens of µm) only
could be grown.
153
Figure 6.6 a) Spectrophotometer traces of PLD films grown using 248 nm excimer laser deposition. The oscillatory behaviour is due to interference within the thin glass layer.
Figure 6.6 b) Absorption coefficient, at a wavelength of 400 nm, derived from the traces in figure 6.6(a), plotted versus oxygen partial pressure used during film growth. The data has been corrected for the film thickness.
Wavelength (nm)300 350 400 450 500 550 600
Tra
nsm
issi
on
0
1
2.0x10-2
4.0x10-23.0x10-2 2.5x10-2
1.0x10-2 O2 partial pressure (mbar)
Oxygen partial pressure (x10-2 mbar)
0 1 2 3 4 5
Abso
rptio
n co
effic
ient
(x 1
03 cm
-1)
0
50
100
150
200
250
154
Figure 6.7 a) Spectrophotometer traces of PLD films grown using 193 nm excimer laser deposition.
Figure 6.7 b) Absorption coefficient at a wavelength of 400 nm, derived from the traces in figure 6.7(a), plotted versus oxygen partial pressure used during film growth.
Wavelength (nm)250 300 350 400 450 500 550 600
Tran
smis
sion
0
1
5.0x10-2 3.5x10-2 3.0x10-2 2.5x10-2 1.5x10-2
O2 partial pressure (mbar)
Oxygen partial pressure ( x10-2 mbar)
1 2 3 4 5 6
Abs
orpt
ion
coef
ficie
nt (x
103 c
m-1
)
0
20
40
60
80
100
@ 400nm
155
The films were effectively opaque due to the high level of internal scattering, and
waveguide modes could not be observed. Using 193 nm excimer laser deposition
however, produced transparent smooth films, with drastically improved optical
properties.
Figures 6.8(a) and 6.8(b) show AFM scans for 5 µm x 5µm areas of films grown using
193 nm and 248 nm excimer laser deposition respectively. It is clear that while figure
6.8(a) shows a fairly uniform, continuous surface, with only a few isolated particulates,
figure 6.8(b) exhibits a much more discontinuous surface, composed almost entirely of
an assembly of particles. A further count of particulates was performed for the films
grown using 193 nm excimer depositions only. An area of 100µm by 100µm was
scanned, using image thresholding and commercial image processing software, to build
up a histogram of particulate size distribution. The results reveal that the mean size lies
between 0.2 and 0.4 µm, with very few particles of sizes greater than 1µm present.
Clearly the presence of this sub-micron sized debris is counterproductive, and can only
contribute to scattering loss within the waveguide.
Figure 6.8 a) AFM scan of the film surface for a 193 nm excimer laser PLD grown film. Note the apparent smooth surface, with micron sized individual particulates present. b) AFM scan of the film surface for a 248 nm excimer laser PLD grown film. The scan here shows that the surface is composed of densely packed sub-micron sized glass particles.
156
Waveguide loss characterization
Waveguide loss measurements were performed on the films produced. All guides were
multimode as the index difference between film and substrate is large (~0.3), and the
guides are ~2 µm thick. Losses were measured by both the sliding prism [6.35] and
imaged streak technique [6.36]. Using this second method, a rutile right-angle prism
was used to couple He-Ne laser light into the waveguide. The streak of light was
imaged by a lens on the surface of a detector. Measurements of the scattered power
were made at various distances along the waveguide, as shown in Figure 6.9. Figure
6.10 shows the final loss results for 5 such films, grown using 193 nm excimer laser
deposition, under different partial pressures of oxygen. The losses measured vary
between 4 dB/cm and 7 dB/cm. These are rather high values, but optimisation of the
fabrication procedure can reduce drastically these figures. Annealing has been carried
out on samples of the films, but this has the adverse affect of reducing, or even
eliminating, the exhibited photosensitivity.
Figure 6.9 Waveguide loss measurement results obtained using the imaged streak technique. The fit is a least squares best-fit curve. Inferred losses for this film, which was grown at an oxygen partial pressure of 3.5 x 10-2 mbar, are 4.5 dB/cm.
Films were also grown from ~1wt% Nd doped glass, using 248 nm excimer laser
deposition. For these films, the substrate rotation axis was offset by ~ 1.5 cm in the
Distance (mm)0 2 4 6 8
Scat
tere
d lig
ht in
tens
ity (A
.U.)
1
10
157
lateral direction, with respect to the target rotation axis, as shown in Figure 6.11,
thereby producing films with a more uniform central region. The losses for these films
should therefore be reduced with respect to the former radially uniform films. Losses
were measured as between 2.1dB cm-1 and 3.4 dB cm-1, using the two-prism technique.
Figure 6.10 Waveguide loss results for films grown using 193nm excimer laser deposition, as a function of the oxygen partial pressure during growth. Higher pressure leads to lower losses within the pressure region investigated.
Figure 6.11 Off-axis deposition arrangement used to achieve uniform thickness in the central film region.
~ 1.5 cm
Substrate
Target
Incident excimer laser radiation
Oxygen partial pressure (mbar)
0.020 0.024 0.028 0.032 0.036
Loss
(dB/
cm)
4
5
6
7
8
158
Is expected that employment of the same offset technique in fabrication of glasses by
using the 193 nm laser radiation will further and drastically improve the uniformity and
the loss characteristics of the grown films.
It is well known that levels of photosensitivity in germania based glasses depend
critically on bond structure with respect to the germanium-oxygen co-ordination
behaviour. Light, particularly within the defect absorption bands centred around the
UV spectral region, can have a pronounced affect on the local refractive index, and
hence the intense recent interest in fibre grating devices. We observe the same general
behaviour in these lead germanate glasses, where the oxygen content, varied during the
PLD growth process, is having a similar effect on the material photosensitivity.
Competition clearly exists between the germanium and lead atoms, for the available
oxygen incorporated within the growing film. Although the comparison may be
qualitative only, lead and germanium oxides, present as powder samples, show similar
colour variation as a function of their oxidation state. Lead for example can be black
(Pb2O), orange-yellow (Pb2O3), or yellow (PbO). Germanium oxide powders may be
black (GeO) or white (GeO2). At this stage, however, it is not possible to further define
the exact role of the material stoichiometry, without extended spectroscopic and
material analysis.
6.7.3 Photosensitivity of Lead Germanate films
This section, discuss the photosensitive properties of the grown lead germanate films.
The photosensitivity was characterized with the 244nm continuous wave (CW)
radiation from a Frequency doubled Ar-Ion Laser. The magnitude of the UV induced
refractive index change ∆n was derived from measurements of the diffraction
efficiency of the inscripted Bragg gratings. These test gratings were written with a
fused silica phase mask with a periods of 1077 nm (QPS Technology Inc.) which was
optimised for use at 244 with a suppressed zero order diffraction order, leading to only
0.8% residual.
The value of the UV induced ∆n can be estimated from the measured value of
diffraction efficiency through the well-known diffraction grating expression [6.37]:
159
⋅⋅⋅∆
=θλ
πηcos
tanh2 dn (6.3)
where η is the diffraction efficiency, d is the height of the grating, and λ is the
wavelength of the diffracted light. If the fabrication conditions allow the grating to
inscripted across the full thickness of the photosensitive film, then d corresponds also
to this film thickness. But if the absorption depth of the film at the writing wavelength
is appreciably smaller than the actual film thickness, then a corrected effective
thickness deff should be used in equation 6.3, since only this reduced thickness
contributes to the diffraction effects.
By growing a series of thin films on silica substrates with different thickness and
estimating afterwards the UV transmission spectra with a spectrophotometer, the
relation of lead germanate film’s transmission versus thickness was established. The
1/e absorption depth at 244 nm wavelength estimated to be 75 nm which corresponds to
an absorption constant of 133 µm-1. We set thus deff = 75nm. Figure 6.12 shows
schematically the grating writing technique adopted here. The phase mask was in close
proximity to the glass film, spaced off by 100 µm thick glass coverslips.
Figure 6.12 Schematic of the grating recording setup.
244 nm UV radiation
100 µm Separation
Phase maskPhotosensitive film on substrate
160
Under those recording conditions, the light intensity pattern has a fundamental period
in the near field (Fresnel diffraction regime) that is half that of the phase mask. For
incident laser power 60 mW at power densities of 0.5 W/cm2, the diffraction efficiency
saturated after 120 seconds. A standard writing time of 4 min was therefore established
for all the samples. Figure 6.13(a) shows the calculated values of induced index change
∆n as a function of the oxygen pressure during film growth. It is well known that the
Germanium oxygen deficient centers (GODC) are responsible for the photosensitivity
in germanosilicate materials [6.25], so the oxygen content and coordination within the
films induced by variable oxygen pressure during growth has a clear effect on the
resultant photosensitivity.
Figure 6.13 a) Plot of the absolute values of the refractive index changes as a function of the oxygen pressure during growth. b) Replot of the calculated values with the sign taken into account
Figure 6.13 shows the estimated ∆n values obtained by the diffraction grating formula
in Eq. 6.3. A sharp minimum on the value of ∆n is observed for an oxygen pressure of
4x10-2 mbars. This effect could be interpreted –as shown later- in terms of competitive
positive and negative index changes. It should be stressed out at this point that
diffraction efficiency measurements are sensitive not to the sign but only to the
magnitude of the refractive index change. To determine the actual sign of the index
change, ellipsometer measurements were performed on films grown at oxygen
pressures 3x10-2 mbars and 6x10-2 mbars. Regions of 5mm x 5mm were exposed to an
Oxygen pressure (x10-2 mbar)
1 2 3 4 5 6 7
Indu
ced ∆
n ch
ange
(x10
-3)
0
2
4
6
8
10
Oxygen pressure (x10-2 mbar)
1 2 3 4 5 6 7
Indu
ced ∆
n ch
ange
(x10
-3)
-10
-8
-6
-4
-2
0
2
4
6
8
161
expanded 244 nm laser beam for period as long as 1 hour to ensure saturated exposure.
Using this additional information the graph 6.13(a) was reploted as seen in graph
6.13(b).
In conclusion, very high photoinduced refractive index changes, of the order of ~10-2
were observed in those lead germanate glasses at 244 nm CW illumination. The index
changes can be either positive or negative depending on the oxygen partial pressure
during growth. Is important also that these index changes were observed without any
additional photosensitization procedure such as hydrogen loading, which is a common
treatment in germanosilicate glasses.
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166
CHAPTER 7
Direct UV-Writing System and Applications
7.1 Introduction
Wavelength selective components such as wavelength Multiplexers/Demultiplexers,
interleavers and Add/Drop filters are of great importance for the future DWDM optical
communication systems. A very promising class of those components is the Bragg
grating based devices. To date almost exclusively these devices have been
demonstrated in optical fibre form –based on photorefractive phase gratings-, due to
their simplicity and compatibility with the installed optical fibre base. As the WDM
channel spacing is decreased –targeting now the 25GHz- and the number of channels is
consequently increased, the need for denser devices with a higher channel count is
absolutely critical. The integration of such devices into a single planar structure seems
a very attractive solution, which is much more environmentally stable than the fibre
based components. With demonstrated UV induced refractive index changes on Ge-
doped silica layers of the order of 10-2 the direct definition of channel waveguides is
also possible. The UV induced definition of waveguides and gratings on a single
substrate offers a very flexible and powerful fabrication technique for the utilization of
Bragg gratings properties into planar integrated devices.
The first demonstration of a photorefractive channel waveguide in Ge-doped silica-on
silicon substrate reported by Mizrahi et. al. [7.1] and was fabricated by 248 nm UV
exposure through a chromium mask. Using a similar technique, Maxwell and Ainslie
fabricated a directional coupler in hydrogen loaded FHD films, by exposure to 262 nm
167
via a metal mask [7.2]. The photosensitive film was a Ge-B co-doped layer index
matched to the cladding layers. The exhibited UV induced refractive index change was
7.5x10-3. The breakthrough in direct UV written waveguides came from the Technical
University of Denmark, where Svalgaard demonstrated a direct point-to-point writing
technique by precision translation of the substrate under a focused spot from a 244 nm
CW frequency doubled argon ion laser [7.3]. Waveguides fabricated with this
technique by using a spot of ~5µm and writing fluences exceeding 3kJ/cm2 have
exhibited very low propagation losses around ~0.2 dB/cm [7.3, 7.4]. This value has
recently further reduced by using index matched three layer film with germania-boron
co-doped core fabricated by PECVD [7.5]. Due to index matching of core and cladding
refractive indices, the waveguide’s mode profile is circularly symmetric –as we have
discussed in Chapter 6 (6.6)- reducing in this way the losses due to waveguide and
fiber mode mismatch. The total insertion loss for a waveguide written in an index-
matched structure can be as low as 0.14 dB for a 3 cm waveguide. This result indicates
that not only the coupling loss but also the propagation loss can be reduced by making
use of those custom structures. All these promising results suggest a great potential for
the future applications of the direct UV writing technology.
This chapter describes the direct UV writing facility implemented in our lab. The fully
functional state of this lab is the result of a group effort of many co-workers, initiated
in 1997. Major issues around the control of the UV writing optics have recently been
considered and proposed and implemented solutions are discussed here. Performed UV
writing experiments have confirmed and justified the full control of the writing UV
spot over the processed materials.
The work presented here, deals also with a major problem in the UV processing of
photosensitive germanosilicate glasses. Hydrogen or deuterium loading of those glasses
–in order to enhance their originally inadequate photosensitivity- raises fabrication
problems due to rapid outdiffusion of the gas with associated continuous
photosensitivity reduction during UV writing. A new efficient method [7.6] -based on
rapid heat treatment of the silica samples prior to UV writing- is proposed here in order
to ‘lock’ and stabilize the enhanced photosensitivity. Successful initial results suggest
168
that this method could enable the UV writing in deuterium-photosensitized materials
under stable conditions, allowing thus the fabrication of long and complex devices,
which require long processing times.
7.2 Direct UV writing system
A schematic representation of the direct UV writing system is shown in Figure 7.1. The
Ultraviolet source of the setup is a Coherent Sabre FredTM intracavity frequency
doubled Argon Ion Laser, with a specified CW power output of 500 mW at 244 nm.
Figure 7.1 Schematic diagram of the direct UV-writing system
Lens translation stage Z-Axis
2 – Axis Translation Stage X-Y
Spherical focusing lens
Sample
500 mw FRED Ar-Ion Laser @244 nm
AOM
+1
0 -1
Iris 1
X6 Beam Expander & Spatial Filter
Iris 2
Beam
White Screen
Interferometer Mirrors
Vacuum ChuckZygo HeNe Laser
Interferometer
A
B C
D
169
As described in Figure 7.1, the output of the laser is passed through a Gooch&Housego
fused silica acousto-optic modulator (AOM), which can either be used to attenuate the
beam or achieve complete on-off modulation for Bragg grating writing. After the AOM
only the +1 order is used for the UV writing and all the other orders are blocked by the
Iris#1. Complete on/off modulation can only be achieved for the non zero orders. The
maximum efficiency of AOM at the +1 order is 74% and hence 370 mW is the
maximum available power at this order, which can be modulated 100%. The beam is
passed through a system of a x6 beam expander and spatial filter. The beam-expanding
telescope is assembled from a 150 mm and 25 mm focal length plano-convex lenses.
Integrated into the beam expander is a 16 µm pinhole located at the focus of the input
lens to provide spatial filtering of the beam. After the spatial filter the beam has
diameter of 3.1 mm. The power efficiency of the spatial filter and beam expander
system is about 66% and thus 250 mW is the maximum UV power that can be obtained
after the position of Iris #2
The second major part of the UV writing system consists of the system of translation
stages and their control system. The sample is rested on and moving by a two axis (X-
Y) Aerotech ABL800020 stacked air bearing translation stage with built in 40nm
resolution position encoders (Heidenhain glass grating type) and travel of 200 mm in
both axes. A perpendicular pair of large area mirrors is mounted to the stage as the
target mirrors for an external two axis Zygo laser interferometer system. This laser
interferometer system is intended for grating writing and has a resolution of 0.63 nm.
Also mounted on the horizontal stage is a is a zerodur vacuum chuck which is manually
leveled relative to the axes of motion of the stages by means of a 2-axis angle tilt stage.
Using a high precision dial gauge, the polished surface of the vacuum chuck can be set
to within 1 µm parallelism to the plane of motion.
The UV writing spot is produced by focusing the laser beam with a 35 mm spherical
lens. The lens is mounted on a motorized linear translation stage, which translates the
focused spot up and down with respect to the target substrate, so defining the spot size
incident on the photosensitive sample and consequently the delivered fluence and
waveguide width.
170
The translation stages are controlled thought a computerized graphical interface and
they can be fully programmed for inscription of almost any arbitrary directly written
structure. Using an extended RS-274 CNC G-code any trajectories can be programmed
and then executed by the according motion of the stages. 7.2.1 Writing spot focusing procedure
One issue of great importance in the direct UV writing procedure is the ability to
control the position of focused beam waist relatively to the photosensitive layer. Figure
7.2 shows schematically the focusing spot at the photosensitive layer for the case of a
3-layer and a 2-layer structure.
Figure 7.2 Focused writing spot coincident with the photosensitive core, for a 2-layer and a 3-layer structure
By controlling the writing-beam waist the delivered fluence and also the UV induced
waveguide characteristics –width, refractive index change- can be adjusted as required.
Our established method deals with the problem with a two-step procedure. Initially the
position of the focusing lens is adjusted in order to achieve coincidence of the focused
beam spot –with minimum waist diameter- with the photosensitive layer. Then, the lens
is moving upwards –away from the sample – in order to achieve the required defocused
beam spot size.
SiO 2 Ge/SiO 2 SiO 2 Silicon
U V U V
171
The location of the beam waist with respect to the photosensitive layer is determined
by inspecting the back-reflected light from the silica-air interface through the focusing
lens. If this interface is coincident with the beam waist, then the back reflected light is
re-collimated by the lens, and this collimated beam is separated using a beam splitter
from the main incident beam for inspection. In practice is has been proved difficult to
determine collimation of the back reflected beam and thus a modified approach is being
followed. As illustrated in Figure 7.1 the back reflected beam is allowed, after traveling
at the path (ABCD) to come to a focus on a white screen (point D) placed at a fixed
distance away from the sample.
Figure 7.3 Three different positions of the focusing lens relative to the substrate
∆ ∆ f
d1 d2
f
f
(a)
(b)
(c)
172
By using simple geometrical optic considerations is easy to prove that there is only one
arrangement between focusing lens and sample, which leads to a focus of the
backreflected light. Figure 7.3 describes the three possible arrangements. Case (a) is the
collimated case where the lens is positioned relatively to the sample in order to produce
a focused spot at the surface of it. In case (b) the distance between lens and sample is
less than the focal length f of the lens, and again no focus of the backreflected light is
produced. In case (c) the lens is positioned relatively to the sample, in a position greater
than f, and this arrangement can lead to a focused spot at the white screen, of the
backreflected light. When this position of the lens is found, then the lens is moved
towards the sample by the offset-correction ∆, and the focal plane will coincide with
the surface of the sample. Based on Figure 7.3(c) this offset-correction can be easily
calculated. From the lens equation we have:
21
111ddf
+∆+
= (7.1)
Using the geometrical relations:
211 , ddDfd +=+∆= (7.2)
and substituting them into Equation 7.1 a second order equation of ∆ is derived, with
parameters f, D, where D is the distance between sample surface and white screen:
0)2(22 22 =+∆−+∆ fDf (7.3)
The offset correction is then given by the solution of the above equation and is:
( )
2422 22 DDfffD +−−−
=∆ (7.4)
173
In our setup, the lens has a focal length of 35 mm and the projection white screen is at
distance 108 cm away for the sample. The offset has been calculated to be 0.528 mm.
Starting now from the focused on the sample spot, we can adjust the writing spot
diameter, by defocusing it. The defocusing takes always place by moving the lens away
from the sample so that the focal plane is outside of the sample, in order to reduce the
risk of surface damage. Based on the standard Gaussian beam optics relations, the
required displacement of the lens can be calculated in order to achieve the desired
writing spot diameter. A Gaussian beam which passes through a circular aperture of
radius wi and is then imaged by a lens of focal length f gives rise to an Airy diffraction
pattern in the focal plane with a 1/e2 radius given by the formula:
i
o wfw⋅⋅
=π
λ (7.5)
where λ is the free space wavelength. The Iris#2 in figure 7.1 allow to pass the central
lobe of the expanded beam with diameters ~3.1 mm. The estimated beam diameter at
the focal point for our setup is estimated to be 3.3 µm. Based now on the formula:
⋅⋅
+=2
222 1)(
oo w
zwzwπλ (7.6)
which gives the Gaussian beam radius w(z) at a distance z from the focal plane, the
distance that the lens should be moved away from the sample in order to achieve the
required writing spot diameter d(z)=a>2 wo is:
22 )(4 o
o dzdd
z −⋅⋅
=∆λ
π (7.7)
Around the focal plane, a displacement of 40 µm results in an increase of 1µm in the
spot diameter.
7.3 Photosensitivity of Germanium doped Silica glasses
Even after more than ten years of exploitation of the photosensitivity properties of
gearmanosilicate glasses for the fabrication of functional devices, there is not yet a
174
coherent theory, which explains the mechanism of UV induced refractive index
changes. There is a growing tendency to believe that there is not a single mechanism
responsible for the effect but a superposition of a number of processes, given the
complexity of structure of the doped glass matrix and also that the high energy of UV
photons is sufficient to trigger a wide range of reactions. The effect of photosensitivity
has appeared in many different types of glasses and for a range of writing laser
wavelengths. Here a brief review of the main mechanisms, which take place in
germanosilicate glasses, is presented.
The pure silica exhibits a tetrahedral structure glass matrix. When silica is co-doped
with a few mole % of Germanium (Ge) the resulted glass structure is very similar
because both Si and Ge have the same valence number of 4. However the properties of
the doped glass are altered from that of pure silica, the melting point is decreased the
absorption in UV is increased and consequently the refractive index is increased. The
exact relation between refractive index change due to a change to the absorption
coefficient ∆α(λ) is described by the Kramers-Kronig relations [7.7]:
∫∞
−∆
=∆0
22 )/'(1')'(
21)(
λλλλ
πλ dan (7.8)
where λ is the free space wavelength. Hence the insertion of a dopant which increases
the absorption in the UV as in the case of Ge-doped silica, results in a positive index
change. The doping introduces also distributed and point defects into the glass matrix.
It is generally accepted that these point defects and their reaction with UV photons are
responsible for the photosensitivity in germanosilicate glasses. The point defects in
germanosilicate glasses, which are associated with the incorporation of the Ge sites into
the matrix, can be classified into two groups. As shown in Figure 7.4 these defects are
classified into diamagnetic species, where all electron spins are paired, and
paramagnetic species, which have an unpaired electron. Diamagnetic defects are usually formed when insufficient oxygen atoms have been
present during the glass formation, leading thus to germanium related oxygen deficient
centres (GODC’s). The most common types of GODC are the Ge2+ defect, with the Ge
atom in the 2+ oxidation state rather than the 4+, and the neutral oxygen vacancy
175
(NOV) where a Si and a Ge atom are directly bonded. Paramagnetic defects can take
the form on non-bridging oxygen hole center (NBOHC), where an oxygen atom is only
bonded to one metallic atom; GeE’defects where a Germanium atom is only bonded to
three other atoms; and Ge(1) defects where a fully bound Ge atom traps a free electron.
The positive UV induced index change is mainly attributed to the GODC’s and is
suggested that UV radiation reacts with these defects, depleting some of them while
producing other paramagnetic defects like GeE’and Ge(1) [7.8].
The strength of the UV absorption in Germanosilicate glasses account-as estimated by
the Kramers-Kronig relation- to index changes of up to few times to 10-4. Demonstrated
Pure Silica Glass Matrix Diamagnetic Defects
Paramagnetic Defects
Ge2+ defect
Neutral oxygen vacancy (NOV)
Si
Ge
O
Unpaired electron
Ge(1) Electron trap center
Ge E’ Non-bridging oxygen hole centre (NBOHC)
Figure 7.4 Common point defects in Germanosilicate glass
176
index changes greater by an order of magnitude are explained by additional
mechanisms like stress and volume changes of the glass matrix [7.9].
The effect of photosensitivity in glasses is in general a complex effect, which appears
in different forms. In germanosilicate glasses there have been identified three different
types of photosensitivity [7.10]. Type I describes the monotonic increase of refractive
index with increasing UV exposure dose, type IIA with a time varying decrease in
index, and type II where a large index change is exhibited, resulting from physical
damage due to high intensity UV pulses. Often there is a combined effect of
mechanisms I and IIA, where an initially positive index change is gradually erased due
to IIA mechanism leading at some point during the UV exposure to a negative index
change. This competition of the two different processes, which leads to varying index
changes, is usually observed when a prolonged UV exposure takes place. This effect
has already been described and characterized in Chapter 2 for the case of Lead-
Germanate glasses. By controlling the UV exposure dose the required index change
and sign can be accordingly controlled.
7.4 Photosensitization of Germanium doped Silica thin films
The degree of photosensitivity depends on many factors, such as the conditions of the
UV irradiation -radiation wavelength, incident power, delivered fluence- and also the
glass material properties. As discussed in the previous section photosensitivity in
germanosilicate glasses relies mostly on the existence of GODC’s and thus is limited
by the number of those centers in that glass matrix. The concentration of these defects
depends on the GeO2 content and the processing conditions or the fabrication method
of a particular glass. Exhibited index changes are in the range of 10-5 - 10-4, and there is
a clear need for enhancement of photosensitivity.
There have been proposed different methods for photosensitization, like high
temperature treatment under reducing conditions [7.11, 7.12], or hydrogen indiffusion
177
prior to UV exposure [7.13]. Hydrogen loading is more effective and has been widely
established as the preferred method. The indiffusion of hydrogen into the glass sample
takes place into a cell where molecular hydrogen is pressurized in a few hundred bars
and under room temperature. Typically the treatment lasts for a few days up to several
weeks until the hydrogen concentration reach the required level. UV exposure in the
loaded sample causes the undiffused hydrogen to react with the glass matrix leading to
index changes of the order of 10-2 .The mechanism of the enhanced photosensitivity
due to hydrogen loading is not fully understood, but there is evidence of formation of
defect species after the thermally driven reactions of hydrogen with the glass matrix
[7.14]. Dissociated H2 reacts with oxygen atoms near to GeO2 sites, while no reaction
takes place near to SiO2 sites [7.14]. This preference to Ge sites is due to the fact that
the oxygen bonds there are weaker than in the normal SiO2 matrix. Heating originated
form the UV exposure causes this reaction to be triggered both photolytically and
thermally. The reaction results to the formation of Ge2+ defects, which as discussed
before are the main GODC species responsible for photosensitivity. So, effectively the
reaction of hydrogen leads to transformation of all the matrix Ge sites into the
photosensitive defects Ge2+ leading thus to photosensitivity enhancement by simply
increasing drastically the number of those defects. The magnitude of the increase of
those sites could be realized by taking into account that only 0.1 – 1% of the Ge atoms
are incorporated as GODC’s –with Ge2+ being by 1-2 orders of magnitude more
common than the NOV [7.15] -in the initial germanosilicate glass matrix.
Indiffusion dynamics The steady state diffusion of hydrogen or deuterium through silica is well characterized
by the diffusion equation with diffusivity given by the Arrhenius equation:
RTEo eDD /−⋅= (7.9)
where Do is a constant, independent of gas pressure and temperature, E is the activation
energy for the diffusion process, R=1.99 cal/J-mol is the gas constant and T is the
absolute temperature. This relation applies for a wide range of temperature from room
temperature to more than 1000oC and does not depend much on the type of silicate
178
glass. For hydrogen and deuterium diffusion the equation (7.9) takes the exact forms
respectively [7.16]:
12/)/4.10(4 sec1065.5
2
−−−= cmexD RTmoleKcalH ,
12/)/5.10(4 sec100.5
2
−−−= cmexD RTmoleKcalD
and is apparent that they exhibit very similar diffusion parameters.
For most effective hydrogen loading the process should be performed under low
temperatures since the solubility is proportional to exp(8.67kJ/mole/RT) and is higher
for lower temperatures. In the diffusion treatment we are interested for the final
equilibrium concentration of hydrogen that has been achieved in to the silica glass
matrixn. It has been estimated [7.17] that at room temperature this concentration is:
C=116 x (10-6 mole H2 –per- mole SiO2) / bar (7.10)
and is proportional to the applied pressure. Our home-made stainless steel
hydrogen/deuterium loading cell can stand a pressure of 100 bar, and thus the
achievable maximum concentration is 1.16 mole %. If we consider a thin film of silica
layer on top of a silicon substrate, the required time to reach the value of 95% of the
equilibrium concentration at the bottom of the glass layer is given (in seconds) [7.4] by:
τ ≈ (0.8 x d2 / D) (7.11)
where d, is the thickness of the film. The required time is estimated with the
assumption that the indiffusion stops at the silicon-silica interface.
Lets consider a realistic example of a three-layer planar waveguide structure on a
silicon substrate. The thickness of the under and upper claddings are 15 µm and the
core thickness 6µm. To sensitize the Ge doped core the total thickness of 36 µm of the
composite structure should be considered, since the indiffusion stops at the silicon
interface only. The estimated 95% equilibrium time for this case is about 6 days, and
has been taken into account in our experiments. The same results can also be applied
for the rate of outdiffusion from the silica glass film.
179
7.5 Photosensitivity locking technique
The outdiffusion of hydrogen or deuterium after removing the glass from the loading
cell is well understood problem in the fabrication of fibre Bragg grating. However due
to relatively very thick cladding of diameter 125µm, the outdiffusion rate is very slow
and does not create significant problems during the writing of short structures like
Bragg gratings. In contrast, in planar geometry the outdifussion time from the thin film
is much shorter leading to rapid degradation of photosensitivity. Also, fabrication of all
UV written integrated devices require long writing times, and so the rapid out-diffusion
of the gas during the UV exposure leads to degradation of the written waveguides.
Based on published experimental results [7.18] can be estimated that a 2% reduction in
the deuterium concentration leads to an additional 0.1 dB insertion loss and 0.25
polarisation dependent loss (PDL) when 20 mm waveguides where fabricated in index
matched Ge-B co-doped layers.
To eliminate the deuterium out-diffusion during the writing process, Svalgaard [7.18]
proposed a solution based on reducing the temperature to -35oC by using Peltier
elements. Using this approach the writing time was extended to 10 hours. However, to
avoid water condensation or frost formation this method requires the sample to be
enclosed in dry nitrogen purged atmosphere, adding considerably to the complexity of
the system and also restricting the geometries of the optical systems that can be used to
write Bragg gratings.
It has been demonstrated by Fokine et al [7.19] that rapid heating of hydrogen-loaded
fibre initiates a reduction reaction to form the germanium oxygen deficiency centers
(GODC) that are responsible for the UV photosensitivity. Atkins et al [7.20] used
exposure with a CO2 laser to demonstrate the same effect. Photosensitivity locking has
also been demonstrated by UV pre-exposure [7.21, 7.22, 7.23] in Germanium doped
fiber and planar thin films. However the required fluencies for UV pre-exposure still
make it impractical to process the entire area of a wafer. The method we propose and
180
demonstrate here is based on a rapid heat treatment using an electric resistance furnace.
This method is inherently compatible with the geometry of large area planar films.
Experiments
The initial experiments were performed on 2-layer Ge-doped Silica-on-Silicon samples
provided by G. Maxwell (British Telecommunications Laboratories). Four different
pieces from this wafer were used for a comparative study. All of them were deuterium
loaded for one week at 21oC under a pressure of 100 bar, yielding an estimated 1.2
mol% deuterium concentration. After removal of the samples from the deuterium
loading cell, they were immediately stored under dry ice (at ~-79oC) to preserve as
much deuterium as possible.
Rapid thermal processing of the samples was effected using an electric resistant furnace
which had been preheated to 1400oC. We operated the furnace with its door open, for
rapid insertion and extraction of wafer samples. Two different heat treatments were
applied, one for 10 seconds and the other for 20 seconds. After the treatment the wafers
were allowed to cool to room temperature in air and left in ambient conditions for 10
days before the UV writing experiments were carried out.
The other two samples were used for control purposes and were not heat-treated. One
sample was kept for a few hours under dry ice before UV writing. The final sample was
left for five hours in ambient air to allow all its deuterium to out-diffuse before its
photosensitivity was characterized.
Identical UV writing experiments were performed upon all the wafers. For all the
samples we used a reduced power of 100 mW since from our previous experiments we
have determined that non-overclad two-layer samples exhibit very low damage
thresholds - in contrast with overcladed three layer samples - and so higher writing
powers can result in the formation of ablated channels. The experiment consisted of the
fabrication of four sets of waveguides with twelve channels per set, such that each set
corresponded to a particular incident spot size (ranging from 3.3 µm to 10.0 µm).
Within each set the twelve channels were written in scan velocities ranging from 120
181
mm/min to 10 mm/min in 10 mm/min increments. All the writing parameters with the
estimated values of intensities and fluencies for all the channels are summarized into
the Table 1 below. The intensity of the writing laser writing spot is defined as the ratio
of the laser power and the writing spot area:
( )22/aP
SPIUV
⋅==π
(7.12)
where α is the 1/e2 writing spot size. The delivered UV fluence from the spot on the
photosensitive film, when the spot is moving relatively to the sample with scanning
speed V is:
V
aIF UV ⋅= (7.13)
Results
After performing the UV writing experiments the fabricated channels were
characterised by launching HeNe laser radiation at 633nm through a fiber, which was
butt-coupled to the polished end face of the sample under examination.
For the control sample, which had been left to outdiffuse its deuterium for a few hours,
no channel waveguides were detected at all. In contrast, for the deuterium loaded
sample -prevented from suffering out-diffusion by storage in dry ice- channel
waveguides were successfully detected. However, in this sample some of the exposures
resulted in ablated channels and not in waveguides. Whereas in the heat-treated
samples no surface damage tracks were detected at all, for any writing conditions. It is
Table 7.1 UV-Writing parameters Incident Laser CW Power (mW) @244 nm
100
Writing spot diameter (µm) 3.3 5.0 7.0 10.0
Intensity (KW/cm2) 1170 510 260 127
Writing speed (mm/min) 120 mm/min to 10 mm/min in 10 mm/min increments 1.9 1.3 0.9 0.6 Fluence (KJ/cm2) (minimum)
(maximum) 23.2 15.3 10.9 7.6
182
speculated that the damage in the glass may have resulted from the rapid out-diffusion
of deuterium under the intense heating of the writing spot for this freshly D2 loaded
sample (Figure 7.5) Finally, we found that for the full range of the writing fluencies
given in Table 1, waveguides were successfully fabricated in the two heat-treated
samples (10 and 20 seconds respectively).
For the fabricated waveguides corresponding to a writing spot size of 3.3 µm, and
writing speed 120 mm/min, the UV induced refractive index change was estimated for
the three different samples, by measuring the numerical aperture of the waveguides
[7.24]. For the freshly loaded sample, the sample heat-treated for 10 seconds and the
sample heat treated for 20 seconds the ∆n are respectively: 6.5x10-3, 2.4x10-3, 3.2x10-3.
Although these values are only indicative they suggest some reduction of the ∆n of the
heat-treated samples compared to the only D2 loaded sample.
An identical set of experiments was performed also in three-layer silica on silicon
samples. These samples were manufactured by KYMATA and provided within the
frame of a recently established collaboration. The buffer layer and overcladding of
those samples is silica of thickness 15 µm, while the core is Ge-doped silica of
thickness 5 µm. The rapid heat treatment method applied to those samples and the
photosensitivity was again locked successfully for 10 days. The exhibited refractive
index change was similar with the index change demonstrated in the 2-layer samples,
for the same writing conditions. UV written waveguides was successfully fabricated for
all the processed samples and for the full range of writing fluencies.
It should be stressed here, that in contrast to the 2-layer samples case, none of the
channels written into the freshly Deuterium loaded 3-layer sample –without heat
treatment- was ablated. This fact supports the scenario that the damage in the glass –in
the 2-layer sample- may have resulted from the rapid out-diffusion of deuterium under
the intense heating of the writing spot, taking into account that the relatively thick
overcladding had reduced drastically the deuterium outdiffusion rate.
183
Figure 7.5 shows optical microscope pictures of the resulted channels in the 2-layer and
3-layer samples fabricated with identical writing conditions.
Figure 7.5 Optical microscope pictures of channels in a two and three layer structures. In the inset is shown the atomic force microscope (AFM) picture of the ablated channel created in the 2-layer waveguide.
In the 2-layer case is clear the existence of a damaged track, whereas in the 3-layer case
the channel is a guiding UV written waveguide. In the inset is shown also an Atomic
Force Microscope (AFM) picture of the ablated channel. The profile gives an estimate
of the shape of the ablated structure; although the exact shape could not be recovered
due to resolution limitation of the used scanning tip in the AFM setup.
7.6 Conclusions
A fully functional direct UV-writing facility has been constructed and demonstrated.
Also control procedures for the focused UV writing spot have been developed and
presented. A novel solution to overcome the problem of rapid outdiffusion from large
area thin films has been proposed with successfully demonstrated results in two and
three layer thin film waveguide structures. The extended photosensitivity lifetime will
allow the fabrication of complex all UV-written devices.
AFM picture
2-layer 3-layer
184
7.7 References
[7.1] V. Mizrahi, R. J. Lemaire, T. Erdogan, W. A. Reed, D. J. DiGiovanni, R. M.
Atkins, “Ultraviolet laser fabrication of ultrastrong optical fiber gratings and of
germania-doped channel waveguides,” Appl. Phys. Lett., vol. 63, pp. 1727-1729, 1993.
[7.2] G. D. Maxwell and B. J. Ainslie, “Demonstration of a directly written directional
coupler using UV-induced photosensitivity in a planar silica waveguide,” Electron.
Lett., vol. 31, pp. 95-96, 1995.
[7.3] M. Svalgaard, C. V Poulsen, A. Bjarklev, O. Poulsen, “Direct UV writing of
buried singlemode channel waveguides in Ge-doped silica films,” Electron. Lett., vol.
30, pp. 1401-1403, 1994.
[7.4] M. Svalgaard, Ultraviolet Light Induced Refractive Index Structures In
Germanosilica, Ph.D. Thesis, Microelectronic Center, Technical University of
Denmark, 1997.
[7.5] D. Zauner, K. Kulstad, J. Rathje, M. Svalgaard, “Directly UV-written silica-on-
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187
CHAPTER 8 Conclusions
8.1 Conclusions
In this thesis have been presented results of the research work undertaken in a broad
range of activities, towards the theoretical understanding, design, modeling and
implementation of novel, high performance devices for WDM optical communication
systems.
A mathematical model developed initially for the analysis of Bragg grating based
devices. Based on normal modes coupled mode theory it can model a wide variety of
coupled waveguide structures, and devices loaded with Bragg gratings. The validity of
the model has been verified through numerous analyses.
Based on this modeling tool, a number of Bragg grating based functional devices have
been analysed. The gained understanding allowed the further optimization and design
of novel high performance devices such as Optical Add/Drop Multiplexers (OADM).
Firstly the OADM based on a null coupler (with zero coupling) and an asymmetric
Bragg grating, was analysed in depth resulting to the development of an optimization
process of three steps, which namely are:
Optimisation of the coupler’s waveguides asymmetry, in order to minimize the
extinction ratio of residual modes.
Employment of a specially designed coupler taper shape, in order to suppress the
coupler crosstalk
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Optimisation of the Bragg gratings tilt in order to minimize the backreflection to
input ports, and optimization of grating transverse extent in order to reduce the
required grating tilt and reduce consequently the associated radiation losses.
An OADM designed accordingly to the proposed optimisation procedure can exhibit a
crosstalk level better than –40 dB, with all the backreflections suppressed at the same
level. The properties of the spectral response can furthermore be fully and
independently tailored by employing a properly apodised Bragg grating.
The class of full-coupler based interferometric OADMs has also been studied in detail.
A novel full-cycle coupler based OADM (FCC OADM) configuration is proposed for
the first time. This device exhibits fully optimised Add and Drop characteristics –at the
expense of a lower bandwidth utilization factor- in contrast to the traditional half-cycle
coupler (HCC) based configuration. The flat top-hat spectral response characteristics of
the proposed device overcome the problem of the uncontrollable insertion loss
associated with the employment of the HCC OADM in a WDM network. The device
can be implemented by symmetric inscription of a Bragg grating at the center of the
uniform coupling region of the FCC.
A general method has been proposed for the optimal implementation of the device. For
a given coupler structure, an optimised Bragg grating needs to be designed. The
proposed method calculates the geometrical characteristics of the grating, based on the
coupler characteristics, the required grating reflectivity and the employed grating
apodisation profile. Central point to this design method/algorithm is the relation
between grating penetration slope and grating reflectivity. We found and propose for
the first time in this thesis the existence of general engineering curves, which relate the
Bragg grating’s penetration slope to its reflectivity for specific apodisation profiles.
These engineering curves together with the design method are of paramount importance
for the optimised design of the FCC OADM.
The designed and analysed OADM filters were evaluated, compared and characterized.
A simulation tool has been developed to model a typical optical communication
system, and can incorporate many system parameters, like different modulation formats
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and line codes, pulse shaping through filters and Mach-Zehnder modulators, filter-
signal spectrum misalignments and cascades. The distortion effects were quantified
through the Eye-Opening Penalty (EOP) parameter.
It has been found through simulations at 40 Gbit/s that even slightly degraded filter
spectral characteristics, which are typical in HCC OADMs, induce excessive system
penalties of at least 0.15 dB, compared to the case of optimised employed filters. HCC
OADMs have been proven also very susceptible to cascading operations. Their
performance together with their associated insertion loss makes their use in high-speed
WDM networks questionable. On the other hand, alternative devices such as the non-
interferometric tilted Bragg grating based OADM or the FCC OADM exhibit superior
in-band characteristics and system performance.
The system implications of group delay ripples in the in-reflection spectrum of optical
filters has been also studied. The distortion effects and the EOP were estimated for 25
GHz and 100 GHz filters operating at 10 Gb/s and 40 Gb/s respectively. Both NRZ and
RZ modulation format were considered. The results suggest that the EOP peaks at time-
delay periods of ~75% of the data bandwidth. The relations between EOP and group-
delay ripple obtained through system simulations were predicted and confirmed by
using a simple analytical figure of merit: the average group delay ripple over the filter
bandwidth. In contrast we found no direct relation between average dispersion and
resonant signal distortion effects. In this thesis is proposed consequently that the
average time-delay and not the average dispersion should be the figure of merit when
specifying optical filter performance.
On the experimental part of the work, is presented a prototype Flame Hydrolysis
Deposition (FHD) setup. The constructed facility can successfully deposit high quality
doped silica for the fabrication of planar waveguides.
Photosensitive lead germanate thin film layers and optical waveguides, fabricated by
Pulsed Laser Deposition were characterized in detail. It has been found that 193nm
ablation laser wavelength gives much better quality films with lower propagation
losses. Based on preliminary results we suggest that losses can be further reduced to a
190
level less than 2 dB/cm. We found that lead germanate glasses exhibit very high degree
of photosensitivity at 244nm UV light. The measured UV induced refractive index
change was of the order of 10-2.
A direct UV writing facility has been also developed and presented and its functionality
has been confirmed through a number of experiments.
A major problem towards the development of all UV written devices is the degraded
photosensitivity of the layers due to rapid outdiffusion of the loaded
hydrogen/deuterium, which is critically necessary in order to enhance their intrinsic
low photosensitivity. A rapid heat treatment technique was proposed for the locking of
photosensitivity and preliminary demonstrated results were presented. By heating Ge-
doped silica-on-silicon samples at 1400oC for just a few seconds we found that the
photosensitive films retained their photosensitivity after left at room temperature for
more than 10 days. The exhibited UV induced refractive index changes for the heat-
treated samples was ~3x10-3, which is an adequate value for the fabrication of directly
UV written devices.
8.2 Proposed future work
The development of directly all-UV written devices requires firstly the photosensitive
base layer. For the accurate control and definition of the waveguides there is the need
of an accurate mapping of the material (e.g. germanolilica) response to UV light. The
UV induced refractive index change needs to be related to the writing power and
fluence. After the establishment of a constant supply of photosensitive layers a series of
experiments needs to be performed in order to establish this relation.
The rapid heat treatment for photosensitivity needs to be incorporated in to this
characterization process, so that the material response will be mapped after the ‘lock in’
of the Deuterium loading enhanced photosensitivity.
191
Also the photosensitivity locking technique needs to be refined, by finding the optimum
heating temperature and heating duration.
Recently we have started exploring alternative methods for Bragg grating writing, in
order to incorporate the waveguide and grating writing processes more efficiently.
Based on an interferometric setup we were able to create periodic grating patterns of
size 10 µm diameter and ~ 0.5µm period, by carefully overlapping two focused UV
spots. By using the high precision -sub nm- interferometric assisted positioning control
it should be possible to define the waveguide and the Bragg grating simultaneously, by
employing the already well-developed stepping writing technique. This new method
will allow the fabrication of advanced Bragg grating based devices where the grating
can be controllably and precisely positioned in the waveguide structure.
Finally, in a recent collaboration with Dr. H. Ebendorff-Heidepriem, and Dr. E. Taylor,
we have been demonstrated a high degree of photosensitivity in Europium doped
phosphate glasses. These novel glasses exhibit a negative dn/dT (refractive index
change over temperature change) and a suitable value of thermal expansion coefficient,
which makes them ideal candidates for athermal applications. Consequently these
glasses are a possible platform for the implementation of temperature insensitive Bragg
grating based filters, devices of paramount importance for WDM networks.
192
PUBLICATIONS I. Journal and Conference Publications
C. Riziotis M. N. Zervas, “Performance Comparison of Bragg-Grating Based Optical
Add-Drop Multiplexers in WDM Transmission Systems,” IEE Proceedings, Circuits,
Devices and Systems.
C. Riziotis, M. N. Zervas, “Effect of in-band group delay ripple on WDM filter
performance,” ECOC 2001, Paper Th.M.1.3, Amsterdam, Sep. 30 - Oct. 4, 2001.
C. Riziotis, P. G. R. Smith, M. N. Zervas, “Performance characteristics of
interferometric Bragg grating based OADMs in WDM transmission systems,” paper
BThC2, in Technical Digest of OSA International Conference in Bragg Gratings,
Photosensitivity and Poling in Glass Waveguides, BGPP 2001, Stresa, Italy, July 4-6
2001.
C. Riziotis, A. Fu, S. Watts, R. Williams, P. G. R. Smith, “Rapid heat treatment for
photosensitivity locking in deuterium-loaded planar optical waveguides,” paper
BThC31, in Technical Digest of OSA International Conference in Bragg Gratings,
Photosensitivity and Poling in Glass Waveguides, BGPP 2001, Stresa, Italy, July 4-6
2001.
C. Riziotis, P. G. R. Smith, M. N. Zervas, “High Performance Integrated Add-Drop
(De)Multiplexer” Participating poster in presentation of the PHOTON Project
(Physical-Layer High-Speed Optoelectronics for Tomorrow’s Optical Networks) in
PHOTONICS 2000 Forum, Manchester, July 2000.
193
C. Riziotis, M. N. Zervas, “Characterization of Optical Add Drop Multiplexers in High
Bit Rate WDM Networks,” in Proceedings of the 2nd IEEE International Symposium
on Communication Systems, Networks and Digital Signal Processing, ( IEEE CSNDSP
2000), Bournemouth, UK, pp.102-107.
C. Riziotis, M. N. Zervas, “Design considerations of optical Add-Drop filters based on
grating assisted mode conversion in null couplers,” IEEE/OSA Journal of Lightwave
Technology, vol. 19, no. 1, pp. 92-104, Jan. 2001.
C. Riziotis, M. N. Zervas, “Optimization of OADMs based on grating assisted mode
conversion in null couplers,” Paper TuD1.6 in Proc. 25th European Conference on
Optical Communication, ECOC ‘99 Nice, France, 1999.
S. Mailis, C. Riziotis, J. Wang, B. Taylor, A. Anderson, S. Barrington, H. N. Rutt, R.
W. Eason, C. Grivas, N. Vainos, “Growth and Characterization of pulsed laser
deposited lead germanate glass optical waveguides,” Optical Materials, vol. 12, no.1,
pp.27-33, 1999.
S. Mailis, C. Riziotis, J. Wang, B. Taylor, A. Anderson, S. Barrington, R. W. Eason, C.
Grivas, N. Vainos, “Photosensitive lead germanate glass waveguides grown by Pulsed
Laser Deposition,” CLEO/Europe 1998, Scotland 13-18 September, Paper CWF51.
Also appeared in Laser Ablation Meeting, London 27 May 1998, organised by
the Quantum Electronics Group of Institute of Physics
II. Patent
M. N. Zervas and C. Riziotis “Full Cycle Coupler Based Interferometric Optical
Add/Drop Multiplexer,” Patent Application
194
III. Other Related Research Publications
(work not described in the Thesis)
J. Koo, P. G. R. Smith, R. B. Williams, C. Riziotis, M. C. Grossel, “UV written
waveguides using crosslinkable PMMA-based copolymers,” Conference on Lasers and
Electro-Optics, CLEO 2002, Long Beach Convention Center, California, USA.
H. Ebendorff-Heidepriem, C. Riziotis, E. Taylor, “Novel photosensitive glasses,” in
Proceedings of 7th International Otto Schott Colloquium, Jena, Germany, July, 2002.
H. Ebendorff-Heidepriem, C. Riziotis, E.R. Taylor, “Novel photosensitive glasses,”
2002 Glass Odyssey: 6th ESG Conference, Montpellier, France, 2-6 Jun 2002.
S. Mailis, C. Riziotis, R. W. Eason, “Continuous wave ultraviolet laser induced
frustration of etching in congruent lithium niobate,” Conference on Lasers and Electro-
Optics, CLEO 2002, Long Beach Convention Center, California, USA.
S. Mailis, A. J. Boyland, C. L. Sones, J. Scott, C. Riziotis, R. W. Eason, “Laser induced
etch frustration of Lithium Niobate single crystals,” Presentation in the workshop
“Towards European Virtual Laser Facilities and Integrated Initiatives” organised by
LIMANS III cluster of Large Scale Laser Facilities, Berlin, Germany, October 2001.
H. Ebendorff-Heidepriem, C. Riziotis, E. Taylor, “Novel photosensitive phosphate
glasses,” in Proceedings of Marie Curie Fellows Workshop, London, Sep. 2001.
J. Koo, C. Riziotis, R. B. Williams, P. G. R. Smith, M. C. Grossel “Direct writing of
waveguides in a crosslinkable PMMA based copolymer,” submitted to Optical
Materials.