All-Optical Wavelength Conversion in Aluminum Gallium ... · nications Technology Institute for their introduction and safety training in cleanrooms. Discussion with Mr. Sean Wagner

All-Optical Wavelength Conversion in Aluminum GalliumArsenide Waveguides at Telecommunications Wavelengths

by

Wing-Chau NG

A thesis submitted in conformity with the requirementsfor the degree of Master of Applied Science

Graduate Department of Electrical and Computer EngineeringUniversity of Toronto

Copyright c© 2010 by Wing-Chau NG

Abstract

All-Optical Wavelength Conversion in Aluminum Gallium Arsenide Waveguides at

Telecommunications Wavelengths

Wing-Chau NG

Master of Applied Science

Graduate Department of Electrical and Computer Engineering

University of Toronto

2010

This thesis aims at both developing highly nonlinear Aluminum Gallium Arsenide waveg-

uides (AlGaAs) and demonstrating all-optical wavelength conversion via cross-phase

modulation in AlGaAs waveguides at telecommunications wavelengths. This work cov-

ers waveguide design, device fabrication, device characterization and system work. The

wafer composition and the waveguide geometry were optimized to give an effective core

area of 4.3 µm2, leading to a nonlinear coefficient of 13.3 /W/m in the TM mode. A

combination of standard photolithography and reactive-ion etching was used to fabricate

the waveguides with the desired dimension. The finished waveguide has a length of 1

cm. Linear characterization shows that the linear loss of the waveguide is approximately

3 dB/cm. The nonlinear optical characterization has shown that the primary nonlinear

absorption mechanism is three-photon absorption with the corresponding absorption co-

efficient of 0.08 cm3/GW2 at 1550 nm for the TM mode. Lastly, error free all-optical

wavelength conversion via cross-phase modulation (XPM-AOWC) at 10 Gbit/s in a 1-

cm-long bulk AlGaAs waveguide was demonstrated with a power penalty of 6 dB. The

conversion bandwidth of XPM-AOWC covers the entire window of telecommunication

wavelengths.

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Acknowledgements

First and foremost, I would like to express my gratitude to my supervisors, Prof.

J. Stewart Aitchison and Prof. Li Qian for their support, resources, advice, experience

and guidance in the completion of this work. Their instructions on waveguide design,

waveguide fabrication and device characterization were crucial for me to obtain important

experimental results.

I would also show my hearty thank to Dr. Ksenia Dolgaleva, of the University of

Toronto, who is also a collaborator of this project responsible for wafer design, waveguide

design and fabrication and device characterization, for her precious and patient direct

teaching on free-space experimental techniques. The waveguide samples fabricated days

and nights by her were the key to success of this project. Her tremendous effort and

advice on my thesis were also important for the completion of my master thesis.

Many thanks and much appreciation are owed to Prof. Leslie A. Rusch and Prof.

Sophie LaRochelle, both of the Universite Laval for their high efficiency in arranging

equipment for the completion of the system work of this project at the Universite Laval.

The speedy responses to my requests on equipment and technical support by Dr. Philippe

Chretien and Dr. Qing Xu were indispensable in my experimental work.

Dr. Wen Zhu, of the University of Toronto, deserves much appreciation for her ar-

rangement of equipment, her help on purchasing components for my work and her ex-

perimental help on using the bit-error-rate tester and fiber splicer.

I also thank Prof. Amr Helmy for his Digital Communication Analyser, Prof. Joyce

Poon for her lensed fiber, Dr. Henry Lee and Yimin Zhou from the Emerging Commu-

nications Technology Institute for their introduction and safety training in cleanrooms.

Discussion with Mr. Sean Wagner on optical properties of AlGaAs, linear and non-

linear characterization techniques and the effective-area calculation method was helpful.

His generous Matlab simulation code for pulse propagation and for calculating AlGaAs

refractive indices were instrumental for quantifying the nonlinear optical properties of

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AlGaAs. Ms. Michelle Xu helped out much at the beginning of my experimental work.

Mr. Arash Joushaghani also helped out a lot in every aspect of my work. Mr. Bhavin

Bijlani generous recipe for AlGaAs etching contributes a lot to waveguide fabrication.

I would like to thank my committee members, Prof. Amr Helmy and Prof. Joyce

Poon and my committee chair, Prof. Willy Wong, for volunteering their time and efforts.

I also extend my gratitude to the Department of Electrical and Computer Engineering

at the University of Toronto for their financial support. Special thanks are given to the

adminstrative staff in Photonics roup, Ms. Linda Liu and Mr. Raj Balkaran, the Graduate

Programs Assistant, Ms. Judith Levene, and the Graduate Programs Administrator, Ms.

Darlene Gorzo, for their professional attitude and super-high efficiency to deal with the

file of my two-year master study. In particular, Ms. Judith Levene’s efficiency in arranging

a conference room (BA7180) and a conference telephone, checking the projectors and

replying my emails with detailed and patient explanation allowed me to have a smooth

master defense on August 20th, 2010.

I thank my groupmates and my colleages in Photonics group for their friendly support:

Mr. Moez Haque, Mr. Luis Fernandes, Mr. Pisek Kultavewuti, Mr. Farshid Bahrami, Mr.

Muhammad Alam, Mr. James Dou, Mr. Chris Sapiano, Mr. Iliya Sigal, Mr. Jason Ng,

Mr. Peyman Sarrafi, Mr. Fei Ye, Mr. Lijun Zhang, Miss Yuemeng Chi, Mr. Eric Zhu,

Mr. Nima Zarien, Mr. Willam La, Mr. Jason Grenier, Mr. Eric Zhang, Dr. Bing Qing,

Dr. Aaron Zilkie, Dr. Walid Mathlouthi.

Last but not least, I express my gratitude to my mother and my sister for their

patience, spiritual and financial support to let me study further after the completion of

my master degree, to Prof. Chester Shu, Prof. Hong-Ki Tsang and Prof. Kong-Pan Poon,

of the Chinese University of Hong Kong, for their support and opinion on my graduate

studies, and to my secondary-school teacher, Mr. Wai-Shing Chan, for his enlightenment

and rational advice for every decision I made for my life.

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Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Recent Statistics of network traffic . . . . . . . . . . . . . . . . . 11.1.2 Current commercial backbone networks . . . . . . . . . . . . . . . 31.1.3 Challenges of 40 Gb/s . . . . . . . . . . . . . . . . . . . . . . . . 41.1.4 Extra device cost due to electronics . . . . . . . . . . . . . . . . . 41.1.5 Power Consumption due to electronics . . . . . . . . . . . . . . . 5

1.2 All-Optical Wavelength Conversion (AOWC) as a solution . . . . . . . . 61.2.1 Recent commercial products . . . . . . . . . . . . . . . . . . . . . 8

1.3 Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Organization of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Literature Review 132.1 SOA-based AOWC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Fiber-based AOWC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Passive-waveguide-based AOWC . . . . . . . . . . . . . . . . . . . . . . . 20

3 Background Theory 263.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Lightwave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.1 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.2 Kerr effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 Nonlinear Schrodinger Equation . . . . . . . . . . . . . . . . . . . 313.2.4 Split-step Fourier method . . . . . . . . . . . . . . . . . . . . . . 32

3.3 Self-Phase Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.1 Maximum Nonlinear Phase Shift . . . . . . . . . . . . . . . . . . 343.3.2 SPM-induced spectral broadening . . . . . . . . . . . . . . . . . . 36

3.4 Cross-Phase Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.1 XPM-induced sidebands . . . . . . . . . . . . . . . . . . . . . . . 40

3.5 Mechanism of XPM-AOWC . . . . . . . . . . . . . . . . . . . . . . . . . 413.5.1 Mechanism of Olsson’s design . . . . . . . . . . . . . . . . . . . . 423.5.2 Dispersion-induced walk-off . . . . . . . . . . . . . . . . . . . . . 443.5.3 Effect of duty cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 45

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3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Optical Properties of AlGaAs 48

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2 Figure of merit for materials . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2.1 Limitation due to linear absorption . . . . . . . . . . . . . . . . . 49

4.2.2 Limitation due to TPA . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.3 Limitation due to 3PA . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3 Optical properties of AlGaAs . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3.1 Large tailorable range of refractive index . . . . . . . . . . . . . . 56

4.3.2 Ultrafast response and high nonlinearity . . . . . . . . . . . . . . 58

4.3.3 Low nonlinear absorption and figure of merit . . . . . . . . . . . . 60

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 Wafer Design and Waveguide Fabrication 63

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2 General Criteria for Wafer Design . . . . . . . . . . . . . . . . . . . . . . 64

5.3 Simulation Results for Wafer Design . . . . . . . . . . . . . . . . . . . . 65

5.4 Waveguide Design and Fabrication . . . . . . . . . . . . . . . . . . . . . 69

5.4.1 Waveguide Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.4.2 Finished Wafer Information . . . . . . . . . . . . . . . . . . . . . 71

5.4.3 Waveguide Fabrication . . . . . . . . . . . . . . . . . . . . . . . . 71

5.5 Estimated Effective Mode Area . . . . . . . . . . . . . . . . . . . . . . . 72

5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6 Device Characterization 79

6.1 Linear Loss Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.1.1 Fabry-Perot Resonance Technique . . . . . . . . . . . . . . . . . . 80

6.1.2 Optical Sources and Device length . . . . . . . . . . . . . . . . . . 82

6.1.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.1.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.1.5 Measurement Errors . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.2 Nonlinear Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.2.1 Higher-order effective area . . . . . . . . . . . . . . . . . . . . . . 91

6.2.2 Inverse Trasmission Squared Method . . . . . . . . . . . . . . . . 93



6.3 Cross-Phase Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 96



6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

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7 System Performance 1017.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.2 Experimental Setup for the Fiber-based Nonlinear Characterization . . . 1017.3 Experimental Results for the Fiber-based Nonlinear Characterization . . 1057.4 Experimental Setup for the Offsetting Filtering with Data Modulation . . 1077.5 Change of Pulse Shape with Different Filter Detunings . . . . . . . . . . 1087.6 XPM-Sideband Extraction and Carrier Suppression . . . . . . . . . . . . 1117.7 Error-free XPM-AOWC in a 1-cm-long AlGaAs waveguide . . . . . . . . 1157.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

8 Conclusion 121

A Nonlinear Absorption 124A.1 Inverse Transmission Squared Curve . . . . . . . . . . . . . . . . . . . . 124A.2 Inverse Transmission Curve . . . . . . . . . . . . . . . . . . . . . . . . . 127

B Scripts for Lumerical MODE solutions 130B.1 Initialization.lsf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130B.2 WidthScan.txt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

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List of Figures

1.1 The evolution of the number of broadbamd users [1]. . . . . . . . . . . . 2

1.2 Total traffic in Japan. Solid circles are evaluated value by Ministry ofInternal Affairs and Communications [3]. The line is the fit assuming a40% annual increase. Bars show the number of FFTH subscribers. . . . . 3

1.3 Estimated power consumption by Internet routers in Japan. Original datais from T. Hasama of AIST. The value for 2001 is based on the actual data.Plots shown by solid circules are the assumed drive of LSI voltage usedin routers. The percentages in the figure are the proportion of the totalpower generation. A 40% increase in traffic will make the router powerconsumption reach 6.4% of the total power generation in 2020 even for alow LSI drive voltage of 0.8V [3]. . . . . . . . . . . . . . . . . . . . . . . 6

1.4 The schematic of all-optical wavelength conversion as a solution to resolvethe traffic contention in WDM systems. MUX and DEMUX stand formultiplexer and demultiplexer respectively . . . . . . . . . . . . . . . . . 7

1.5 Picture of a fully packaged CIP’s wavelength converter (2R regenerator);from the CIP’s white paper [2]. . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Schematic diagram of the operation of a MZI-based 2R wavelength con-version; from the CIP’s white paper [2] . . . . . . . . . . . . . . . . . . . 9

2.1 (a) Spectra at the output of the SOI device (blue) and of the SOA (red)(b) Conversion efficiency as function of the input signal detuning when thepump was at 1552 nm; red for SOA and blue for non-dispersion-engineeredsilicon waveguide. The conversion efficiency is defined as the power ratioof the input signal to the wavelength-converted signal via non-degeneratedFWM. [24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 The configuration of a typical AOWC with a single SOA . . . . . . . . . 16

2.3 Measured values of the nonlinear index (n2) versus linear index (n0) for arange of glasses (colored symbols) and Miller’s rule (straight black line) [58]. 19

3.1 Visualization of the coordinates of the pump pulse at the input and theoutput of the nonlinear medium. . . . . . . . . . . . . . . . . . . . . . . . 36

3.2 The time evolutions of the electric field in a Gaussian-shaped pulse withoutchirp (top) and with SPM-induced chirp after passing through a Kerrmedium (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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3.3 Normalized SPM-broadened spectra (normalized to the pulse spectral peakvalue) of the 2-ps unchirped Gaussian pump pulse at 1570 nm with differ-ent peak powers in a lossless nonlinear medium. Spectra are labeled by themaximum nonlinear phase shift. The simulation was based on Mr. SeanWagner’s Matlab code for the symmetrized split-step Fourier method [138]. 39

3.4 The temporal and spectral visualization of XPM on the CW. The pulseenvelope without the corresponding electric field is shown at the top. TheCW’s electric field as well as its constant envelope is shown at the middle.The temporal movement of the CW carrier caused by XPM is shown atthe bottom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.5 Normalized spectra (normalized to the CW carrier maximum value) ofXPM-sidebands on the CW at 1520 nm induced by the 2-ps unchirpedGaussian pump pulse at 1570 nm with different peak powers in a losslessnoinlinear medium.. Spectra are labeled by the maximum nonlinear phaseshift defined in Section 2.2. The vertical axes are in dB scale. The simu-lation was based on Mr. Sean Wagner’s Matlab code for the symmetrizedsplit-step Fourier method [138]. . . . . . . . . . . . . . . . . . . . . . . . 42

3.6 Experimental setup of the XPM-AOWC, reproduced from [55]. . . . . . . 433.7 Transmission through the loop mirror filter from [55] (left) and illustration

of the zero-noise cleaning by XPM-AOWC (right). The shaded regionrefers to the position of the bandpass filter. . . . . . . . . . . . . . . . . . 44

3.8 Dispersion-induced walk-off between the pulse and the CW. The CW trav-els faster than the pump pulse shown at the top. The CW travels slowerthan the pump pulse shown at the top. is shown at the bottom. The tem-poral evolution of the electric field of the CW corresponds to the originalpump pulse without walk-off, shown at the middle. . . . . . . . . . . . . 44

3.9 Effect of the duty cycle of the pump pulses on the XPM-sideband level.The pumps of smaller duty cycle and of larger duty cycle are shown at thetop and at the bottom, respectively. . . . . . . . . . . . . . . . . . . . . 46

4.1 Figure of merit T as a function of photon energy normalized to the bandgapof a semiconductor [92] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2 Normalized transmission in the bar state (dashed curve, left scale) andswitching power (solid curve, right scale) versus V for CW inputs in ahalf-beat-length nonlinear direction coupler [100]. . . . . . . . . . . . . . 54

4.3 (a) Face-centered cubic lattice, (b) the diamond crystal lattice is obtainedby displacing the lattice atoms of (a) by (a/4, a/4, a/4). Therefore, thediamond structure belongs to the face-centered cubic (FCC) structure.(c) when the displaced lattice atoms are different from the original latticeatoms, the crystal structure is called the zinc-blende crystal structure. . . 55

4.4 The band structures of GaAs [107] (left) and AlAs [103] (right). . . . . . 554.5 Bandgap energies corresponding to the valence band maxima and the con-

duction band minima of Γ-Valley, X-valley and L-valley as a functionof aluminum concentration x in AlxGa1−xAs. Transition from direct toindirect bandgap takes place when x is 0.45. . . . . . . . . . . . . . . . . 57

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4.6 Evolution of bandgaps in AlxGa1−xAs as x increases. . . . . . . . . . . . 57

4.7 The refractive index of AlGaAs with different Al-concentration as a func-tion of wavelengths, calculated by the empirical model by Gehrsitz [117].The legend represents the percentage of aluminium concentration in AlGaAs. 58

4.8 The measured dispersion of n2 for the TE-polarized mode (solid dots) andthe TM-polarized mode (solid triangles) for Al0.18Ga0.82As [115] . . . . . 59

4.9 Nonlinear phase shift versus input peak power for a 1-cm-long (left) and a5-cm-long (right) waveguides having effective core areas of 7 µm2 respec-tively. The red and the blue lines represent the linear loss of 0.1 dB/cmin Al0.18Ga0.82As and As2S3 chalcogenide glass respectively. The blackand green lines represent the linear loss ranging from 1 to 10 dB/cm inAl0.18Ga0.82As and As2S3 chalcogenide glass, respectively . . . . . . . . . 60

4.10 Left: Experimental values of TPA coefficient as a function of wavelengthfor the TE-polarized mode (solid circles) and the TM-polarized mode(open circles) in an AlGaAs waveguide having a 1.5 µm-thickAl0.18Ga0.82Asguiding layer. Right: Experimental values of 3PA coefficient for the TE-polarized mode as a function of wavelength in an AlGaAs waveguide havinga 1.5 µm-thick Al0.18Ga0.82As guiding layer[115]. . . . . . . . . . . . . . . 61

4.11 Left: Wavelength dependence of the figure of merit T for TE- and TM-polarized modes in an AlGaAs waveguide having a 1.5 µm-thickAl0.18Ga0.82Asguiding layer. Right: The low-nonlinear-absorption spectral window ofAl0.18Ga0.82As [115]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1 Effective core areas as a function of waveguide widths for 40-18-30 (lefttop) and 40-18-24 (right top), and the simulated mode shapes of the 2-µm-wide waveguides in the TM and TE modes for 40-18-30 (left bottom) and40-18-24 (right bottom). The waveguide’s etch depth is chosen to be 1.35µm for simulation. The values of the effective core area calculated usingLumerical MODE Solution were reproduced from Dr. Ksenia Dolgaleva’sdesign and the corresponding results. . . . . . . . . . . . . . . . . . . . . 66

5.2 Effective core areas as a function of waveguide widths for 24-18-24 (lefttop), 50-18-24 (middle top) and 70-18-24 (right top), and the simulatedmode shapes of the 2-µm-wide waveguides in the TM and TE modes for24-18-24 (left bottom) , 50-18-24 (middle bottom) and 70-18-24 (rightbottom). The waveguide’s etch depth is chosen to be 1.35 µm for sim-ulation. The values of the effective core area calculated using LumericalMODE Solution were reproduced from Dr. Ksenia Dolgaleva’s design andthe corresponding results. . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.3 Effective core areas as a function of waveguide widths for 70-18-20 (lefttop) and 70-18-40 (right top), and the simulated mode shapes of the 2-µm-wide waveguides in the TM and TE modes for 24-18-20 (left bottom) and70-18-40 (right bottom). The waveguide’s etch depth is chosen to be 1.35µm for simulation. The values of the effective core area calculated usingLumerical MODE Solution were reproduced from Dr. Ksenia Dolgaleva’sdesign and the corresponding results. . . . . . . . . . . . . . . . . . . . . 68

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5.4 Effective core areas as a function of waveguide widths for the TE modeusing the 50-20-24 wafer calculated using Lumerical MODE Solution 3.0.The corresponding script for simulation can be found in Appendix B. . . 70

5.5 Effective core areas as a function of waveguide widths for the TM modeusing the 50-20-24 wafer calculated using Lumerical MODE Solution 3.0.The corresponding script for simulation can be found in Appendix B. . . 70

5.6 The values of the effective mode area ( in µm2) for the fundamentalTM mode are shown for different waveguide ridge heights and widths ofthe AlGaAs strip-loaded waveguides with the designed wafer composition.The shaded region of the table refers to single-mode operations (This ta-ble/figure was given by Dr. Ksenia Dolgaleva). . . . . . . . . . . . . . . . 71

5.7 Procedures of waveguide fabrication at the University of Toronto. (a) Thecomposition and structure of the AlGaAs wafer from CPFC; (b) Spin-coating the positive photoresist S1818; (c) Ultra-Violet (UV) light expo-sure; (d) Development of the photoresist using MF321; (e) Dry-etching ofsilica mask via RIE; (f) Dry-etching of AlGaAs via RIE; (g) The devicestructure of the finished AlGaAs waveguide. Dr. Ksenia Dolgaleva wasresponsible for the fabrication process. . . . . . . . . . . . . . . . . . . . 75

5.8 The SEM image (taken by Dr. Ksenia Dolgaleva) of the 2-µm-wide AlGaAswaveguide with a depth of 1.2 µm. . . . . . . . . . . . . . . . . . . . . . 76

5.9 The refractive index profile (left) and the mode image (right) of the 2-µm-wide AlGaAs waveguide with a depth of 1.2 µm, simulated by LumericalMODE solution at 1550 nm. . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.10 Effective mode areas of TM and TE modes as a function of the width of theAlGaAs waveguide with a etch depth of 1.2 µm, simulated by LumericalMODE solution, at 1550 nm. . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.11 Effective mode areas for TM and TE modes as a function of the edge depthof the 2-µm-wide AlGaAs waveguide at 1550 nm. The step change of theetch depth is 50 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.12 Nonlinear coefficients for TM and TE modes as a function of the edgedepth of the 2-µm-wide AlGaAs waveguide at 1550 nm. The step changeof the etch depth is 50 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.1 Left: Transmission intensity trace versus optical path difference for a 1-cm-long GaAs waveguide with a linear loss of 1 dB/cm for different op-tical source linewidths w . The center wavelength was chosen to be 1550nm. Right: Dependence of calculated apparent loss on the optical sourcelinewidth (a) for 1-cm-long GaAs waveguides with actual losses of 0.1,1.0, and 5 dB/cm, respectively, and (b) for 0.1 dB/cm actual loss GaAswaveguides with lengths of 0.3, 0.5, and 1 cm, respectively [127]. . . . . . 83

6.2 Experimental setup for the linear loss measurement. . . . . . . . . . . . . 85

6.3 The normalized transmission spectrum near 1550 nm for a 1-cm-long Al-GaAs waveguide in the TM mode. . . . . . . . . . . . . . . . . . . . . . . 86

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6.4 Left: The fringe contrast ratio versus the total loss of a waveguide. Differ-ent facet reflectivities are shown for comparison. Right: The reflectivitiesof the TM and TE modes versus the angle of incidence. The simulatedeffective indices for the TM and TM modes are 3.2339 and 3.2353, respec-tively. The inset is a magnified plot showing the difference between theTM’s and TE’s reflectivities near the normal incidence (zero degree). . . 87

6.5 Left: Reflectivity versus the angle of incidence. Right: Fringe contrastratio versus waveguide loss. . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.6 Comparison between the linear loss coefficients versus different waveguidewidths measured using both facets R1 and R2 of the 1cm-long AlGaAssample near 1550 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.7 Experimental setup for the nonlinear optical characterization of AlGaAswaveguide samples (from Dr. Ksenia Dolgaleva). . . . . . . . . . . . . . . 95

6.8 Measured inverse transmission squared curve plotted as a function of thesquared intensity peak inside the waveguide at 1550 nm. The discrete datapoints represent the experimental data. The dashed line is the best least-square fitting curve for the experimental data (from Dr. Ksenia Dolgaleva). 96

6.9 The spectrum of XPM between 2-ps (FWHM) pump pulses at 1567 nmand the CWs at different wavelengths (from Dr. Ksenia Dolgaleva). . . . 97

6.10 The spectrum of XPM between 2-ps (FWHM) pulses at 1500 nm andCWs at different wavelengths in a 1-cm-long AlGaAs waveguide (from Dr.Ksenia Dolgaleva). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.1 Experimental setup for the fiber-based nonlinear characterization. . . . . 1027.2 The spectral transmission of the 0.8-nm-wide FBG for suppressing the

out-of-band ASE noise of the pump at 1550 nm. . . . . . . . . . . . . . . 1037.3 The spectral transmission of the 0.2-nm-wide tunable filter for suppressing

the out-of-band ASE noise of the CW. . . . . . . . . . . . . . . . . . . . 1037.4 Comparison of the spectra of XPM in a 1-cm-long AlGaAs waveguide when

the pump power were varied from 10dBm (10 mW) to 20 dBm (100 mW)at 1551nm. The CW power was fixed at 12.7dBm (18.6mW) at 1537 nm. 105

7.5 The comparison of XPM spectra with the CWs at different wavelengths.The pump power was maintained at 20dBm (100mW) at 1550 nm, whilethe CW powers were around 20mW. . . . . . . . . . . . . . . . . . . . . 106

7.6 The XPM-sidebands appeared on the CW at 1558.6nm. The pump powerat 1551nm and the CW power were 20 dBm and 17.6 dBm respectively. . 106

7.7 The experimental for the offset filtering with data modulation. . . . . . 1077.8 The temporal pulse shape of the wavelength-converted data observed on

the DCA with different amounts of filter detuning (a) +0.9 nm (b) +0.5nm (c) + 0.4 nm (d) +0.35 nm (e) +0.25 nm (f) 0 nm (g) -0.3 nm. . . . 109

7.9 Diagrams illustrating the differences of XPM-sideband levels with differentCW powers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.10 Three-stage filtering for XPM-AOWC. . . . . . . . . . . . . . . . . . . . 1127.11 The spectral transmission of the WDM filter, detuned from the CW by

1.2 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

xii

7.12 The output of the WDM filter (the first stage) . . . . . . . . . . . . . . . 1147.13 The spectral transmission of the commercial tunable filter JDSU TB15,

detuned from the CW by 1.1nm . . . . . . . . . . . . . . . . . . . . . . . 1147.14 The output of the commercial tunable filter JDSU TB15 (the second stage)1157.15 The spectral transmission of the commercial tunable filter JDSU TB9,

detuned from the CW by 1.2nm . . . . . . . . . . . . . . . . . . . . . . . 1157.16 The output of the commercial tunable filter JDSU TB9 (the overall output

of the AOWC). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167.17 Experimental setup of system measurement of the XPM-AOWC in a 1-

cm-long AlGaAs waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . 1167.18 The graph of the logarithm of the bit-error-rate versus receiver sensitivity

of the wavelength-converted output signal at 1558 nm, with three differentpump power levels at 1551 nm. . . . . . . . . . . . . . . . . . . . . . . . 117

7.19 Eye diagrams of the pump at 1551 nm before entering the waveguide (left), after passing through fiber-fiber (middle) and after passing through fiber-waveguide-fiber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.20 Eye diagrams of the pump at 1551 nm before entering the waveguide (left), and of the wavelength-converted signal at 1556.8 nm . . . . . . . . . . . 119

xiii

List of Tables

2.1 Comparison of the effective core area and the Kerr nonlinearity amongdifferent types of fibers used in all-optical wavelength conversion . . . . . 21

2.2 Comparison of the effective core area and the Kerr nonlinearity among dif-ferent types of passive waveguides used in all-optical wavelength conversion 25

8.1 Comparison of the effective core area and the Kerr nonlinearity amongdifferent types of passive waveguides including AlGaAs waveguides (ofthis thesis) used in all-optical wavelength conversion . . . . . . . . . . . . 123

xiv

Chapter 1

Introduction

1.1 Background

1.1.1 Recent Statistics of network traffic

The invention of optical fibers and lasers initiated the development of optical communi-

cations, enabling high-speed, broadband and long-distance networks. However, optical

communications were still not so popular before 2005 [1] since the introduction of the

copper-based Asymmetric Digital Subscriber Lines (ADSL) delivery was able to deal with

the internet traffic at that time. Network operators had little incentive to install opti-

cal physical layers for transmission and network cores as they saw little revenue growth

opportunity. A factor of only two to three times traffic growth was not a problem for

the basic scalability of the traditional electronics network architectures, and therefore

the current ADSL-driven broadband era is still sustainable through extrapolation and

growth of traditional network designs together with careful management of pricing and

costs [2].

It was not until recently that, due to the bandwidth-hungry applications such as real-

time video applications and large-volume data transfer, the demand for much faster access

speeds increases the pressure on operators and administrations to put high bandwidth

1

Chapter 1. Introduction 2

Fiber-To-The-Home (FTTH) networks in places. FTTH is a peer-to-peer network con-

figuration of fiber deployment that allows the end user to directly access the high-speed

optical network resource through an optical fiber. The recent completion of IEEE 802.3av

10G-EPON standardization in September, 2009 [1] indicates the potentially pressing de-

mand for the FTTH. As shown in Fig. 1.1, the total number of the FFTH customers in

Japan has exceeded that of the ADSL customers since the end of 2007.

Figure 1.1: The evolution of the number of broadbamd users [1].

Fig. 1.2 shows the total internet traffic in Japan, evaluated by the Ministry of Internal

Affairs and Communications, Japan. The solid line extrapolated using the statistics

from 2004 to 2007 represents the estimated growth of the total internet traffic after

2008, assuming a 40% annual increase. One of the reasons for this rapid increase is the

increasing number of users subscribed to broadband services.

As the FTTH deployment in the access network is accelerating, telecommunication

operators [6, 7] and network equipment vendors [8, 9, 10] are now starting to announce

commercial deployments of higher-data-rate (40 Gb/s per wavelength channel) optical

transmission systems to deal with the expanding network traffic. This commercial trend

is expected to continue in the future as telecommunications and data services further

become the underpinning infrastructure that supports knowledge-based economies [11].


Figure 1.2: Total traffic in Japan. Solid circles are evaluated value by Ministry of InternalAffairs and Communications [3]. The line is the fit assuming a 40% annual increase. Barsshow the number of FFTH subscribers.

1.1.2 Current commercial backbone networks

In practice, a combination of both TDM (Time Division Multiplexing) and WDM (Wave-

length Division Multiplexing) techniques is used to increase network capacity. The cur-

rent commercial backbone networks employ TDM to combine multiple data channels

from access networks into a single wavelength channel at 2.5 or 10 Gbit/s. A number of

2.5 or 10 Gbit/s wavelength channels are then multiplexed using WDM and then trans-

mitted through optical fibers1 [12]. Achieving higher TDM bit-rates for each individual

WDM channel is always the main research focus for increasing the overall network ca-

pacity. Commercial (single-channel) 40 Gbit/s TDM systems have been on the market

since 2002 and companies are now putting effort on deploying 40 Gbit/s-based WDM

optical transmission systems.

1In WDM, 100 carrier wavelengths per fiber are allocated within a 80 nm wide spectral band, deter-mined by the bandwidth of the erbuim-doped fiber amplifier.


1.1.3 Challenges of 40 Gb/s

A couple of issues will arise when the single-channel bit-rate of backbone networks is

increased to 40 Gb/s [17]. For instance, signal degradation due to the channel impair-

ments such as noise accumulation, chromatic dispersion, polarization mode dispersion

and fiber nonlinearities are more difficult to overcome at 40 Gb/s than at 10 Gb/s. In

addition, traffic contention occurs in WDM systems when multiple optical packets at the

same wavelength simultaneously are transmitted from different source nodes to the same

destination node. Using electrical buffering to resolve traffic contention requires OEO

(Optical-Electronic-Optical) conversions, which will pose a limitation on the channel

bit-rate of backbone networks, known as electronic bottleneck at 40 Gb/s.

1.1.4 Extra device cost due to electronics

The present industrial solutions for mitigating the channel impairments and for resolving

the traffic contention at 10 Gb/s or below per channel are to use OEO regeneration

and OEO wavelength conversion, respectively, where optical signals are detected and

electronically processed before being re-modulated onto a separate optical source [16].

From the industrial viewpoint, historically, an increase in channel bit-rate by a factor

of four has always led to 40% cost savings [17]. However, as the network’s channel

bit-rate increases to 40 Gb/s, the situation for OEO regeneration and OEO wavelength

conversion becomes much worse: the costs of the detectors, electronics and modulator

within the OEO process for 40 Gb/s are much more higher than those for 10 Gb/s, as

well as increasing technical difficulties in packaging, routing and power handling such as

powering up and cooling down the electronics for 40Gb/s electrical signals. The typical

projected cost of a 40 Gb/s OEO module is estimated to be $25k-30k in [17], which does

not give the expected 40% economic cost reduction for an increase in channel bit-rate by

a factor of four.


1.1.5 Power Consumption due to electronics

Reducing power consumption is always one of the biggest issues for a long-term man-

agement of a company. In the current optical networks, powering up and cooling down

electronic devices as well as controlling the temperatures of erbium-doped fiber amplifiers

(EDFA) and semiconductor-optical-amplifier(SOA)-based devices are the main source of

the huge energy consumption. Moreover, a major part of traffic is caused by indispens-

able network services such as constantly monitoring the quality of transmission channels.

As energy crisis is imminent in a few decades, the expense due to power consumption

would be soaring beyond expectation. From a global viewpoint, the increasing energy

cost is also a hindrance to economic growth as well as technology development in the

world. Therefore, it is of paramount importance to reduce the expenditure on power con-

sumption by selecting appropriate power-saving physical tools for providing increasingly

popular internet services.

Fig. 1.3 shows the electrical router power consumption in Japan estimated by T.

Hasama of AIST (National Institute of Advanced Industrial Science and Technology).

The power consumption in 2001 is obtained based on the actual data. Assuming a 40%

annual increase in traffic and reduction of the CMOS-LSI drive voltage, plotted as closed

circles in the figure, the power consumption of routers will reach 6.4% of the total power

generation in 2020 even for the low CMOS-LSI drive voltage of 0.8 V . If the drive voltage

reduction of CMOS-LSI is insufficient, the power consumption will still easily reach a few

tens of a percentage point or more after a decade. This means that we cannot benefit

from larger capacity networks through electronic networks.

The major cause of the huge power consumption in the present network is due to

the use of WDM systems with electrical routing of the packet signals, in which the

optical signals are converted into electrical signals at the network node for electrical signal

processing, and subsequently are changed back to the optical form for transmission. As

the channel bit-rate of networks increases, the electronics at network nodes are required


Figure 1.3: Estimated power consumption by Internet routers in Japan. Original data isfrom T. Hasama of AIST. The value for 2001 is based on the actual data. Plots shownby solid circules are the assumed drive of LSI voltage used in routers. The percentages inthe figure are the proportion of the total power generation. A 40% increase in traffic willmake the router power consumption reach 6.4% of the total power generation in 2020even for a low LSI drive voltage of 0.8V [3].

to deal with a larger amount of network traffic, leading to additional power consumption.

1.2 All-Optical Wavelength Conversion (AOWC) as

a solution

To eliminate the electronic bottleneck at 40 Gb/s, to reduce the cost of electronic devices

as well as to reduce the network power consumption, all-optical signal processing will

be introduced. One of all-optical signal processing techniques is All-Optical Wavelength

Conversion (AOWC). In high-speed optical communications systems, AOWC is used to

convert the carrier of high-bit-rate data from one wavelength to another, without trans-

forming optical signals into electrical form, reducing the cost and the power consumption

due to electronics.

In WDM systems, optical data packets are routed to the destination nodes according


to their corresponding carrier wavelengths serving as IP addresses for routing. However, if

two or more incoming data packets are at the same wavelength, one of the data packets

has to be delayed to solve the contention problem. However, optical-electrical-optical

(OEO) conversion and electrical buffers limit the bitrate of backbone network. In view

of this, AOWC can be used to resolve the traffic contention in WDM systems. In Fig.

1.4, for example, two incoming data packets from source 1 and source 2 both at the same

wavelength λa arrive a network node simultaneously, the wavelength converter inside the

network node will convert the two data packets from λa into λ1 and λ2 , respectively.

The converted data packets at the new wavelengths λ1 and λ2 will then be transmitted

to destination 1. Similarly, the data packets coming from source 1 and source 2 at the

same wavelength λb will be converted into λc and λd , respectively, and then be routed

to destination 2. Since the conversion process does not involve neither OEO conversion

nor electrical buffers, AOWC does not limit the network bitrates [19], eliminating the

electronic bottleneck at 40 Gb/s.

Figure 1.4: The schematic of all-optical wavelength conversion as a solution to resolvethe traffic contention in WDM systems. MUX and DEMUX stand for multiplexer anddemultiplexer respectively

.


1.2.1 Recent commercial products

One of the companies providing the commercial products for all-optical signal processing

is CIP, a company from United Kingdom, that has introduced a new optical regenerator

or wavelength converter solution, in which semiconductor optical amplifiers (SOAs) are

used as a nonlinear medium in optical switches or wavelength converter based on Mach-

Zender Interferometer (MZI), which has been the research focus in the early 1990’s.

Figure 1.5: Picture of a fully packaged CIP’s wavelength converter (2R regenerator);from the CIP’s white paper [2].

Fig. 1.6 shows a SOA-MZI-based optical switch or wavelength converter which com-

prises two arms and two 3-dB couplers. As a wavelength converter, an input CW at a

wavelength different from that of the incoming data is halved by the 3-dB coupler at the

input. These two CWs of equal power then propagate individually through the two MZI

arms having identical lengths. The input data is coupled into the SOA in one of the MZI

arms, with a well-adjusted power level to cause a gain reduction in the SOA, resulting

in a phase modulation on the CW. At the output coupler, the phase-modulated CW

interferes with the unchanged CW on the other arm. A phase difference of π between

the two CWs causes the output CW light to be completely redirected from one output

port to the other.


Figure 1.6: Schematic diagram of the operation of a MZI-based 2R wavelength conversion;from the CIP’s white paper [2]

.

The SOA is composed of indium-phosphide-based multiple quantum wells, with a

carrier recovery time at 1/e of 10 ps, suitable for 40 Gb/s regeneration and error-free

wavelength conversion [18]. It is nowadays considered the most efficient device for AOWC

below 40 Gbit/s due to itslarger nonlinearity and low input power requirement, compared

to fiber-based devices. However, SOA-based AOWC does not help reduce the overall

power consumption due to the additional heatsink platform for temperature control.

1.3 Motivation and Objective

1.3.1 Motivation

All-optical wavelength conversion (AOWC) is considered to have the most potential to

eliminate the electronic bottleneck beyond 40 Gb/s, to reduce the cost of electronic

devices as well as to reduce the network power consumption.

The current solutions such as SOA-based AOWC cannot reduce the device’s power

consumption due to the additional heat-sink platform required for temperature control.

The channel bit-rate of AOWC is limited by the SOA’s long carrier lifetime. Fiber-based

AOWC has ultrafast nonlinear response, but is bulky and thus sensitive to environmental


perturbations. Passive waveguide-based AOWC based on the third-order optical nonlin-

earity (Kerr effect) has recently received much attention due to its ultrafast response, the

absence of amplified spontaneous emission (ASE) noise as well as the simple fabrication.

Unlike SOAs, it does not require any temperature control. Examples include silicon and

chalcogenide waveguides based on Kerr effect that require simpler fabrication processes

compared to Periodically-Poled Lithium Niobate (PPLN) based on the second-order op-

tical nonlinearity. Despite their low costs and compatibility to the CMOS technology,

silicon and chalcogenide glasses require at least 5-cm-long waveguides to achieve suffi-

cient Kerr effect. Another material, Gallium Arsenide (GaAs) has high nonlinearity that

allows millimeter-long waveguides for AOWC, however, its strong two-photon absorption

(TPA) increases the input power thresholds and limits the device’s throughputs. Ulti-

mately, a power-saving solution relies on a suitable material as the technology platform

for signal processing in optical networks.

One well-studied ultrafast nonlinear material for C-band operation is Aluminum Gal-

lium Arsenide (AlGaAs). Unlike silicon and chalcogenide, AlGaAs can be integrated with

III-V lasers and indium-phosphide-based optical amplifiers with the current techonol-

ogy. Much work has been done in the early 1990’s to characterize the nonlinear optical

properties of AlGaAs at telecommunication wavelengths, showing that its ultrafast non-

linearity 650 times higher than that of silica, 3 times higher than that of silicon and

4 times higher than that of As2S3-chalcogenide, together with low two-photon absorp-

tion within C-band. These properties indicate that AlGaAs is suitable for high-speed

passive-waveguide-based AOWC. As the predicted power consumption due to the soar-

ing network traffic increases, low-cost silicon photonics does not emerge as an appropriate

power-saving solution. This rekindles our interest in AlGaAs in spite of its high cost.


1.3.2 Objective

The objective of this project is to implement all-optical wavelength conversion (AOWC)

via Cross-Phase Modulation (XPM) within C-band in Aluminum Gallium Arsenide

(AlGaAs) waveguides, in collaboration with Dr. Ksenia Dolgaleva, of the University of

Toronto, who was responsible for wafer design, waveguide fabrication and device charac-

terization. A bitrate of 10 Gbit/s was chosen as a foundation of building up a high-speed

system in future. The system work of AOWC at 10 Gbit/s was carried out in collabora-

tion with Prof. Leslie Ann Rusch, of the Universite Laval.

1.4 Organization of thesis

This thesis covers wafer design, waveguide fabrication, device characterization and sys-

tem work for implementing all-optical wavelength conversion in AlGaAs waveguides at

telecommunication wavelengths.

In Chapter 2, the recent development in all-optical wavelength conversion (AOWC)

are discussed. Semiconductor-optical-amplifier-, fibers- and passive-waveguide-based AOWC

are compared in details.

In Chapter 3, the basic theories of all-optical wavelength conversion via cross-phase

modulation in passive materials are given to inexperienced readers to understand this

thesis.

In Chapter 4, the definitions of figure of merits at off-resonance wavelengths in dif-

ferent nonlinear absorption regimes will be given in order to quantify the performance of

materials with respect to their achievable nonlinear phase shifts. The optical properties

and advantages of AlGaAs are introduced.

In Chapter 5, design criteria are given to optimize the wafer composition and the

waveguide geometry in order to minimize the effective core area. The waveguide fabrica-

tion procedures are discussed in details. The effective mode area of the finish waveguide


is estimated.

In Chapter 6, the linear and nonlinear optical properties of the finished AlGaAs

waveguides are examined. The principles of the linear and nonlinear characterization

methods and the corresponding results with error analysis are discussed.

In Chapter 7, the experimental setup and the system work for the demonstration of

all-optical wavelength conversion via cross-phase modulation in AlGaAs waveguides at

the Universite Laval are presented.

Finally, Chapter 8 gives a summary of the conclusions drawn from all the experimental

results in this thesis.

Chapter 2

Literature Review

2.1 SOA-based AOWC

Semiconductor Optical Amplifier (SOA) is an active waveguide-based device to amplify

optical signals. Today’s commericial SOAs are composed of indium-phosphide-based

materials whose bandgaps overlap the entire C-band. Owing to band-to-band resonant

transitions, SOAs have high nonlinearity usually of 7 orders higher than that of silica

fibers [20] which allows nonlinear optical signal processing with much shorter devices (in

hundreds of micrometers) and with lower input powers (in milli-watts). The three main

nonlinear processes that are used to implement SOA-based AOWC are cross-gain mod-

ulation (XGM) [21], cross-phase modulation (XPM) [23] and four-wave mixing (FWM)

[22].

XGM in SOAs is a linear resonant process in which the marks (logic ones) of a strong

optical data saturates the gain of an SOA while the zeros leave the gain unchanged or

allow the gain to recover. A CW at another wavelength will be amplified according to the

temporal gain variation, resulting in an inverted logic of the optical data. XPM in SOAs

is a result of XGM in which the gain change induced by the marks of the optical data

will temporally change the refractive index of the gain medium, which is governed by the

13

Chapter 2. Literature Review 14

Henry-factor (also called the linewidth enhancement factor), and thus the CW will be

phase-modulated, forming spectral sidebands on the CW carrier component. By filtering

out the spectral sideband, the data can be duplicated at the CW wavelength. FWM in

SOAs is a third-order nonlinear process in which the data and the CW beat together to

form a wave-mixing product at a new wavelength that carries the same logic as the input

data. However, due to the strong spectral dispersion of the resonant nonlinearity, the

FWM conversion bandwidth at 3 dB in SOAs is limited to ∼3 nm [24] shown in Fig. 2.1

Figure 2.1: (a) Spectra at the output of the SOI device (blue) and of the SOA (red)(b) Conversion efficiency as function of the input signal detuning when the pump wasat 1552 nm; red for SOA and blue for non-dispersion-engineered silicon waveguide. Theconversion efficiency is defined as the power ratio of the input signal to the wavelength-converted signal via non-degenerated FWM. [24]

One of the most up-to-date products for all-optical signal processing is the highly

nonlinear indium-phosphide (InP) -based multiple quantum well SOA from CIP, with

a carrier recovery time at 1/e of 10 ps, suitable for 40 Gb/s regeneration and error-free

wavelength conversion [18]. It is nowadays considered the most efficient device for AOWC

below 40 Gb/s due to its larger nonlinearity and much lower input power requirement,


compared to bulk SOAs amd passive devices.

However, as the bit rate of networks increases, SOAs suffer from data patterning

effect on individual WDM channels, i.e., the output signal quality is dependent on the

input data pattern due to the slow carrier recovery in SOA. The crosstalk between WDM

channels as well as the instrinsic ASE noise of active devices also degrades output signal

qualities or require larger power penalties for error-free detection at receiver ends.

Since 2000, tremendous effort has been put into the removal or reduction of patterning

effects appeared in optical signal processing in InP-based SOAs. In order to achieve

SOA-based AOWC at higher than 40 Gb/s in OTDM systems, ultrafast optical effects

in semiconductors such as spectral hole burning (SHB) and carrier heating (CH) [25,

26, 27] in InP-based SOAs are required, followed by a clumsy cascaded filtering [23] for

extracting induced spectral sidebands. However, as the channel bit-rate increases, the

power penalties required for error-free operations increase as well.

One of the recent advanced designs in high-speed OTDM systems is Turbo-switch

from Yang [28], demonstrated at 160 Gb/s per channel, in which two cascading SOAs

are required to firstly undergo XGM and then Self-Gain Modulation (SGM) using CH-

and SHB-induced fast gain recoveries, and subsequently a delay-interferometer inverts

and sharpens the wavelength-converted data pulses. The offset filter [23] or the delay

interferometer [28] at the SOA output extracts the sideband of the modulated CW carrier

as well as suppresses the carrier component of the target wavelength, showing a few dB

power penalty.

While these OTDM systems have achieved varying degrees of success in eliminating or

reducing patterning effects, they also lead to increased system complexity, much reduced

device throughputs and increased receiver power penalties. Still, the crosstalk between

40 Gb/s channels in WDM systems remain unsolved. This problem can be attributed

to the fact that different WDM channels share the same ”carrier reservoir” of the gain

medium, in which the gain variation induced by a WDM channel will modulate another


WDM channel. The ultimate solution to eliminate the channel crosstalk in high-speed

WDM systems is to use nonresonant nonlinearities for wavelength conversion.

Regarding power efficiency and energy consumption, the converted output from the

SOA-based AOWC at 40 Gb/s per channel is always below milli-Watt [28] [23] , meaning

that the SOA’s amplification cannot be utilized to give sufficiently high wavelength-

converted powers for transmission. In other words, SOAs only offers large nonlinearity

induced by interband carrier transitions, rather than amplification, for optical signal

processing.

Figure 2.2: The configuration of a typical AOWC with a single SOA.

Fig. 2.2 illustrates the configuration of a typical AOWC using a single SOA. The input

data power is well-controlled by a 10-dBm EDFA as a power booster to avoid the full-

gain saturation in SOAs that leads to patterning effect. The tunable laser source provides

a continuous wave (CW) whose power level ranges from 0 mW to 10 mW . The SOA

converts the data signal from the original wavelength to the CW wavelength. At the end,

another EDFA boosts up the converted signal for detection. The two EDFAs, the SOA

and the tunable laser source require in total 4 temperature controllers, which accounts

for the major power consumption in AOWC. This motivates the research of passive-

waveguide-based AOWC which does not require temperature control on the device.


2.2 Fiber-based AOWC

Silica fibers were originally used for transmitting light at telecommunication wavelengths.

Unlike semiconductor materials such as indium phosphide used in SOAs, fibers are made

of silica or glass material whose direct or indirect bandgap lies in UV or visible light

region. Thus the attenuation of light within C-band caused by photon absorption at

moderate powers is minimized. Fiber-based devices for optical communications are de-

signed to utilize the ultrafast non-resonant nonlinearity of silica, and therefore patterning

effects due to slow carrier recovery can be eliminated. However, since the non-resonant

nonlinearity of conventional silica fibers is very low (2.2× 10−20m2/W ) at 1550 nm com-

pared to the resonant nonlinearity of SOAs , high input power levels (> 500 mW ) and

larger fiber lengths (in kilometers) are required. Moreover, long silica fibers also introduce

polarization instability into the propagating signals.

The common nonlinear processes in fiber-based passive devices are FWM and XPM.

FWM in fibers is a purely nonresonant 3rd order nonlinear process while XPM is, unlike

in SOAs, a nonresonant 3rd -order nonlinear process in which the refractive index of fibers

is being modulated by the strong data. A second CW will then be phase modulated,

forming spectral sidebands on the CW carrier. Extracting the sidebands using filters will

give a wavelength-converted signal with the same logics as the input data.

The effective Kerr nonlinearity, or the nonlinear coefficient, Γ, of a fiber is defined as

[133]

Γ =2π

λ

n2

Aeff

(2.1)

where λ is the optical wavelength, Aeff [µm2] is the effective core area of the single-

mode field, and n2 [m2/W ] is the nonlinear refractive index of the material. Standard

single-mode silica fiber (SMF) has an effective core area of ∼ 90 µm2 at 1550 nm, n2

of 2.2 × 10−20m2/W , resulting in a nonlinear coefficient of ∼ 1 /W/km. Over the last

two decades, researchers have been engaged in changing the physical structure of fibers


(reducing Aeff ) or using highly nonlinear glass materials (increasing n2) to enhance the

Kerr nonlinearity in fiber-based devices as well as to reduce the fiber lengths.

Historically, dispersion-shifted fibers (DSF) were developed in the 1980’s in order to

minimize the chromatic dispersion in conventional single-mode silica fibers. The core-

cladding index profile in DSFs are tailored to shift the zero-dispersion wavelength from the

original 1300 nm to µm2 1550 nm (within silica’s minimum-loss window). The effective

core areas of DSFs can then be reduced from 90 µm2 to around 60 µm2, enhancing fibers’

Kerr nonlinearity. In the early 1990’s, dispersion-shifted fibers (DSF) with Γ of µm2 3

/W/km were used to demonstrate optical signal processing [44] [45] that require kilometer

lengths and moderately high input powers [53] [54] [55]. However, fiber-based devices

using FWM did not benefit from kilometer lengths in which the overall zero dispersion

wavelength fluctuation was serious [47] and polarization instability will degrade the signal

quality of wavelength-converted signals.

In the late 1990s, highly nonlinear silica-based fibers (HNF) with Γ of 3 - 8 times

higher than DSF were made by both reducing the effective core area from ∼ 50 µm2 to ∼

10 µm2 and enhancing n2 by higher GeO2 doping in the core [46, 47]. Thus, high-speed

applications were enabled in hundred-meter long nonlinear fibers [40].

To increase Γ towards 100 /W/km, a tighter mode confinement can be achieved in

holey-structured silica fibers [52], in which a large air-filling fraction in the fiber cladding

provides a high effective core-cladding refractive index contrast, resulting in a smaller

effective mode area. However, for pure silica holey fibers, the lower limit for Aeff is ∼ 1.5

µm2, corresponding to an effective nonlinearity of ∼ 70 /W/km [51][52], 70 times larger

than that of conventional SMFs.

The use of compound glasses (also called soft glasses) with higher n2 allows a further

drastic increase in fiber nonlinearity. As predicted by Miller’s rule [58] shown in Fig. 2.3,

the compound glasses having higher refractive indices have larger nonlinear refractive

coefficients, and thus are able to enhance their nonlinearities beyond 1000 /W/km.


Figure 2.3: Measured values of the nonlinear index (n2) versus linear index (n0) for arange of glasses (colored symbols) and Miller’s rule (straight black line) [58].

.

In the early 2000s, highly nonlinear compound glass holey fibers (HF) have been

demonstrated using bismuth silicate [32], lead silicate [29] [30] and tellurite [31] glasses

whose nonlinear refractive coefficients at 1550 nm are 14.5, 18.6 and 20 times higher

than that of silica, respectively. The achieved nonlinearity in SF57-lead silicate HF was

675 /W/km [30] in 2003, and then improved to 1860/W/km in 2005 [33], while that

in bismuth silicate HF was 1100 /W/km [35, 36] in 2005. Although an unstructured

fiber (non-HF) having Aeff of 3.28 µm2 made of bismuth borate glasses (whose n2 is

50 times higher than that of silica) gave a nonlinear coefficient up to 1360 /W/km

[34], the fiber nonlinearity is ultimately limited by material’s n2. In addition, the huge

difference in Aeff between the highly nonlinear glass fiber and the standard SMF results

in a high coupling loss. To enhance the overall power efficiency, chalcogenide glasses are

of particular interest because their nonlinear coefficients can be 500 times greater than

that of silica [38] and larger effective areas can be used to reduce coupling losses. In 2006,


the achieved nonlinearity of a 1-m-long unstructured As2Se3 fiber having an Aeff of 37

µm2 was 1200 /W/km, which was used to demonstrated error-free wavelength conversion

at 10 Gb/s with an input pump power of 72 mW , showing the lowest power requirement

in fiber signal processing compared to the other nonlinear fibers [48].

To further shorten the fiber lengths, As2Se3 chalcogenide glass having a refractive

index of 2.8 is able to form fiber tapers to reduce the diameter of single-mode fibers

adiabatically from 75 µm to 1.2 µm, resulting in an Aeff of 0.64 µm2 and a Γ of 68000

/W/km [39]. Although, for a fixed fiber length, the required input power for As2Se3

fiber tapers is theoretically reduced by 56.6 times (17.5 dB), the small-core section can

only be, in practice, made in millimeter long, as a longer small-score section will make

the fiber taper more fragile and susceptible to mechanical perturbations. For easing

the fabrication process, the corresponding device length is usually up to 15 cm [39, 50].

Moreover, the 4-dB fiber-to-waveguide coupling loss as well as the 3-dB tapering loss [39]

is considered too high that most of the input power is not fully utilized for generating

nonlinear effects.

Despite these recent developments, the lengths of fiber devices are still on the order

of 1 meter [48] while those of fiber-taper devices can only be down to 15 cm, resulting in

bulky devices sensitive to environmental perturbations [39]. Moreover, fiber devices are

not monolithically integrable with the current III-V semiconductor lasers and amplifiers.

2.3 Passive-waveguide-based AOWC

While SOA-based AOWC utilizes the highly nonlinear resonant effect of direct-bandgap

III-V semiconductor suffering from slow carrier recovery, passive-waveguide-based AOWC

utilizes the ultrafast non-resonant nonlinearity of materials operating below or outside

the Γ-valley direct bandgaps at telecommunication wavelengths. Therefore, passive-

waveguide-based AOWC does not have intrinsic ASE noise and does not require tem-


Table 2.1: Comparison of the effective core area and the Kerr nonlinearity among differenttypes of fibers used in all-optical wavelength conversion

Type of fibers n2 (m2/W ) Aeff (µm2) Γ (/W/km)

Standard SMF 2.2× 10−20 (= nSiO22 ) 8090 1

Silica DSF 2.2× 10−20 (= nSiO22 ) 60 1.9

Silica HNF (Ge-doped)[47] 4.6× 10−20 (∼ 2.1nSiO22 ) 12 17.5

Pure silica holey fiber [51] 2.2× 10−20(∼2.1nSiO22 ) 1.5 70

Tellurite (TeO2) glass conventional fiber [58] 55× 10−20 (∼ 25nSiO22 ) 9.23 260

Tellurite Holy Fiber [31] 55× 10−20 (∼ 25nSiO22 ) 3.3 675

Lead silicate glass holey fiber SF57 (2003)[30] 41× 10−20 (∼18.6nSiO22 ) 2.6 640

Lead silicate glass holey fiber SF57 (2005)[31] 41× 10−20 (∼ 18.6nSiO22 ) 0.9 1860

Bismuth silicate conventional fiber 32× 10−20 (∼14.6nSiO22 ) 20.3 64

Bismuth silicate glass holey fiber [35] 32× 10−20 (∼14.6nSiO22 ) 1.2 1100

Bismuth borate glass conventional fiber [34] 110× 10−20 (∼50nSiO22 ) 33 1360

Chalcogenide glass As2Se3 fiber [38] 1100× 10−20 (∼500nSiO22 ) 37 1200

Remarks:

1 nSiO22 is the nonlinear coefficient of silicon oxide = 2.2× 10−20m2/W

2 the above parameters are taken at 1550 nm

perature control. During the 1990’s, periodical-poled lithium niobate (PPLN) attracted

much research interest because of its high conversion efficiency given by its second-order

nonlinearity χ(2). However, the conversion efficiency and the coversion bandwidth of

χ(2)-based AOWC depend on phase-matching condition which requires complicated fab-

rication techniques to compensate the effect of material dispersion in lithium niobate.

Since 2005, XPM-based waveguides have been the research focus for AOWC as it does

not require phase matching condition, simplifying fabrication processes. Recent examples

include the high-index materials such as silicon, chalcogenide and III-V semiconductors

whose nonlinear refractive coefficients are 2 orders higher than that of silica. They can

be structured into waveguides to provide tight confinement of light to further enhance

the Kerr-based nonlinear effects such as XPM and FWM for wavelength conversion. The

resulting much larger nonlinearity compared to fibers help reduce the device length from

meters to centimeters.


Silicon is an indirect-bandgap material having a high refractive index of sim 4 that

allows a very tight mode confinement to enhance the Kerr nonlinearity. As silicon pho-

tonics has emerged as a promising technology platform for low-cost solutions to optical

communications and for its compatibility with CMOS technology, researchers are aim-

ing at a high-speed silicon photonic transceiver circuit which monolithically integrates

different kinds of functionalities. Examples include silicon raman lasers, silicon optical

amplifiers, SiGe photodetectors, silicon optical modulators and wavelength converters

[61].

For wavelength converters, Intel corporation in 2006 demonstrated the first AOWC

via FWM in a 8-cm-long silicon waveguide having an effective core area of 1.6 µm2

, resulting in a nonlinear coefficient of 23000 /W/km [62]. Although the linear optical

absorption in silicon at wavelengths of 1.3-1.7 µm is small [62, 61], two-photon absorption

(TPA) and TPA-assisted free carrier absorption in silicon [64] that occur at high pump

powers limit the achievable nonlinear effect, thus increasing the operating input powers

as well as limiting the device’s throughputs. Although the TPA-induced FCA and the

corresponding free-carrier life time can be significantly reduced by introducing a reverse

biased p-i-n diode structure embedded in a silicon waveguide, the maximum bit-rate was

only 40 Gb/s [63].

Chalcogenide glasses have also been the research focus of nonlinear integrated optics

since 2004 due to its high refractive index as well as its high nonlinearity. As2Se3, with a

refractive index of ∼ 2.8, receives much attention as its nonlinear refractive coefficient is

500 times higher than that of silica. However, As2Se3 suffers from serious TPA at high

powers within C-band [68], meaning that the material is not suitable to make waveguides

for achieving high intensity. Another type of chalcogenide, As2S3, with a refractive

index of ∼ 2.3 and a nonlinear refractive coefficient 100 times higher than that of silica,

does not suffer from TPA within C-band. In 2006, XPM-AOWC at 10 Gb/s has been

demonstrated by Eggleton in a 5-cm-long As2S3-glass-rib waveguide with a core size of


∼ 5.7 µm2 [69]. In 2007, the same group demonstrated XPM-AOWC at 40 Gbit/s in a

22.5-cm-long serpentine As2S3 waveguide a core size of ∼ 7.1 µm2 [70].

Due to their differences in lattice constants, both silicon and chalcogenide cannot be

monolithically integrated with III-V semiconductors lasers and InP-based optical ampli-

fiers, and therefore hybrid integration technology will be required to bond materials with

different lattice constants together, resulting in an extra cost as well as additional com-

plexity or lower yield in fabrication. In addition, chalcogenide (As2S3) waveguides need

to be at least 5 cm long to generate sufficient nonlinear effect for error-free operation

with the on-chip powers usually larger than 100 mW (20 dBm) [69, 70, 74]. A 3-dB or

larger fiber-to-waveguide coupling loss as well as the unavoidable 50% coupling loss at

the 3-dB coupler for signal combination at the input make the required input powers at

least 400 mW (26 dBm), resulting in a wastage of 75% (300 mW ) of the overall power

consumption. Although chalcogenide photonic crystal waveguides [38] as well as silicon

nanowires [73] have been recently developed to further lower the on-chip powers, the

huge coupling loss per facet (> 10dB) must be reduced by additional tapers that also

introduce tapering losses.

As the predicted network power consumption will grow tremendously due to the

recent increasing popularity of FTTH networks for real-time video streaming, using highly

nonlinear materials to reduce the power consumption would be a unique solution to lower

the operational costs. This rekindles the research interest of using III-V semiconductors

for optical signal processing despite their high costs.

In particular, Gallium Arsenide (GaAs) has a n2 ∼ 1300 times higher than that of sil-

ica, 5 times higher than that of chalcogenide and 3 times higher than that of silicon, which

further lowers the input power requirement and shorten the device length toward millime-

ters, compared to silicon and chalcogenide-based devices. In 2009, Astar demonstrated

the first AOWC via XPM and FWM at 10 Gb/s in a 6-mm-long GaAs waveguide with a

core size of 1.8 µm2, resulting in a nonlinear coefficient of 65000 /W/km. However, as the


GaAs-based device is operated at above-half-bandgap, TPA and TPA-induced FCA limit

the achievable nonlinear phase shift, and thus requires much more input power (40%)

than expected [75].

Further reduction of waveguide core sizes were realized in nanowires [60, 59]. However,

the huge fiber-to-waveguide coupling loss does not help reduce the overall network power

consumption. Very small waveguide cores also increase the difficulties in photonic pack-

aging, which is considered the major cost of device production. Reducing coupling loss

is still an issue with current technology. Ultimately, the problem converges to finding a

suitable material that offers ultrafast response, high Kerr nonlinearity and low nonlinear

absorption.

One well-studied ultrafast nonlinear material for C-band operation is Aluminum Gal-

lium Arsenide (AlGaAs). Much work has been done in the early 1990’s to characterize

the nonlinear optical properties of AlGaAs at telecommunication wavelengths, showing

that its ultrafast nonlinearity 650 times higher than that of silica, 3 times higher than

that of silicon and 4 times higher than that of As2S3-chalcogenide, together with low two-

photon absorption within C-band. These properties indicate that AlGaAs is suitable for

high-speed passive-waveguide-based devices for optical communication. By making use

of low-scattering-loss waveguides, all-optical switching based on Kerr effect such as non-

linear directional couplers [77], Mach-Zehnder interferometers [79] and X-junctions [80]

have been demonstrated. Moreover, the temporal solitons [81, 82] and spatial [83, 84]

can also be formed by using AlGaAs waveguides. These devices show that the low-TPA

AlGaAs allows an achievable nonlinear phase shift much larger than other materials such

as GaAs, chalcogenide and silicon. Since the mid 1990’s, AOWC has been done via the

second-order nonlinearity such as sum-frequency generation and difference-freququency

generation in periodically-reversed AlGaAs waveguides [85, 86, 87, 88, 89], which re-

quires complicated fabrication procedures. To the best of our knowledge, there has been

no demonstration of AOWC in AlGaAs waveguides via Kerr nonlinearity up to this time,


and this thesis is going to be the starting point for realising high-speed Kerr-based AOWC

in AlGaAs waveguides, in order to show that using Kerr-based AlGaAs waveguides helps

simplify the fabrication processes and reduce the overall power consumption in optical

networks in the near future.

Table 2.2: Comparison of the effective core area and the Kerr nonlinearity among differenttypes of passive waveguides used in all-optical wavelength conversion

Material Nonlinear process Linear loss (dB/cm) Waveguide length Effective Length n2 (m2/W ) Aeff (µm2) Γ (/W/km)

Silicon [63] FWM (40 Gb/s) 0.4 8 cm 5.6 cm 900× 10−20 (∼ 400 nSiO22 ) 1.6 22800

As2S3 [69] XPM (10 Gb/s) 0.2 5 cm 4.23 cm 300× 10−20 (∼ 136 nSiO22 ) 5.7 2080

As2S3 [70] XPM (40 Gb/s) 0.05 22.5 cm 21.72 cm 300× 10−20 (∼ 136 nSiO22 ) 7.1 1700

As2S3 [72] FWM (40 Gb/s) 0.05 6 cm 3.25 cm 300× 10−20 (∼ 136 nSiO22 ) 1.23 9800

GaAs [75, 73] XPM + FWM (10 Gb/s) 6 4.5 mm 3.4 mm 2900× 10−20 (∼ 1300 nSiO22 ) 1.8 65000

Remarks:



Chapter 3

Background Theory

3.1 Introduction

Currently, XPM and FWM are the two common 3rd-order nonlinear processes used to

implement all-optical wavelength conversion (AOWC) in fibers and passive waveguides.

As opposed to FWM, XPM is a broadband process that does not require phase matching.

As the chromatic dispersion has a negligible effect on XPM with C-band, the XPM-based

AOWC only requires a low-loss waveguide with a sufficiently small core to maximize the

Kerr effect, while the FWM-based AOWC requires a complicated waveguide or nanowire

design procedure to compensate material dispersion with waveguide dispersion in order to

enhance the FWM conversion bandwidth and efficiency. In addition, the FWM conversion

bandwidth and efficiency are very sensitive to the deviation in waveguide dimension, and

thus a high fabrication precision is required. Due to simplicity and fabrication tolerance,

only XPM-based AOWC will be covered in this thesis.

In this chapter, the background theory of XPM-based AOWC will be introduced.

26

Chapter 3. Background Theory 27

3.2 Lightwave Propagation

The electric field of light wave is commonly represented by

E(z, t) = A(z, t)ejθ(z,t) (3.1)

where A(z, t) is the slowly-varying envelope of an optical pulse or a continuous wave. It

is a function of time t for optical pulses and is constant for continuous waves. The phase

of the electric field θ(z, t) is defined as

θ(z, t) = ωot− [no(λ) + ∆n(I)]koz (3.2a)

=

θo︷︸︸︷ωot− no(λ)koz−∆n(I)koz (3.2b)

where θo represents the intensity-independent phase evolution of the electric field, ωo is

the carrier frequency of the light accounting for the temporal periodicity of the wave, ko is

the propagation constant in free space accounting for the spatial periodicity of the wave,

no is the refractive index of the medium, ∆n is the change of refractive index caused by

the nonresonant Kerr nonlinear effect induced by an intense optical field, I represents

the temporal and spatial profile of the optical intensity inside the medium.

Based on no(λ) and ∆n(I) in Eqn. (3.2b), the effects of chromatic dispersion and

Kerr nonlinearity of a medium on the propagating lightwave can be anaylsed.

3.2.1 Dispersion

Dispersion refers to the wavelength-dependent refractive index of a medium, i.e. no is a

function of wavelengths. Different wavelengths experience different propagation constants

nko (or phase shift), and thus travel at different velocities through a dispersive medium.

It is a linear process because it changes the temporal envelope but not the spectral content

of an optical pulse.

In a single-mode waveguide, the chromatic dispersion arises from material dispersion

and waveguide dispersion. Material dispersion originates from the material’s wavelength-


dependent refractive index. Waveguide dispersion occurs because the light propagates

differently in the waveguide core and in the surrounding air or cladding, resulting in a

mode propagation constant dependent on the core size, the core-cladding index difference

and the wavelengths.

In mathematics, a single-mode waveguide exhibits chromatic dispersion if the mode

propagation constant varies nonlinearly with the angular frequency. Assuming that the

spectral width of an optical pulse is sufficiently small such that β can be approximated

using the first three terms in a Taylor series expansion about the center frequency of the

pulse ωo

β(ω) = n(ω)ω

c= βo + β1(ω − ωo) +

1

2β2(ω − ωo)2 +

1

6β3(ω − ωo)3 (3.3)

βm = (dmβ

dωm)|ω=ωo ;m = 0, 1, 2, ... (3.4)

where βo is the propagation constant in the material, β1 is the inverse of the group

velocity of the pulse, or physically means the time required by a pulse to travel a unit

distance inside the waveguide. β2, called the second-order dispersion coefficient or GVD

parameter, refers to the group velocity dispersion causing temporal pulse broadening (or

narrowing). β3 is called the third-order dispersion coefficient, whose effect is significant

only when the second-order dispersion disappears at the zero dispersion wavelength of

the waveguide or when the femtosecond pulses having very broad spectra are propagating

through the waveguide. β3 will not be considered in this thesis.

Another common parameter that accounts for group velocity dispersion of a medium

is called dispersion parameter (ps/nm/km), defined as

D =−2πc

λ2β2. (3.5)

If an optical pulse with a 1/e pulse half-width of T in1/e travels through the medium having

a length of L, the 1/e half-width of the pulse at the output T out1/e becomes

T out1/e =√T in1/e

2+ ∆τ 2, (3.6)


where

∆τ = Lβ2∆ω1/e = LD∆λ1/e (3.7)

is the pulse spread due to the group velocity dispersion, while ∆ω1/e and ∆ω1/e correspond

to the 1/e spectral half width of the pulse in terms of the angular frequency and the

wavelength, respectively.

3.2.2 Kerr effect

∆n is a function of optical intensity and represents the change of refractive index caused

by the nonresonant Kerr effect induced by an intense optical pulse. Any nonlinear effects

modify the spectral content but not the temporal shape of the pulse. The temporal and

spatial index change due to the third-order nonlinearity along a nonlinear medium is a

function of the optical intensity I(x, y, z, t) inside the medium, defined as

∆n(x, y, z, t) = n2I(x, y, z, t), (3.8)

where n2 is called nonlinear refractive index or Kerr coefficient [cm2/W ]. For simplicity,

the time dependence of the optical intensity is ignored. In a three-dimensional rectangular

waveguide structure, the guided mode has a non-uniform intensity distribution in the

transverse cross-section, and thus ∆n is also a function of x and y. To eliminate the

dependence of the index change on the transverse optical intensity inside the waveguide

structure, the effective index change is defined as

∆neff (z) =

∫ +∞−∞

∫ +∞−∞ ∆n2(x, y, z)I(x, y, z)dxdy∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy

(3.9a)

=

∫ +∞−∞

∫ +∞−∞ n2I

2(x, y, z)dxdy∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy

(3.9b)

= n2

∫ +∞−∞

∫ +∞−∞ I2(x, y, z)dxdy

[∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy]2

[

∫ +∞

−∞

∫ +∞

−∞I(x, y, z)dxdy] (3.9c)

∆neff (z) = n2P (z)

Aeff

(3.9d)

(3.9e)


where

P (z) =

∫ +∞

−∞

∫ +∞

−∞I(x, y, z)dxdy (3.10)

The effective area Aeff is defined such that the optical intensity given by P/Aeff can

be used to describe the third-order nonlinear effect averaged over the transverse optical

intensity:

Aeff =[∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy]2∫ +∞

−∞

∫ +∞−∞ I2(x, y, z)dxdy

. (3.11)

This definition applies for the effective core area of waveguide in this thesis. Note that

the effective core area of the waveguide is also a function of wavelength. For example, in

a single-mode waveguide, the effective core area can be smaller for shorter wavelengths.

By substituting Eqn. (3.9a) into Eqn. (3.2b) and including the time-dependence into the

effective index change, the phase in Eqn. (3.2b) becomes

θ(z, t) = θo(z, t)−φNL(z, t)︷︸︸︷

∆neff (z, t)koz = θo(z, t)− φNL(z, t), (3.12)

where the nonlinear phase shift φNL(z, t) can be rewritten as

φNL(z, t) = n2P (z, t)

Aeff

2π

λz = Γ(λ)P (z, t)z (3.13)

where

Γ(λ) =2π

λn2

1

Aeff

(3.14)

Γ is called the nonlinear coefficient [/W/km] which is a function of wavelengths 1. A more

nonlinear material (having a larger n2) and a tighter mode confinement (a smaller Aeff )

result in a larger nonlinear coefficient at a fixed wavelength. The nonlinear coefficients

of different devices are listed in Table 2.1 and Table 8.1.

1n2 and Aeff are also wavelength dependent. In addition, their polarization dependences make Γdifferent for different polarizations


3.2.3 Nonlinear Schrodinger Equation

Starting from the nonlinear Schrodinger equation [133] (in the reference frame moving

at the group velocity vg of the light), the propagation of an intense pump pulse with a

co-propagating continuous-wave (CW) in a waveguide structure can be modeled as

∂Ap∂z

=

Propagation loss︷︸︸︷−αp

2Ap −j β2,p

2

∂2Ap∂T 2

+β3,p

6

∂3Ap∂T 3︸︷︷︸

Dispersion

+

Kerr nonlinearity︷︸︸︷jγp(|Ap|2 + 2|Acw|2)Ap (3.15)

where Ap is the slowly-varying envelope of the pulse at the pump wavelength, while

Acw is the constant envelope of the continuous wave at a wavelength different from the

pump. The new moving time-coordinate T = t − zvg

follows the group velocity of the

pulse, which is independent of the absolute time t, and T is defined as zero at the pulse

center. The first term of the RHS of Eqn. (3.15) accounts for the attenuation of the pump

amplitude due to the linear absorption, the scattering loss and the nonlinear absorption

of the material. For further details, please refer to Section 6.2 ”Nonlinear Absorption”.

The second term and the third term describe the changes in the pulse envelope caused

by the dispersion of the waveguide. β2,p and β3,p are the second-order and the third-

order dispersion coefficients at the pump wavelength, respectively. The fourth and the

last term describe the changes in phase or spectral content of the pulse via self-phase

modulation (SPM) and cross-phase modulation (XPM), respectively. Γp is the nonlinear

coefficient at the pump wavelength, expressed as

Γp =2π

λpn2,p

1

Aeff ,p

, (3.16)

where n2 ,p and Aeff ,p are the nonlinear refractive index and the effective core area at the

pump wavelength, respectively.

Similarly, the propagation of the CW beam with the co-propagating pump pulse in a

waveguide structure can be modeled as

∂Acw∂z

=

Propagation loss︷︸︸︷−αcw

2Acw −j

β2,cw

2

∂2Acw∂T 2

+β3,cw

6

∂3Acw∂T 3︸︷︷︸

Dispersion

+

Kerr nonlinearity︷︸︸︷jγcw(|Acw|2 + 2|Ap|2)Acw (3.17)


with an interchange of the subscripts between p and cw. Γcw is the nonlinear coefficient

at the CW wavelength, expressed as

Γcw =2π

λcwn2 ,cw

1

Aeff ,cw

(3.18)

3.2.4 Split-step Fourier method

To accurately compute the effect of loss, dispersion and nonlinearity of a medium on the

temporal and the spectral evolution of the pulse and of the CW, the split-step Fourier

method will be used, in which the dispersion and the nonlinearity of the medium in

which the pulse and the CW propagate can be considered independent of each other over

a small propagation distance ∆z. Thus, the nonlinear Schrodinger equation is divided

into a linear term (that changes the temporal shape but not the spectral content of the

pulse) and a nonlinear term (that changes the spectral content but not the temporal

shape of the pulse):

∂Ap∂z

= (DTp + Np)Ap (3.19)

where

DTp = −αp

2− j β2,p

2

∂2

∂T 2+β3,p

6

∂3

∂T 3(3.20a)

Np = jγp(|Ap|2 + 2|Acw|2) (3.20b)

Here Np is the operator accounting for the Kerr nonlinearity, and DTp is the operator

accounting for both the propagation loss and the dispersion of the waveguide. By tak-

ing intergral on both sides of Eqn. (3.19) from z to ∆z, the solution of the nonlinear

Schrodinger equation becomes

z+∆z∫z

dA(z, T )

A(z, T )=

z+∆z∫z

(DT + N)dz (3.21a)

where A(z + ∆z, T ) = A(z, T )e(DT+N)∆z. (3.21b)


It shows that over a sufficiently small distance, the complicated nonlinear Schroedinger

equation can be solved numerically by separating the exponential term into two steps

corresponding to dispersion and nonlinearity, respectively.

For the dispersion step, the operator DT involves higher-order time derivatives that

make the exponential term e(DT∆z) difficult to be evaluated in the time domain. As

the time-derivative operator ∂n

∂Tncorresponds to (iω)n in the Fourier domain, where

n = 1, 2, 3, the dispersion term will be evaluated in the Fourier domain. As shown

in Eqn. 3.22a, the electric field B(z, T ) will firstly be Fourier-transformed, and then

multiplied with an exponential term with the Fourier-transformed dispersion operator,

such that different frequency components will receive different amounts of phase delays

over ∆z according to the dispersion operator in the Fourier domain. Finally, the resultant

electric field is transformed back to the time domain for the subsequent nonlinear step:

F(B(z, T ))→ eDT (jω)∆zF(B(z, T ))→ F−1eDT (jω)∆zF(B(z, T )) = e(DT∆z)B(z, T )

(3.22a)

The accuracy of the split-step Fourier method can be improved by sandwiching a non-

linear step with two halved dispersion steps over the same small distance ∆z

A(z + ∆z, T ) = e(DT∆z2

)e(N∆z)e(DT∆z2

)A(z, T ). (3.23)

This scheme is known as the symmetrized split-step Fourier method.

3.3 Self-Phase Modulation

To explain the effect of Kerr nonlinearity, only the SPM term in the nonlinear Schrodinger

equation will be considered. The resulting nonlinear Schrodinger equation becomes

∂Ap∂z

= −αp2Ap + jγp(|Ap|2)Ap. (3.24)

The solution of Eqn. (3.24) is

Ap(z + ∆z) = Ap(z)e−αp2zejγp

∫ z+∆zz |Ap(z)|2dz, (3.25)


where |Ap|2 is equivalent to the power of the optical pulse. The phase information is lost

by taking the absolute value of the amplitude, meaning that |Ap|2 represents the pulse

envelope. The above equation shows that the phase of the pump pulse is modulated

by the pulse envelope itself, leaving the temporal shape (amplitude) of the pump pulse

unchanged. Thus this effect is called self-phase modulation (SPM).

3.3.1 Maximum Nonlinear Phase Shift

Given a known n2 and a known Aeff , the conventional way to characterize the Kerr

nonlinearity of a medium at a certain wavelength is to find the maximum nonlinear phase

shift caused by SPM when a pulse having a peak power of Po is propagating through the

medium. However, the maximum nonlinear phase shift shown in Eqn. (3.25) depends

on the pump-pulse amplitude. In order to eliminate the dependence of the phase shift

on the absolute amplitude of the pump pulse, the pulse amplitude is normalized to its

maximum value, such that

Up(z, T ) =Ap(z, T )

|Ap(z, T )|, (3.26)

where the pump pulse reaches its maximum when T is zero (at the pulse center):

max Ap(z, T ) = |Ap(z, T = 0)| =√Poe

−αz2 . (3.27)

As a result, the maximum normalized amplitude of the pump pulse is unity, such that:

max Up(z, T ) = |Up(z, T = 0)| = 1. (3.28)

Through normalization, the spatial-dependent attenuation due to propagation loss can

be removed from the pulse amplitude, and thus the normalized pulse amplitude Up(z, T )

accounts for the pulse shape only, with a maximum value of unity. Then, Eqn. (3.24)

can be reduced to

∂Up(z, T )

∂z= jγpPoe

−αz|Up(z, T )|2Up(z, T ) (3.29)


As Up is now independent of z, the value of Up at 0 is the same as that at z, shown in

Eqn. (3.26), meaning that only phase change takes place during the spatial evolution of

the pulse amplitude. Thus, the normalized pulse amplitude at z can be written as

Up(z, T ) = Up(0, T )ejφNLp (z,T ), (3.30)

where φNLp (z, T ) is the phase of the pump pulse at z, while Up(0, T ) is the normalized

pulse amplitude at the input of the medium, as shown in Fig. 3.1. By substituting Eqn.

(3.30) into Eqn. (3.29), Eqn. (3.29) becomes

Up(0, T )∂

∂zejφ

NLp (z,T ) = jγpPoe

−αz|Up(0, T )ejφNLp (z,T )|2Up(0, T )ejφ

NLp (z,T ). (3.31)

Taking the finite integral on both sides from the lower limit z = 0 (input) to the upper

limit z = L (output), where L is the device length,

∂

∂zφNLp (z, T ) = γpPoe

−αz|Up(0, T )|2 =⇒∫ z=L

z=0

∂φNLp (z, T ) =

∫ z=L

z=0

γpPoe−αz|Up(0, T )|2dz,

(3.32)

where φNLp (0, T ) and φNLp (L, T ) are the nonlinear phase shifts of the pump pulse at the

input and output of the nonlinear medium, respectively:

φNLp (L, T ) = φNLp (0, T ) + |Up(0, T )|2 · γpPo∫ z=L

z=0

e−αzdz (3.33)

The finite integral in the last term of Eqn. (3.33)accounts for the attenuation of light

due to the optical loss inside the nonlinear medium, which reduces the effective length

of the medium, defined as

Leff =

∫ z=L

z=0

e−αzdz =1− e−αz

α(3.34)

From Eqn. (3.33), the nonlinear phase shift is maximum at the pulse center Up(0, 0). The

maximum change of phase shift of the optical pulse can be written as

∆φNLp,max = φNLp (L, T )− φNLp (0, T ) = γpPoLeff . (3.35)


The above equation shows that the maximum nonlinear phase shift is the product of the

nonlinear coefficient at the pump wavelength, the peak power of the incident pulse Po

and the effective length of the nonlinear medium Leff . It is generally used to quantify

the amount of the achievable Kerr nonlinearity for a fixed device length at a given pulse

power with a known nonlinear coefficient of the material at the pulse wavelength. For

example, in the XPM-based AOWC concerned in this thesis, the maximum nonlinear

phase shift required for error-free operation is below 0.5π radian.

Figure 3.1: Visualization of the coordinates of the pump pulse at the input and theoutput of the nonlinear medium.

3.3.2 SPM-induced spectral broadening

According to Eqn. (3.12), the phase of the electric field at the waveguide input is

θin(0, t) = θo(0, t)− φNLp (0, T ), (3.36)

while the phase of the electric field at the waveguide output is

θout(L, t) = θo(L, t)− φNLp (L, T ). (3.37)


The angular frequency of the electric field at the input is the derivative of the phase with

respect to t:

ωin =∂

∂t[θin(0, t)− φNLp (0, T )] (3.38a)

=∂

∂t[ωot− no(λ)ko · 0− φNLp (0, T )] (3.38b)

= ωo −∂

∂tφNLp (0, T ) (3.38c)

= ωo −∂

∂TφNLp (0, T )

∂T

∂t(3.38d)

ωin(T ) = ωo −∂

∂TφNLp (0, T ). (3.38e)

Similarly, the angular frequency of the electric field at the output, using Eqn. (3.33) and

Eqn. (3.34), is

ωout(T ) = ωo −∂

∂TφNLp (0, T )− γpPoLeff ·

∂

∂T|Up(0, T )|2. (3.39)

The frequency change, or commonly called frequency chirp, is defined as the output

angular frequency minus the input angular frequency

∆ω(T ) = ωout(T )− ωin(T ) (3.40a)

= −γpPoLeff ·∂

∂T|Up(0, T )|2. (3.40b)

From the above equation, the instantaneous optical frequency chirp is proportional to the

derivative of the temporal pulse profile, with a proportionality constant of −ΓpPoLeff ,

meaning that the frequency chirp can have two opposite signs. Moreover, ∆ω is a function

of the moving time-coordinate, the value of the frequency chirp depends on the pulse

shape.

Concenptually, on the rising edge of the pulse, Up(0, T ) is increasing, resulting in a

positive derivative of the temporal pulse profile. The frequency change is thus negative,

causing a red shift. Similarly, on the falling edge, a blue shift occurs. At the pulse center,

the frequency change is zero because the derivative of the temporal pulse profile is zero.


Figure 3.2: The time evolutions of the electric field in a Gaussian-shaped pulse withoutchirp (top) and with SPM-induced chirp after passing through a Kerr medium (bottom).

Thus the pulse spectrum is widened with a positive nonlinear coefficient. This effect is

known as SPM-induced spectral broadening.

Fig. 3.2 shows the time evolutions of the electric field of a Gaussian-shaped pulse

without chirp and with SPM-induced chirp after passing through a Kerr medium. In time

domain, however, the SPM-induced chirp does not change the temporal pulse envelope

in the absence of dispersion.

From Eqn. (3.40b), sharper pulses increase the SPM-induced spectral broadening. In

addition, the magnitude of frequency chirps is larger for higher peak pulse powers. Fig.

3.3 shows the SPM-induced spectral broadening of a pulse with different peak powers


corresponding to different maximum nonlinear phase shifts.

Figure 3.3: Normalized SPM-broadened spectra (normalized to the pulse spectral peakvalue) of the 2-ps unchirped Gaussian pump pulse at 1570 nm with different peak powersin a lossless nonlinear medium. Spectra are labeled by the maximum nonlinear phaseshift. The simulation was based on Mr. Sean Wagner’s Matlab code for the symmetrizedsplit-step Fourier method [138].

3.4 Cross-Phase Modulation

Cross-Phase Modulation (XPM) is also a third-order optical nonlinear process in which

the rising edge and the falling edge of a sufficiently intense optical pulse temporally

modulate the refractive index of the Kerr medium. A second optical wave at a different

wavelength will experience the corresponding index change, and thus be phase-modulated

when passing through the same medium.


In literature, there are three types of Cross-Phase Modulation (XPM): XPM between

an optical pulse and a CW at different wavelengths, XPM between two optical pulses at

different wavelengths as well as XPM between the two orthogonal polarizations of the

same pulse. In this thesis, XPM refers to the interaction between an optical pulse and a

continuous wave (CW) at two different wavelengths.

3.4.1 XPM-induced sidebands

In time domain, the intense optical pulse temporally modifies the refractive index of the

Kerr medium via SPM, and a CW at another wavelength experiences the corresponding

index change. In spectral domain, one may imagine that the CW carrier component is

shifted to longer wavelengths by the rising edge of a high-intensity pulse, and is then

shifted to shorter wavelengths by the falling edge of the same pulse. Experimentally, an

optical pulse train of a high repetition rate (∼MHz for the free-space optical parametric

oscillator; ∼ GHz for fiber-modelocked laser source in telecommunications), instead of

an individual pulse is being sent into a Kerr medium together with a CW at another

wavelength. The Optical Spectral Analyzer (OSA) and our human eyes are unable to

resolve the temporal movement of the CW carrier. Therefore, two sidebands are observed

on the CW carrier shown in Fig. 3.4.

Similar to SPM, sharper pump pulses can widen the XPM-induced sidebands on the

CW. A sharper pulse can be imagined as a higher peak power for a fixed pulsewidth.

Fig. 3.5 shows the XPM-induced sidebands on the CW with different peak pump pow-

ers corresponding to different maximum nonlinear phase shifts. From Eqn. (3.17), the

nonlinear phase shift induced by XPM is double of that induced by SPM.


Figure 3.4: The temporal and spectral visualization of XPM on the CW. The pulseenvelope without the corresponding electric field is shown at the top. The CW’s electricfield as well as its constant envelope is shown at the middle. The temporal movement ofthe CW carrier caused by XPM is shown at the bottom.

3.5 Mechanism of XPM-AOWC

In 1994, Rauchenbach [90] demonstrated XPM-AOWC in a nonlinear optical loop mirror

(NOLM) with a 4.5-km-long DSF as a nonlinear medium. Rauchenbach’s design, similar

to that of the SOA-MZI optical switch, utilized a NOLM serving as a single-arm interfer-

ometer to provide a switching window for a CW at another wavelength to pass through.

The maximum nonlinear phase shift required by the NOLM is π.

It was not until 2000 that Olsson [55] proposed the first AOWC via XPM converter

whose required maximum nonlinear phase shift can be much less than π2 [55]. Thus the

input pump power can be reduced.

2The wavelength converters based on MZI-SOA or on NOLM require a nonlinear phase shift of π,while those based on Olsson’s design do not require a fixed value of the nonlinear phase shift. The valueof the required nonlinear shift depends on the filter detuning, the filter shape as well as the pulse shape.Generally, the required nonlinear phase shifts can be less than π radian


Figure 3.5: Normalized spectra (normalized to the CW carrier maximum value) of XPM-sidebands on the CW at 1520 nm induced by the 2-ps unchirped Gaussian pump pulse at1570 nm with different peak powers in a lossless noinlinear medium.. Spectra are labeledby the maximum nonlinear phase shift defined in Section 2.2. The vertical axes are in dBscale. The simulation was based on Mr. Sean Wagner’s Matlab code for the symmetrizedsplit-step Fourier method [138].

3.5.1 Mechanism of Olsson’s design

Unlike MZI-SOI or NOLM, Olsson’s design does not rely on the interferometric technique

to create a switching window, but relies on the temporal movement of the CW carrier

induced by the strong pump pulses.

According to [55], a 40-Gb/s On-Off-Keying (OOK) data with a pulsewidth of 2

ps at 1536 nm is combined with a CW at 1540 nm and coupled into in a 10-km-long

dispersion shifted fiber (DSF), in which the rising edge and the falling edge of the marks

induces red chirp and blue chirp, respectively, thus forming XPM-sidebands on the CW,


shown in Fig. 3.6. The XPM-sidebands contain the same logics as the input pump data,

while the CW component always exists. A loop mirror filter, consisting of a short piece

of birefringent fiber in a Sagnac interferometer with a spectral transmission shown in

Fig. 3.7, is used as a notch filter to suppress the CW carrier, leaving two amplitude

modulated sidebands and the residual pump. The red sideband (longer wavelength)

originates from the derivative of the rising edge of marks and the blue sideband (shorter

wavelength) originates from the derivative of the falling edge of marks. The subsequent

bandpass filter blocks the residual data at the pump wavelength and selects one of the

XPM-sidebands, with a bandwidth matching the spectral width of the sideband. The

pulsewidth of the wavelength-converted output should ideally be shorter than the input

pulse due to the derivative origin of the XPM-sidebands.

Figure 3.6: Experimental setup of the XPM-AOWC, reproduced from [55].

Since low pump powers are unable to cause spectral broadening via SPM as well as

to induce XPM-sidebands on the CW, the low-intensity noise of the input data at the

pump wavelength will not pass to the wavelength-converted signal, shown in Fig. 3.7.


Figure 3.7: Transmission through the loop mirror filter from [55] (left) and illustration ofthe zero-noise cleaning by XPM-AOWC (right). The shaded region refers to the positionof the bandpass filter.

Figure 3.8: Dispersion-induced walk-off between the pulse and the CW. The CW travelsfaster than the pump pulse shown at the top. The CW travels slower than the pumppulse shown at the top. is shown at the bottom. The temporal evolution of the electricfield of the CW corresponds to the original pump pulse without walk-off, shown at themiddle.

3.5.2 Dispersion-induced walk-off

The dispersion-induced temporal walk-off between the pulse and the CW in a long dis-

persive nonlinear medium is destructive to XPM. As shown in Fig. 3.8, when the CW


travels faster than the pump pulse within the dispersion medium, the rising edge of the

pulse starts to temporally walk off from the previously XPM-induced red chirp on the

CW, and cannot keep generating red-chirp along the medium 3. As the pulse and the

CW propagate along the medium, the rising edge of the pulse overlaps the previously

XPM-induced blue chirp on the CW, resulting in a reduction or cancellation of blue

chirp. Thus, the XPM-induced spectral broadening on the CW is reduced. To avoid the

temporal walk-off between the pulse and the CW, the length of the dispersive nonlin-

ear medium must be shorter than the walk-off length. The walk-off length, using the

definition in Eqn. (3.7), is

LW = To/(D∆λ) (3.41)

where To is the 1/e half-width of the pump pulse, D is the dispersion coefficient of the

medium [ps/nm/km], ∆λ is the wavelength separation between the pump wavelength

and the CW wavelength.

3.5.3 Effect of duty cycle

In telecommunications, the duty cycle is defined as the ratio of the duration of marks

(logic one) to the duration of a bit slot. The effect of the duty cycle of the pump on the

XPM-sideband level is illustrated in Fig. 3.9, in which the XPM-sideband level is defined

as the maximum level of the XPM-sideband on the CW. As shown in the previous section,

the XPM-sidebands contain the same logic as the input data, and the corresponding level

should be as high as possible to prevent any noises from corrupting the sidebands.

In Fig. 3.9, the pump pulsewidth is kept constant so that the frequency chirp (the

degree of broadening)remains unchanged. For a smaller duty cycle, a smaller portion of

the CW carrier is being shifted towards the red side as well as the blue side. Thus, in

spectral domain, the XPM-sideband level is much lower than the CW peak level. As

3Without dispersion-induced walk-off, the rising edge of a pulse will red-shift the previously generatedred-chirp, making a broader XPM-sideband to ease the filtering requirement


Figure 3.9: Effect of the duty cycle of the pump pulses on the XPM-sideband level. Thepumps of smaller duty cycle and of larger duty cycle are shown at the top and at thebottom, respectively.

the duty cycle of the pump increases, a larger portion of the CW carrier is being shifted

towards the red side as well as the blue side. Therefore, in the spectral domain, the

XPM-sideband level grows higher and closer to the CW peak level for a larger duty

cycle.

It implies that XPM-AOWC in a passive nonlinear medium can have a good per-

formance at higher-bitrate OTDM systems in which picosecond pulses induce broader

XPM-sidebands for filtering while the larger duty-cycle makes the XPM-sideband level

higher, allowing a higher signal-to-noise ratio at the output.


3.6 Summary

In this chapter, chromatic dispersion and Kerr effect were conceptually introduced. By

using the nonlinear Schrodinger equation, the maximum nonlinear phase shift is defined

to characterize the achievable Kerr effect in a nonlinear device. It depends on the pump

peak power, the nonlinear coefficient and the effective length of a device. The SPM-

induced spectral broadening of a pump pulse and the XPM-induced sidebands on a CW

corresponding to different maximum nonlinear phase shifts have been simulated using

the symmetrized split-step Fourier method. The mechanism of XPM-AOWC by Olsson

was then explained in details. The cascaded filtering in the XPM-AOWC is responsible

for CW carrier suppression, XPM-sideband selection and pump blocking in order to

obtain the wavelength-converted data at the output. The device length is limited by

the dispersion-induced walk-off length to maintain observable XPM-sidebands. The duty

cycle of the pump data must be large enough such that more energy on the sidebands can

be filtered out, suggesting that XPM-AOWC is suitable for high-speed OTDM systems.

Chapter 4

Optical Properties of AlGaAs

4.1 Introduction

Before designing optical communication devices based on Kerr effect, it is necessary to

find a suitable material to maximize the achievable amount of nonlinear phase shift. This

depends mostly on the strength of Kerr nonlinearity1, the amount of power that can be

delivered to the device, and the level of optical confinement in the waveguide. However,

any optical losses in a material also limit the Kerr effect by reducing the power available

for generating phase changes. Thus, it is necessary to take into account both the linear

and the nonlinear losses when evaluating a nonlinear material for Kerr-based AOWC.

In this chapter, off-resonance2 figure of merits will be defined to quantify the perfor-

mances of the constitutive materials used in optical devices. The basic optical properties

of AlGaAs such as bandgap, refractive index, nonlinear refractive index and nonlinear

absorption coefficient will be discussed.

1The strength of Kerr nonlinearity of a material is usually represented by the nonlinear refraction n2.2”Off-resonance” here refers to the incident photon energies that are below the material’s bandgap.

48

Chapter 4. Optical Properties of AlGaAs 49

4.2 Figure of merit for materials

By ignoring the linear loss due to scattering, the attenuation of the optical intensity due

to absorption inside a medium can be characterized by a total absorption coefficient

α = α1 + α2I + α3I2, (4.1)

where α1 is the single-photon absorption coefficient, α2 is the two-photon absorption

coefficient, α3 is the three-photon absorption coefficient of the material.

To quantify and compare the performances of different materials in terms of their

nonlinearities and absorption losses, figure of merits are defined based on a fixed nonlinear

phase shift for a certain nonlinear process. Historically, a nonlinear phase shift of 4π

required by a half-beat-length nonlinear directional coupler (NLDC) is used [97] as a

bench mark.

For optical devices that are operated at resonance wavelengths, the single-photon

interband transition will be the major contribution to the attenuation of the optical

intensity propagating along the device length, disregarding the scattering loss inside the

devices. In this thesis, figure of merits are defined only for the materials operating below

the bandgap. In the following, figure of merits will be separated into three different cases,

depending on which absorption mechanism is dominant at the operating wavelengths.

4.2.1 Limitation due to linear absorption

Once the operating wavelength is detuned from the resonance wavelengths, the interband

single-photon transition should theoretically disappear while the Kerr nonlinearity will be

dominant. In reality, impurities or defects introduce additional energy states that allow

carriers to transit from the ground state to these excited states, leading to a significant

amount of photon absorption. Thus, the key parameters limiting the device performance

are the low-power absorption coefficient α1 and the maximum (saturated) index change

∆nsat. The saturating effect will limit the maximum change of the refractive index, i.e.


once the impurity or defect states are filled up with carriers, further increase in optical

powers will not induce any single-photon absorption3. Thus, increasing input powers

cannot further increase the nonlinear phase shift.

Assuming that the linear absorption dominates the overall loss and limits the effective

device length4, such that

α = α1, (4.2a)

and Leff ∼1

α1

(4.2b)

and assuming that the index change induced by the linear absorption dominates that

induced by the nonresonant Kerr nonlinearity, the nonlinear phase shift can be, using

Eqn. 3.35, approximated by

∆θNL =2π

λ∆n

1

α1

. (4.3)

The figure of merit for single photon absorption W is defined as the normalized phase

shift for a nonlinear directional coupler whose minimum required nonlinear phase shift

is 4π:

W =∆θNL

2π> 2 (4.4a)

=⇒ W =∆n

λα1

> 2 (4.4b)

This condition also defines the mimimum required value of ∆nsat. Both a larger α1 and

a larger ∆nsat mean that the material contains a larger amount of impurities or defects.

The response of the material may be thus slower due to the finite carrier lifetime in the

trap states. Therefore, W should be as large as possible to guarantee that the constitutive

material is of good quality and has a fast response.

3By using Kramers-Koenig transformation, photon absorption correspond to refractive index change.The resonance effect caused by photon absorption will increase the material’s nonlinearity

4The effective length of a lossy device is defined by Leff = 1−e−αLα < 1

α , where L is the actual devicelength. The effective length will simply be approximated by Leff ∼ 1

α


4.2.2 Limitation due to TPA

Assuming that the two-photon absorption5 dominates the overall loss and limits the

effective device length, such that

α = α2I, (4.5a)

and Leff ∼1

α2I(4.5b)

then the nonlinear phase shift can be approximated by

∆θNL =2π

λn2I

1

α2I. (4.6)

The figure of merit for two-photon absorption T 6 is defined as the inverse of the normal-

ized phase shift for a nonlinear directional coupler whose minimum required nonlinear

phase shift is 4π:

T =2π

∆θNL< 0.5 (4.7a)

=⇒ T =2α2λ

n2

< 1 (4.7b)

Another figure of merit for TPA [68] is defined as the normalized phase shift for optical

switching in MZI whose minimum required nonlinear phase shift is 2π:

n2

α2λ> 1 (4.8)

In general, for a larger required nonlinear phase shift, a smaller T must be required to

realize a practical device. Specifically, when T increases to values larger than unity, the

power required for switching rises, the switching becomes incomplete, and the throughput

drops dramatically [92]. Fig. 4.1 shows the figure of merit T as a function of the photon

energy normalized to the semiconductor bandgap, which is derived from the analytical

form of the dispersion of n2 and α2 proposed by Sheik-Bahae and co-workers [112]. The

5For the detailed description of two-photon absorption, please refer to Section 6.2 Nonlinear Absorp-tion.

6From now on, T is re-defined and different from the moving time-coordinate in Section 3.


Figure 4.1: Figure of merit T as a function of photon energy normalized to the bandgapof a semiconductor [92]

value of T shown in Fig. 4.1 was calculated based on the value of the photon energy rela-

tive to the bandgap energy, which is independent of material’s exact bandgap structure,

bandgap degeneracy, and additional states introduced by defects.

For photon energies less than the half-bandgap energy, α2 (and thus T ) is theoretically

equal to zero in Sheik-Bahae’s model. If exciton features and the existence of defect and

trap states in the bandgap are taken into account, α2 will not be zero for some wavelengths

below the half-bandgap [92]. As the photon energy reaches the half-bandgap, T becomes

greater than unity. This suggests that the material should be operated at below the

half-bandgap in order to use the non-resonanat nonlinearity of semiconductors with low

TPA.


4.2.3 Limitation due to 3PA

Assuming that the three-photon absorption7 dominates the overall loss and limits the

effective device length, such that

α = β2[I(5)]2, (4.9a)

and Leff <1

β2[I(5)]2, (4.9b)

where I(5) =|A|2

A(5)eff

(4.9c)

is the optical intensity corresponding to the fifth-order nonlinear effect, A(5)eff is the fifth-

order effective core area8, and |A|2 is the optical power9. Then the nonlinear phase shift

can be approximated by

∆θNL =2π

λn2I

(3) 1

β3[I(5)]2(4.10a)

where I(3) =|A|2

A(3)eff

(4.10b)

is the optical intensity corresponding to the third-order nonlinear effect, A(3)eff is the third-

order effective core area. The figure of merit for three-photon absorption is defined as the

inverse of the normalized phase shift for a nonlinear directional coupler whose minimum

required nonlinear phase shift is 4π:

V =2π

∆θNL< 0.5 (4.11a)

=2π

2πλn2|A|2

A(3)eff

1

β3[|A|2

A(5)eff

]2

< 0.5 (4.11b)

=⇒ V =β3λ

n2

A(3)eff

[A(5)eff ]2

< 0.5 (4.11c)

7For the detailed description of three-photon absorption, please refer to Section 6.2 Nonlinear Ab-sorption.

8for the mathematical derivation of the fifth-order effective core area, please refer to Section 6.1Nonlinear Absoprtion.

9|A|2 refers to the peak power and to the average power for optical pulses and CWs, respectively.


Unlike T in Eqn. (4.11c), V depends not only on the optical properties of materials, but

also on the physical structures of waveguides.

Figure 4.2: Normalized transmission in the bar state (dashed curve, left scale) and switch-ing power (solid curve, right scale) versus V for CW inputs in a half-beat-length nonlineardirection coupler [100].

A comprehensive model using the coupled-mode theory for a nonlinear directional

coupler was used by Yang [100] to simulate the normalized transmission in the bar state

versus the figure of merit V, shown in Fig. 4.2. The figure of merit V was found to be

upper-bounded by 0.68 for at least 50% transmitted (switched) power.

4.3 Optical properties of AlGaAs

Aluminum gallium arsenide (AlxGa1−xAs) is a III-V alloy semiconductor in which the

variable x in the formula is a value between 0 and 1, indicating an arbitrary alloy be-

tween gallium arsenide (GaAs) and aluminium arsenide (AlAs). At normal pressure,

AlxGa1−xAs forms crystals with a cubic, zinc-blende structure. Simply speaking, the

zinc-blende structure is a diamond structure in which the displaced lattice atoms are

different from the original lattice atoms, as shown in Fig. 4.3. Crystals such as GaAs,

GaP , AlAs, InAs, InSb belong to the zinc-blende structure. The lattice constant a for

a zinc-blende crystal is defined by the length of the face-centered cube edge. At room


Figure 4.3: (a) Face-centered cubic lattice, (b) the diamond crystal lattice is obtained bydisplacing the lattice atoms of (a) by (a/4, a/4, a/4). Therefore, the diamond structurebelongs to the face-centered cubic (FCC) structure. (c) when the displaced lattice atomsare different from the original lattice atoms, the crystal structure is called the zinc-blendecrystal structure.

temperature (300 K), the stress-free lattice constants of GaAs and AlAs are 5.6605 A

and 5.6533 A, respectively [105]. The difference in lattice constants (also called strain or

misfit) between GaAs and AlAs is ∼ 0.13 %. GaAs has a direct bandgap ( Γ1c−Γ15v)10 of

Figure 4.4: The band structures of GaAs [107] (left) and AlAs [103] (right).

1.42 eV [105] while AlAs has an indirect bandgap (X1c−Γ15v) of 2.13 eV [103] as shown

in Fig. 4.4. According to Vegard’s law, the material properties of ternary alloys such as

lattice constant, bandgap, refractive index etc. can be adjusted smoothly by changing

the doping concentration [105]. Thus, the bandgap of AlxGa1−xAs can be engineered

10The direct bandgap Γ1c − Γ15v of GaAs corresponds to Γ6c − Γ8v in [111] based on a more compre-hensive band-structure calculation.


between 1.42 eV (GaAs’s direct bandgap) and 2.13 eV (AlAs’s indirect bandgap) [108],

depending on the aluminum concentration. According to Casey [108, 105], the bandgap

(eV ) of the alloy AlxGa1−xAs on x is

Eγg (x) =

1.424 + 1.247x if x ≤ 0

1.424 + 1.247x+ 1.147(x− 0.45)2 if x > 0

(4.12a)

EXg (x) = 1.900 + 0.125x+ 0.143x2 (4.12b)

ELg (x) = 1.708 + 0.642x (4.12c)

(4.12d)

where Eγg (x), EX

g (x) and ELg (x) are the energy bandgaps between the valence band

maximum inside the Brillouin zone and the conduction band minima at Γ-valley, X-valley

and L-valley, respectively. Fig. 4.5 and Fig. 4.6 illustrate the evolution of the bandgaps

with aluminum concentration in AlxGa1−xAs. When x is smaller than 0.45, the bandgap

is direct because the conduction band minimum at X-valley is higher than that at Γ-

valley. When x is larger than 0.45, the bandgap is indirect because the conduction band

minimum at X-valley is lower than that at Γ-valley. The crossover point at x = 0.45

occurs when the conduction band minimum at X-valley lies on the same energy level as

that at Γ-valley [108, 109].

4.3.1 Large tailorable range of refractive index

The refractive index of AlxGa1−xAs depends on the concentration of aluminum in the

material. For instance, it changes from 3.34 and 3.03 when the Al-concentration varies

from 10% to 70% at 1550 nm, which is calculated using the empirical model by Gehrsitz

[117].

Such high index contrast of 0.3 enables different kinds of integrated nonlinear op-

tics. For XPM-AOWC, the index contrast between the high-index guiding layer and

the cladding layers of the waveguide can be made sufficiently large by optimizing the


Figure 4.5: Bandgap energies corresponding to the valence band maxima and the con-duction band minima of Γ-Valley, X-valley and L-valley as a function of aluminum con-centration x in AlxGa1−xAs. Transition from direct to indirect bandgap takes place whenx is 0.45.

Figure 4.6: Evolution of bandgaps in AlxGa1−xAs as x increases.

Al-concentration and the waveguide structure, enabling single-mode propagation with a

strong confinement of light. Thus the required input power for nonlinear optical pro-

cesses can be lowered or the device length can be reduced to avoid significant pulse-walk

off caused by the material dispersion of AlGaAs and to make devices more compact.

Moreover, the high index contrast provided by AlGaAs also offers flexibility in waveg-

uide design. Examples include FWM-AOWC, supercontinuum generation and wideband

parametric amplification in chalcogenide and silicon, in which the waveguide dispersion


Figure 4.7: The refractive index of AlGaAs with different Al-concentration as a func-tion of wavelengths, calculated by the empirical model by Gehrsitz [117]. The legendrepresents the percentage of aluminium concentration in AlGaAs.

can compensate or reduce the material dispersion within a certain range of wavelengths,

allowing broadband coherent processes [118, 119, 120, 121, 122, 123]

4.3.2 Ultrafast response and high nonlinearity

Since the 1990’s, the optical properties of AlGaAs having 18%-aluminum concentration

such as two-photon absorption and three-photon absorption at telecommunication wave-

lengths have been experimentally studied by Villeneuve [101] and Kang [94], respectively.

After the low-absorption window within the C-band had been found, a precise measure-

ment of the nonlinear refractive index n2 of Al0.18Ga0.82As was done by Aitchison in

1997 [115]. In this thesis, Al0.18Ga0.82As is chosen to be the nonlinear medium for XPM-

AOWC within the C-band.

Al0.18Ga0.82As has a direct bandgap of 1.648 eV, and the telecommunication wave-

lengths lies below the half-bandgap of the material. The corresponding optical non-

linearity does not involve resonant electronic transition, and thus the material has an

ultrafast response within C-band. The strength of the nonresonant nonlinearity becomes


Figure 4.8: The measured dispersion of n2 for the TE-polarized mode (solid dots) andthe TM-polarized mode (solid triangles) for Al0.18Ga0.82As [115]

smaller towards longer wavelengths, as shown in Fig. 4.8. From [115], the nonlinear

refractive indices n2 of Al0.18Ga0.82As for TM and TE modes at 1550 nm were found

to be 1.43 × 10−17m2/W and 1.5 × 10−17m2/W , respectively. In general, the nonlinear

refractive index of Al0.18Ga0.82As is ∼ 650 times higher than that of silica, ∼ 4 times

higher than that of As2S3 chalcogenide glass and ∼ 3 times higher than that of silicon

at 1550 nm.

Fig. 4.9 shows the comparison between the nonlinear phase shifts versus input peak

power in AlGaAs waveguides and As2S3 waveguides having the same effective core area

of 7 µm2. When the waveguide length is 5 cm, AlGaAs waveguides with a linear loss of 5

dB/cm can achieve a similar nonlinear phase shift as that achieved by As2S3 waveguides

with a linear loss of 0.1 dB/cm at a certain input peak power(Note that the linear loss

here refers to the scattering loss caused by surface roughness). It suggests that, compared

to silicon and As2S3, AlGaAs’s high nonlinearity can make waveguides more tolerant of

linear losses, thus lowering the requirement on fabrication quality. When the waveguide

length is reduced to 1 cm, the nonlinear phase shift achieved by an AlGaAs waveguide

with a linear loss of 10 dB/cm is 0.5π larger than that achieved by As2S3 waveguides

with a linear loss of 0.1 dB/cm at a certain input peak power, meaning that AlGaAs’s


high nonlinearity can make devices more compact.

Figure 4.9: Nonlinear phase shift versus input peak power for a 1-cm-long (left) and a5-cm-long (right) waveguides having effective core areas of 7 µm2 respectively. The redand the blue lines represent the linear loss of 0.1 dB/cm in Al0.18Ga0.82As and As2S3

chalcogenide glass respectively. The black and green lines represent the linear loss rangingfrom 1 to 10 dB/cm in Al0.18Ga0.82As and As2S3 chalcogenide glass, respectively

4.3.3 Low nonlinear absorption and figure of merit

Nonlinear absorption of an optical device depends on the material bandgap energies as

well as the allowable energy states formed by the device structure. For optical commu-

nications, the constitutive materials in fibers or waveguides with larger bandgaps can be

chosen to eliminate nonlinear absorption within C-band. Examples include silica, bis-

muth oxide and tellurite oxide whose direct or indirect bandgaps lie on UV or visible

light regions. However, the strength of nonresonant nonlinearity will decrease accord-

ingly. Therefore, the constitutive materials for nonlinear processes should be so chosen

that the C-band overlaps the low-absorption-loss spectral window between the one-half

and the one-third bandgaps of the materials (Eg/2 > hν > Eg/3) in order to eliminate

TPA as well as to maximum the nonresonant nonlinearity.

From [94], the one-half and the one-third bandgaps of Al0.18Ga0.82As correspond

to 1.5 µm and 2.25 µm, respectively. At 1550 nm, the TPA and 3PA coefficients of


Al0.18Ga0.82As for TM mode were found to be 0.2 cm/GW and 0.06 cm3/GW 2, respec-

tively, as shown in Fig. 4.10.

To quantify a material for nonlinear processes, the figure of merits T and V of

Al0.18Ga0.82As were plotted as Fig. 4.11, showing that the low-absorption spectral win-

dow lies on the C-band. At 1550 nm, T and V of Al0.18Ga0.82As were found to be 0.2

and 0.1, respectively, which fulfilled the conditions T < 1 and V < 0.68.

Figure 4.10: Left: Experimental values of TPA coefficient as a function of wavelength forthe TE-polarized mode (solid circles) and the TM-polarized mode (open circles) in anAlGaAs waveguide having a 1.5 µm-thick Al0.18Ga0.82As guiding layer. Right: Experi-mental values of 3PA coefficient for the TE-polarized mode as a function of wavelengthin an AlGaAs waveguide having a 1.5 µm-thick Al0.18Ga0.82As guiding layer[115].

Figure 4.11: Left: Wavelength dependence of the figure of merit T for TE- and TM-polarized modes in an AlGaAs waveguide having a 1.5 µm-thick Al0.18Ga0.82As guidinglayer. Right: The low-nonlinear-absorption spectral window of Al0.18Ga0.82As [115].


4.4 Conclusion

In this chapter, figure of merits for materials used for nonlinear processes were defined.

The conditions of low-absorption loss (W > 2, T < 1, V < 0.68) must be fulfilled by the

constitutive materials in order to make the nonlinear effects efficient.

Al0.18Ga0.82As is chosen to be the nonlinear medium for XPM-AOWC due to its ultra-

fast high nonlinearity, low two-photon and low three-photon absorption at telecommuni-

cation wavelengths. The low-absorption-loss spectral window of Al0.18Ga0.82As overlaps

the C-band, which was experimentally verified by previous work [115]. The figure of

merits T and V were found to be 0.2 and 0.1, respectively. The large tailorable refractive

index of AlGaAs allows a tighter confinement of light inside the highly nonlinear and

low-loss Al0.18Ga0.82As core, resulting in a reduction of input powers or device lengths.

Chapter 5

Wafer Design and Waveguide

Fabrication

5.1 Introduction

In this chapter, an AlGaAs wafer is designed such that the effective core area and the

nonlinear absorption of the waveguide are minimized for a single-mode operation. Thus,

the required input power for Kerr-based wavelength conversion at telecommunication

wavelengths can be reduced. Dr. Ksenia Dolgaleva, of the University of Toronto, is

responsible for wafer design, waveguide design and waveguide fabrication. The general

criteria for designing the wafer composition are introduced in Section 5.2. Based on

the optimized wafer composition [126, 125, 115] supported by simulation results shown

in Section 5.3, the AlGaAs wafer1 was grown by the Canadian Photonics Fabrication

Centre (CPFC), followed by waveguide fabrication at the University of Toronto with an

appropriate strip-loaded geometry shown in Section 5.4.1, 5.4.2 and 5.4.3. Lastly, the

effective core area of the finished waveguide is estimated in Section 5.5.

1Only the AlGaAs epitaxial layers were grown by CPFC on a GaAs substrate

63

Chapter 5. Wafer Design and Waveguide Fabrication 64

5.2 General Criteria for Wafer Design

Based on a previous wafer design [125, 126], the AlGaAs wafer consists of three layers.

The top cladding will be patterned and etched by a combination of standard photolithog-

raphy and reactive ion etching to form a strip-loaded waveguide. In 1994, the strip-loaded

waveguides were fabricated by Stegeman [126] on a wafer with a 1.5-µm-thick upper

cladding, a 1.5-µm-thick guiding layer and a 4-µm-thick lower layer that contained 24%,

18% and 24% of aluminum, respectively, resulting in a minimum2 effective area of 12 µm2

for the fundamental mode. After an year, the strip-loaded waveguides were fabricated

by Villeneuve [125] on a wafer whose 1.5- µm-thick upper cladding, 1-µm-thick guiding

layer and 4-µm-thick lower layer contained 30%, 18% and 40% of aluminum, respectively,

resulting in a minimum effective area of 6 µm2 for the fundamental mode. In this section,

using the wafer structure proposed in [125], suitable Al-concentrations for each layer in

an AlGaAs wafer will be found based on the following criteria:

1. According to [125, 126], the high-index guiding layer of the wafer should be chosen

to have 18% of aluminum, leading to a bandgap of 750 nm, with the corresponding

half-bandgap at 1550 nm. Related experiments showed that both the two-photon

absorption-loss (2PA) and three-photon absorption (3PA) are minimized at 1550

nm, providing a low-nonlinear-absorption spectral window between 1530 nm and

1550 nm for optical communications shown in Fig. 4.11 (right).

2. The index contrast between the high-index guiding layer and the lower cladding

should be sufficiently high such that the light within C-band is well confined within

the guiding layer, avoiding leakage loss to the high-index GaAs substrate. The

thickness of the lower cladding is usually designed to be 4 µm to isolate the guiding

layer from the GaAs substrate to minimize the leakage loss.

2In the paper, the minimum effective area was obtained by optimizing the waveguide width and theetch depth.


3. The index contrast between the upper cladding and the high-index guiding layer

should be sufficiently high to prevent the mode field from extending to the waveg-

uide sidewalls (i.e. to achieve sufficiently strong lateral mode confinement), so that

the linear loss due to light scattering by the sidewall roughness can be minimized.

4. Considering the circular Gaussian beam coming out from commercial lensed fibers,

the two index contrasts mentioned above should be small enough to make the mode

shape as circular as possible, reducing the coupling loss due to the mode-shape

mismatch between the lensed-fiber spotsize and the waveguide core size.

5.3 Simulation Results for Wafer Design

Starting from the optimized AlGaAs wafer structure and composition in [125], simula-

tions using Lumerical MODE Solutions 3.0 as well as Rsoft FemSIM 3.1 were done

at 1550 nm to calculate the effective mode areas of the waveguide with different widths.

Rsoft BeamPROP 8.1 was used at the beginning, but the corresponding results show

a large difference from those simulated using Lumerical MODE Solutions. As the

Finite Element Method (FEM) is suitable for solving the modes of high-index-contrast

waveguides, using Rsoft FemSIM gave results closer to those simulated by Lumerical

MODE Solutions.

The discrete refractive indices (Fig. 4.7) corresponding to 18%, 20%, 24%, 30%, 40%,

50% and 70% of aluminum, calculated by Gehrsitz’s model [117], were selectively used for

reducing computational time. The simulation results show that different wafer composi-

tions have a minimum effective mode area when the waveguide width is close to 2 µm.

Besides, the effective core area of the TM modes is usually smaller than that of the TE

modes in most of the wafer compositions. In the following, the waveguide’s etch depth

is chosen to be 1.35 µm for simulations. The notation ”40-18-30” represents a wafer

whose 1.5-µm-thick upper cladding, 1-µm-thick guiding layer and 4-µm-thick lower layer


consist of 30%, 18% and 40% of aluminum, respectively. Only the TM modes of different

wafer compositions corresponding to a waveguide width of 2 µm and an etch depth of

1.35 µm were chosen for comparison in order to find a wafer composition with a minimal

effective core area based on the aforementioned design criteria.

Figure 5.1: Effective core areas as a function of waveguide widths for 40-18-30 (left top)and 40-18-24 (right top), and the simulated mode shapes of the 2-µm-wide waveguidesin the TM and TE modes for 40-18-30 (left bottom) and 40-18-24 (right bottom). Thewaveguide’s etch depth is chosen to be 1.35 µm for simulation. The values of the effectivecore area calculated using Lumerical MODE Solution were reproduced from Dr. KseniaDolgaleva’s design and the corresponding results.

Fig. 5.1 (left top) shows that the 40-18-30 wafer gives out an elliptical spatial profile

and an effective core area of 3.94 µm2. Considering the circular mode shape of the

commercial lensed fiber, the index contrast between the upper cladding and the high-

index guiding layer was reduced from 0.0620 to 0.0319 by decreasing the Al-concentration


of the upper cladding from 30% to 24%, shown in Fig. 5.1 (right). This results in a more

circular mode shape having an effective mode area of 3.8 µm2 shown in Fig. 5.1 (right

bottom) Next, based on the wafer 40-18-24, the Al-concentration of the lower cladding

Figure 5.2: Effective core areas as a function of waveguide widths for 24-18-24 (left top),50-18-24 (middle top) and 70-18-24 (right top), and the simulated mode shapes of the2-µm-wide waveguides in the TM and TE modes for 24-18-24 (left bottom) , 50-18-24(middle bottom) and 70-18-24 (right bottom). The waveguide’s etch depth is chosento be 1.35 µm for simulation. The values of the effective core area calculated usingLumerical MODE Solution were reproduced from Dr. Ksenia Dolgaleva’s design and thecorresponding results.

was changed to 24%, 50% and 70%, making index contrasts of 0.0319, 0.1583 and 0.2537

with the high-index guiding layer, respectively, to investigate the effective mode area in

Fig. 5.2 (top) as well as the mode shape shown in Fig. 5.2 (bottom). At the waveguide

width of 2 µm, the effective mode areas for 24-18-24, 50-18-24 and 70-18-24 are 8.59

µm2, 3.49 µm2 and 3.24 µm2, respectively. Since 24-18-24 gives a much larger effective

mode area compared to 50-18-24 and 70-18-24, with a substantial amount of mode field

extending to the lower cladding, the wafer 24-18-24 was not considered.

As the effective mode area of 70-18-24 is smaller than that of 50-18-24, the Al-


Figure 5.3: Effective core areas as a function of waveguide widths for 70-18-20 (left top)and 70-18-40 (right top), and the simulated mode shapes of the 2-µm-wide waveguidesin the TM and TE modes for 24-18-20 (left bottom) and 70-18-40 (right bottom). Thewaveguide’s etch depth is chosen to be 1.35 µm for simulation. The values of the effectivecore area calculated using Lumerical MODE Solution were reproduced from Dr. KseniaDolgaleva’s design and the corresponding results.

concentration of the lower cladding and the guiding layer of 70-18-24 were fixed while

the Al-concentration of the upper cladding was changed to 20% and 40%, making index

contrasts of 0.0108 and 0.1102 with the high-index guiding layer, respectively. Fig. 5.3

(top) shows the variation of effective area, while the changes in mode shape of the 2-µm-

wide waveguides are shown in Fig. 5.3 (bottom). For the waveguide width of 2 µm , the

effective mode areas for 70-18-20 and 70-18-40 are 3.26 µm2 and 3.47 µm2, respectively,

slightly larger than that in 70-18-24. The mode field of 70-18-20 extends substantially to

the upper cladding, leading to a high linear loss due to light scattering by the waveguide


sidewall roughness. Moreover, both 70-18-20 and 70-18-40 give elliptical mode shapes,

and hence the wafer compositions of 70-18-20 and 70-18-40 were not considered further.

From the simulation results, 50-18-24 and 70-18-24 give more circular mode shapes

and smaller effective areas of 3.49 µm2 and 3.24 µm2, respectively, compared to other

wafer compositions. The wafer 50-18-24 was finally chosen as the optimized wafer com-

position for Kerr-based wavelength conversion at telecommunication wavelengths, since

its slightly larger effective core area (3.49 µm2) compared to 70-18-24 (3.24 µm2) helps

reduce the fiber-to-waveguide coupling loss3.

5.4 Waveguide Design and Fabrication

In this section, simulations using Lumerical MODE Solutions will be re-visited using

Al-compositions of the finished wafer received from the the Canadian Photonics Fabrica-

tion Centre (CPFC). According to the information given by the CPFC, the guiding layer

of the grown wafer contained 20% of aluminum, slightly different from the desired 18%.

An optimized value of the waveguide etch depth will be obtained for a minimal effective

core area in single-mode propagation.

5.4.1 Waveguide Design

Simulations on effective mode areas versus different waveguide widths and etch depths

were repeated for the modified wafer composition 50-20-24 using Lumerical MODE Solu-

tions. The etch depth of the waveguide can be adjusted in the fabrication process. Fig.

5.4 and Fig. 5.5 show that a larger etch depth results in a stronger mode confinement or

a smaller effective mode area, thus enhancing the nonlinear phase shift for Kerr-based

optical signal processing. Another set of simulation results was also done for the modi-

3The commercially available lensed fibers from OZoptics, Ottawa, have a spotsize (mode field diam-eter) of 2.5 µm, corresponding to a effective circular mode area of 4.91 µm2


Figure 5.4: Effective core areas as a function of waveguide widths for the TE mode usingthe 50-20-24 wafer calculated using Lumerical MODE Solution 3.0. The correspondingscript for simulation can be found in Appendix B.

Figure 5.5: Effective core areas as a function of waveguide widths for the TM mode usingthe 50-20-24 wafer calculated using Lumerical MODE Solution 3.0. The correspondingscript for simulation can be found in Appendix B.

fied wafer composition by varying the waveguide width and the etch depth and in order

to investigate the single-mode behavior, as shown in the shaded region in Fig. 5.6. Only

the fundamental TM modes were considered due to their smaller effective core areas com-

pared to the fundamantal TE modes. A larger etch depth, say, 1.4 µm, can reduce the


effective core area, but the waveguide will thus support multiple modes if the waveguide

width is larger than 2.5 µm. To assure a single-mode operation with tolerance on fabri-

cation error as well as with a minimum effective core area, the etch depth and the width

of our waveguide were chosen to be less than or equal to 1.2 µm and 2 µm, respectively.

Figure 5.6: The values of the effective mode area ( in µm2) for the fundamental TM modeare shown for different waveguide ridge heights and widths of the AlGaAs strip-loadedwaveguides with the designed wafer composition. The shaded region of the table refersto single-mode operations (This table/figure was given by Dr. Ksenia Dolgaleva).

5.4.2 Finished Wafer Information

The AlGaAs wafer with the designed composition has been grown by a metal-organic

chemical vapor deposition (MOCVD) technique at the Canadian Photonics Fabrication

Centre (CPFC). A 200-nm-thick layer of SiO2 was pre-deposited on the wafer surface

via Plasma-Enhanced Chemical Vapor Deposition (PECVD), serving as a hard mask for

AlGaAs-etching. The schematic of the finished wafer is shown in Fig. 5.7(a).

5.4.3 Waveguide Fabrication

After waveguide design, standard photolithography was used to transfer the waveguide

pattern onto the top-cladding of the AlGaAs wafer. Dr. Ksenia Dolgaleva is responsbile

for waveguide fabrication using the SiO2-etching recipe given by Mr. Bhavin Bijlani.


A commercial positive photoresist S1818 was first spin-coated on top of the 200-nm-

thick SiO2 layer covering the small samples cleaved from the AlGaAs wafer (Fig. 5.7, b).

A photomask, designed to have 8 series of waveguides with different widths ranging from

1.5 to 5 µm with a 0.5-µm step change, was then used for UV-light exposition of the

photoresist (Fig. 5.7, c). After the development of the photoresist using MF321 (Fig.

5.7, d), the SiO2 layer was anisotropically dry-etched (Fig. 5.7, e) via reactive ion etching

(RIE) with inductively coupled plasma (ICP), based on Mr. Bhavin Bijlani’s recipe. The

dry-etched SiO2 layer was subsequently treated in gaseous buffered oxide for 30 seconds

to smoothen the edges, while the residual photoresist layer was stripped off. The resulting

waveguide pattern in the SiO2 layer serves as a hard mask for the subsequent AlGaAs

etching. Finally, the sample’s top-cladding was anisotropically dry-etched, using a Trion

Minilock etcher via RIE with BCl3, chlorine and ICP, for 50 seconds (Fig. 5.7, f). The

finished waveguide was cleaved to 1 cm long with a diamond scriber and whose etch depth

was measured to be ∼ 1.2 µm using the scanning electron microscope (SEM) shown in

Fig. 5.8. The schematic of the device structure is shown in Fig. 5.7 (g). The refractive

index profile and the mode image of the 2-µm-wide AlGaAs waveguide with a depth of

1.2 µm simulated by Lumerical MODE solution at 1550 nm are shown in Fig. 5.9

5.5 Estimated Effective Mode Area

The spatial profiles of guided modes and effective indices of the finished sample were

determined using Lumerical MODE Solutions. The mode solver was set in two-

dimensional mode with a mesh of 250 × 250 points over a simulation area of 20 µm

× 8 µm with metal boundaries. Perfectly matched layer (PML) was also chosen as the

boundary condition to repeat the simulation, and the corresponding values of the simu-

lated effective core areas were close to that of using metal boundaries. The effective core

area is defined as the third-order effective area of the single mode of the waveguide at


1550 nm, as shown in Eqn. (3.11). The calculated effective mode areas of the 2-µm-wide

waveguide are ∼ 4.3 µm2 in the TM mode and ∼ 5 µm2 in the TE mode, corresponding

to nonlinear coefficients of 13.3 /W/m and 12.3 /W/m at 1550 nm, respectively.

Errors in estimating the effective core areas were mainly due to the uncertainty in

determining the waveguide etch depth. Fig. 5.4 and Fig. 5.5 show the effective mode area

for the TE and TM modes, respectively, as a function of the etch depth of the 2-µm-wide

AlGaAs waveguide at 1550 nm. For a 2-µm-wide AlGaAs waveguide, a fabrication error

of 50 nm in the etch depth results in variations in the effective core area of up to 7.7% in

the TM mode and 11% in the TE mode shown in Fig. 5.11, corresponding to variations

in nonlinear coefficients of 7.6% and 9.7% at 1550 nm, respectively, shown in Fig. 5.12.

From Fig. 5.4 and Fig. 5.5, fabrication tolerance of the etch depth variation can be

enhanced by making the waveguide width larger than 3.5 µm. However, multimode

behavior starts to appear (shown in Fig. 5.6) and the Kerr nonlinearity of the waveguide

is decreasing due to the increasing effective core area. Therefore, there is always a

tradeoff between fabrication tolerance and the single mode operation as well as between

fabrication tolerance and the waveguide’s Kerr nonlinearity for the strip-loaded waveguide

geometry on the AlGaAs wafer concerned in this thesis.

5.6 Conclusion

In this chapter, an AlGaAs wafer was designed to minimize the effective core area for

single-mode operation. Simulation results in Section 5.3 suggests that the wafer should

have a 1.5-µm-thick upper cladding, a 1-µm-thick guiding layer and a 4-µm-thick lower

layer that contain 50%, 18% and 24% of aluminum, respectively. Based on the finished

wafer grown by the CPFC, in which the 1-µm-thick guiding layer contain 20% of alu-

minum, simulations on waveguide design were re-visited. The etch depth and the width

of the desired waveguide were chosen to be less than or equal to 1.2 µm and 2 µm,


respectively, to assure single-mode propagation with tolerance on fabrication error as

well as with a minimum effective core area. After waveguide design, a combination of

standard photolithography and RIE was used to transfer the waveguide pattern onto the

top-cladding of the AlGaAs wafer. A 1-cm-long finished AlGaAs waveguide has an etch

depth of 1.2 µm. Lastly, the effective core areas of the finished waveguide are calculated

to be ∼ 4.3 µm2 (with an error up to 7.7%) for the TM mode and ∼ 5 µm2 (with an

error up to 11%) for the TE mode, corresponding to nonlinear coefficients of 13.3 /W/m

and 12.3 /W/m at 1550 nm, respectively.


Figure 5.7: Procedures of waveguide fabrication at the University of Toronto. (a) Thecomposition and structure of the AlGaAs wafer from CPFC; (b) Spin-coating the positivephotoresist S1818; (c) Ultra-Violet (UV) light exposure; (d) Development of the photore-sist using MF321; (e) Dry-etching of silica mask via RIE; (f) Dry-etching of AlGaAs viaRIE; (g) The device structure of the finished AlGaAs waveguide. Dr. Ksenia Dolgalevawas responsible for the fabrication process.


Figure 5.8: The SEM image (taken by Dr. Ksenia Dolgaleva) of the 2-µm-wide AlGaAswaveguide with a depth of 1.2 µm.

Figure 5.9: The refractive index profile (left) and the mode image (right) of the 2-µm-wide AlGaAs waveguide with a depth of 1.2 µm, simulated by Lumerical MODE solutionat 1550 nm.


Figure 5.10: Effective mode areas of TM and TE modes as a function of the width of theAlGaAs waveguide with a etch depth of 1.2 µm, simulated by Lumerical MODE solution,at 1550 nm.

Figure 5.11: Effective mode areas for TM and TE modes as a function of the edge depthof the 2-µm-wide AlGaAs waveguide at 1550 nm. The step change of the etch depth is50 nm.


Figure 5.12: Nonlinear coefficients for TM and TE modes as a function of the edge depthof the 2-µm-wide AlGaAs waveguide at 1550 nm. The step change of the etch depth is50 nm.

Chapter 6

Device Characterization

In this chapter, I am responsible only for measuring the linear loss of the finished waveg-

uide. For nonlinear absorption measurement and cross-phase modulation, the results

were given by Dr. Ksenia Dolgaleva.

6.1 Linear Loss Measurement

The linear losses of waveguides refer to the losses that occur when the input light intensity

coupled into the waveguide under test is sufficiently low such that the optical nonlinear

effects do not take place. The linear losses include scattering, leakage, absorption1 and

power loss due to directional coupling.

Scattering losses are caused by the surface roughness of the waveguide sidewalls that

usually arises due to imperfections in the mask used for etching as well as inhomogeneities

in the etching process itself, resulting in an attenuation of the propagating light due to

radiative scattering into the surrounding material. Stronger light confinement should be

ensured to prevent the mode field from extending into the sidewalls2.

Another two types of linear losses, leakage losses and directional coupling losses de-

1e.g. Single-photon absorption2Epilayer roughness is another mechanism for the scattering loss.

79

Chapter 6. Device Characterization 80

pend on the waveguide geometries. Leakage losses result from imperfect confinement of

the mode in the waveguide core which leads to power being coupled to the substrate.

Directional coupling between adjacent waveguides also leads to waveguide loss. In the

samples fabricated by Dr. Ksenia Dolgaleva, the spacing between waveguides was 50

µm and thus the power loss due to the directional coupling is negligible for a 1-cm-long

AlGaAs waveguide.

Absorption losses refer to the attenuation of light caused by single-photon absorption,

in which carriers in the valence band are excited to the conduction band, or to the

additional states introduced by impurities or defects. Since the incident photon energies

considered in this thesis are far below the bandgap, the corresponding absorption losses

are negligible3.

In this section, the linear loss of the 1-cm-long AlGaAs waveguide is measured using

the Fabry-Perot resonance technique.

6.1.1 Fabry-Perot Resonance Technique

In 1985, Regener and Sohler [129] proposed the Fabry-Perot resonance technique for

estimating the linear loss of single-mode Ti:LiNbO3 optical waveguide resonators. The

technique relies on the cleaved facets of Ti:LiNbO3 waveguides that serve as the two mir-

rors with Fresnel reflectivity (between the air and the semiconductor) of approximately

15%4 to form a Fabry-Perot (FP) cavity. As a result of constructive and destructive

interferences between multiple reflections, different wavelengths will have different trans-

mitted intensities after passing through the FP cavity. As a result, spectral fringes are

formed.

The advantage of using the Fabry-Perot resonance technique5 is that it does not

3In terms of the figure of merit for single-photon absorption, the condition W >> 1 is fulfilled forbelow the half-bandgap

4For Ti:LiNbO3, the effective index for single-mode propagation is usually between 2.25Or commonly called Fabry-Perot technique


require the knowledge of coupling efficiency at the waveguide input facet. The measured

linear loss depends on the effective index, reflectivity and the length of the waveguide

(shown in the following). In practice, the measurement accuracy using the FP technique is

affected by the determination of the fringe contrast as well as the reflectivity of waveguide

facets, whhile the facet reflectivity is also a strong function of the fundamental-mode

effective index as well as the angle of incidence of light.

Since the end of the 1980’s, the FP technique has been found to be more suitable

to measure the linear losses of semiconductor waveguides, as the Fresnel reflectivity of

approximately 30%6 provided by semiconductors allow a stronger interference (compared

with Ti:LiNbO3 waveguides) between multiple reflection within the semiconductor FP

cavity, resulting in a larger fringe contrast that eases data analysis [128].

The mathematical derivation of the FP resonance is based on the assumption that the

optical source is perfectly coherent monochromatic light7, with which the optical power

through the FP cavity can be derived from a convergent geometric series obtained by

adding the wave amplitudes from successive reflections. The intensity transmission of a

passive FP cavity8 is then given by

ItIi

=(1−R)2G

(1−GR)2 + 4GRsin2(δ/2), (6.1)

where It and Ii are the transmitted intensity coming out from the FP cavity and the

input intensity coupled into the FP cavity, respectively, R is the Fresnel reflectivity of

the waveguide facet calculated using the effective index of the single-mode waveguide9, G

is the total internal loss or gain experienced by the light inside the FP cavity, independent

6For semiconductors, the effective index for single-mode propagation is usually between 3.2 and 3.5.A larger reflectivity allows more reflected light energy for interference within the FP cavity

7”Perfectly coherent monochromatic light source” refers to the light source having zero spectrallinewidth

8”Passive” means the constitutive material of the FP cavity is operated at off-resonance wavelengths

9The facet reflectivity R can be calculated as R =(neff −1neff +1

)2, where neff is the fundamental-mode

effective index of the waveguide.


of the coupling loss, δ is the round-trip phase shift given by

δ =4πneffL

λ, (6.2)

where neff is the fundamental-mode effective index of the FP cavity, L is the cavity

length, λ is the wavelength. The maximum transmission takes place when the sinusoidal

term is equal to zero, such that

(ItIi

)|max =(1−R)2G

(1−GR)2, (6.3)

while the minimum transmission occurs when the sinusoidal term is equal to one(ItIi

)|max =

(1−R)2G

(1 +GR)2, (6.4)

The contrast ratio r is defined by the ratio of the maximum transmission to the minimum

transmission

r =(It/Ii)|max(It/Ii)|min

=

(1 +GR

1−GR

)2

, (6.5)

where

G = e−αL =1

R

√r − 1√r + 1

(6.6)

The linear loss per unit length, called the linear loss coefficient αo [dB/cm], of the passive

FP cavity is given by

αo = − 1

Lln

(1

R

√r − 1√r + 1

)(6.7)

From Eqn. (6.7), the linear loss coefficient is a function of waveguide length, Fresnel

reflectivity of waveguide facets, and fringe contrast, and is independent of coupling effi-

ciency.

6.1.2 Optical Sources and Device length

From the previous section, the linear loss measurement is based on the assumption that

the optical source provides perfectly coherent monochromatic light (See Eqn. (6.1)). For


Figure 6.1: Left: Transmission intensity trace versus optical path difference for a 1-cm-long GaAs waveguide with a linear loss of 1 dB/cm for different optical source linewidthsw . The center wavelength was chosen to be 1550 nm. Right: Dependence of calculatedapparent loss on the optical source linewidth (a) for 1-cm-long GaAs waveguides withactual losses of 0.1, 1.0, and 5 dB/cm, respectively, and (b) for 0.1 dB/cm actual lossGaAs waveguides with lengths of 0.3, 0.5, and 1 cm, respectively [127].

low loss waveguides (< 1dB/cm), obtaining accurate loss values using this technique is

difficult due to scattered data caused by non-ideal coherent sources.

In 1994, Yu [127] experimentally showed the dependence of the measurement accu-

racy of the linear loss on the laser spectral linewidth. Fig. 6.1 (left) shows that the fringe

contrast generated by a 1-cm-long semiconductor waveguide having a linear loss coeffi-

cient of 1 dB/cm decreases with increasing laser spectral linewidth w. Fig. 6.1 (right;

a) shows the measured linear loss coefficients using tunable CW lasers having different

spectral linewidths. For a very low loss waveguide (0.1 dB/cm), the linewidth w of 0.01

A and 0.02 A can cause an error of approximately 80% and 400%, respectively, using

the Fabry-Perot technique. For 1 dB/cm, a laser linewidth of less than 0.01 A must be

chosen to ensure accurate results (5% error).

Other than the laser linewidth, the errors of the measured linear losses increase with

increasing length. The fringe separation is defined as the wavelength separation between


two neighbouring spectral fringes

∆λp−p = λ2/2ngL (6.8)

where λ is the center wavelength of the laser source, L is the waveguide length, ng is

the fundamental-mode group index. In Fig. 6.1 (right; b), errors introduced by a 1-cm-

long waveguide are larger than those by a 0.3-cm-long waveguide, because the 1-cm-long

waveguide was so long that the fringe contrast could not be completely resolved by a

tunable laser source having a finite step size. For example, when a tunable laser source

having a step size of 0.01 nm, at a center wavelength of 1550 nm, the spacing between

two neighbouring fringes of a semiconductor waveguide with a group index of 3.4 is 0.035

nm, meaning that only 3 - 4 data points are taken between two neighbouring fringes. As

the fringe peaks cannot be resolved, a reduction of fringe contrast ratio results in a larger

estimated linear loss coefficient. On the other hand, short waveguides may suffer from

optical mode distortion and other irregularities present in the output mode structure

which are dependent on input coupling conditions. To allow a stable mode distribution

to be developed, a waveguide length of between 0.3 and 0.5 cm is suitable for the Fabry-

Perot technique for analyzing very low loss waveguides with higher accuracy.

In short, according to Yu [127], the linear loss measurement error is proportional to

the spectral linewidth w of a laser source and is inversely proportional to the spectral

fringe separation ∆λp−p obtained from the intensity transmission spectrum:

error ∼ w

∆λp−p. (6.9)

6.1.3 Experimental Setup

In Fig. 6.2, infra-red light from the tunable laser10 was fiber-coupled to a collimator, and

then coupled into the AlGaAs sample using the free-space end-fire rig. TM or TE mode

10a JDS SWS15101 tunable laser with step resolution 0.001 nm was used as the laser source for themeasurements, with a tuning Range of between1520 and 1600 nm


can be chosen at the input by turning the half-wave plate and the rotatable polarization

beam splitter to a suitable angle. During the experiment, the beam splitter was used to

monitor input powers before the objective lens while the wavelength of the tunable laser

sourse (TLS) was being swept across the spectral region of concern. A 25X objective

was used to couple light into the waveguide under test, while a 40X objective was used

to collimate the transmitted light coming out from the waveguide under test to the

IR detector. The objective at the output has a magnification ratio of 40X in order to

spatially filter out any light that does not belong to the transmitted mode.

Figure 6.2: Experimental setup for the linear loss measurement.

6.1.4 Experimental Results

The linear loss of the 1-cm-long AlGaAs sample was measured with a tunable laser source

with a step size of 0.002 nm that gives sufficient resolution within their free spectral

ranges (18 data points between two neighbouring peaks). Fig. 6.3 shows the normalized

transmission spectrum around 1550 nm for the TM mode. The fringe separation is 0.0347

nm, corresponding to a cavity length of 1 cm. The original data was averaged over three

samples to smoothen the fringe pattern, resulting in a fringe contrast slightly smaller

than the actual one, as shown in the averaged curve. The smaller fringe contrast gives a


Figure 6.3: The normalized transmission spectrum near 1550 nm for a 1-cm-long AlGaAswaveguide in the TM mode.

larger estimated linear loss coefficient.

The peaks and the troughs in the transmission curve were fitted to two different

cubic polynomials. The fringe contrast was calculated by averaging the ratios of the

peak-curve values to the trough-curve values taken at the wavelengths continuously over

ten fringes within the spectral region of concern (from 1549.75 nm to 1550.1 nm). The

estimated linear loss coefficients of the 1-cm-long, 2-µm-wide AlGaAs waveguide were

approximately 3 dB/cm for TM mode and 3.5 dB/cm for TE mode at 1550 nm.

6.1.5 Measurement Errors

Estimation errors were introduced when fitting the transmission peaks and troughs into

cubic polynomials, averaging the values of the fringe contrasts based on the cubic poly-

nomials over the spectral region of concern as well as smoothing of the original data

curve.

The uncertainties in the reflectivity of the facets, the angle of light incidence, the

facet quality as well as the waveguide length also introduce measurement errors.


As shown in Fig. 6.4, for a given waveguide loss, a larger facet reflectivity allows more

reflection for interference inside a FP cavity, resulting in a larger contrast ratio r. When

there is no intereference inside the FP cavity (i.e. R = 0%), the maximum intensity

transmission is equal to the minimum intensity transmission, resulting in r = 1; when

the facets are perfect mirrors (i.e. R = 100%), a complete cancellation of reflected light

due to destructive interference results in a zero minimum intensity transmission, resulting

in r →∞ .Thus, the contrast ratio r in Eqn. (6.5) varies from unity to infinity

Figure 6.4: Left: The fringe contrast ratio versus the total loss of a waveguide. Differentfacet reflectivities are shown for comparison. Right: The reflectivities of the TM andTE modes versus the angle of incidence. The simulated effective indices for the TM andTM modes are 3.2339 and 3.2353, respectively. The inset is a magnified plot showingthe difference between the TM’s and TE’s reflectivities near the normal incidence (zerodegree).

Oblique incidence of light will decrease the value of reflectivity R. Assuming that the

light incidence is oblique only in the azimuth direction φ, the dependence of the Fresnel

reflectivity on the angle of incidence can be modeled as [135]

R(φ) = Roe−(

2πneffWxφ

λo)2

, (6.10)

where Ro is the facet reflectivity at normal incidence, neff is the effective index of the


fundamental mode of the waveguide, Wx is the field width parameter for the waveguide’s

transverse field, λo is the wavelength of the incident light. By taking λo = 1550 nm,

Wx = 2 µm (for a 2-µm-wide waveguide), neff = 3.2339 and 3.2353 for TM and TE,

respectively (from the simulation results using Lumerical MODE Solutions), the facet

reflectivity can be plotted as a function of the incident angle of light, as shown in Fig. 6.4

(right). For example, a change in the angle of incidence of light from 0 degree (normal

Figure 6.5: Left: Reflectivity versus the angle of incidence. Right: Fringe contrast ratioversus waveguide loss.

incidence) to 1 degree (oblique incidence) corresponds to a change in the facet reflectivity

from 27.84% to 22.58%, as shown in Fig. 6.5 (left). Assuming that the actual linear loss

of a 1-cm-long waveguide is 2.86 dB/cm, the fringe contrast ratio will drop from 1.8

(normal incidence) to 1.6 (oblique incidence), by following the vertical downward arrow

in Fig. 6.5 (right). In practice, the contrast ratio of 1.6 caused by the oblique incidence

will be misinterpreted as the actual contrast ratio for normal incidence obtained from

the intensity transmission spectrum, and thus the calculated linear loss coefficient will

become 3.77 dB/cm, by following the horizontal arrow in Fig. 6.5 (right). Therefore, an

angular deviation of 1 degree from the normal incidence will introduce approximately


30% error in the measured linear loss coefficient.

To experimentally illustrate the errors introduced by the facet angle as well as the facet

quality, Fig. 6.6 shows a comparison of the linear loss coefficients for different waveguide

widths using both facets of the same sample. Ideally, the linear loss coefficients measured

using either facet R1 and R2 should be the same, given that the angles of incidence on

R1 and R2 are equal. However, in practice, the angles of incidence cannot be guaranteed

the same for both measurements due to artificial misalignment as well as asymmetrical

and angled cleaved facet surfaces. In the experiment, the linear losses measured using

facet R1 are smaller than those using facet R2, except for the waveguide width of 3.5 µm

whose facet R1 may have been damaged, leading to a higher loss. The generally larger

linear loss coefficients measured using facet R2 is possibly resulted from the angled light

coupling introduced during re-alignment of the sample. The values of the estimated linear

loss coefficients using R1 was finally chosen in this thesis.

Figure 6.6: Comparison between the linear loss coefficients versus different waveguidewidths measured using both facets R1 and R2 of the 1cm-long AlGaAs sample near 1550nm.

The error introduced by the uncertainty in determining the effective index of the


fundamental mode is considered neligible, since the deviation between the TM’s and

TE’s reflectivities is approximately 0.2%, as shown in Fig. 6.4 (right). On the other

hand, assuming the precision of measuring wavelength lengths is ± 0.5 mm, an error of

approximately 5% will be introduced for a 1-cm-long waveguide. In this thesis, only the

error (∼ 30%) caused by oblique incidence will be considered.

As a result, the estimated linear loss coefficients of the 2 µm-wide AlGaAs waveguide

were 3 ± 0.9 dB/cm for TM mode and 3.5 ± 1.05 dB/cm for TE mode at 1550 nm.

6.2 Nonlinear Absorption

Nonlinear absorption, or nonlinear multi-photon absorption, is a nonlinear process in

which two or more photons are simultaneously absorbed by a material. For example,

two-photon absorption (TPA) is a third-order nonlinear process in which two phase-

coherent photons of the same energy or different energies are simultaneously absorbed to

excite an electron from the original state in the valence band to an excited state in the

conduction band in a material whose bandgap corresponds to the sum of the energies

of the two incident photons. In case of the strong mono-chromatic excitation, TPA is

proportional to the square of the optical intensity. Three-photo absorption (3PA) is a

fifth-order nonlinear process in which three phase-coherent photons of the same energy

or different energies are simultaneously absorbed to excite an electron from the original

state in the valence band to an excited state in the conduction band in a material whose

bandgap corresponds to the sum of the energies of the three incident photons. In case

of the strong mono-chromatic excitation, 3PA is proportional to the cube of the optical

intensity.

The nonlinear absorption of an optical device depends on the material bandgap as

well as the allowable energy states formed by the device structure. For a bulk device for

optical communications, materials are usually chosen with a bandgap energy Eg such that


the photon energies within C-band are between Eg/3 and Eg/2, therefore allowing 3PA

and not TPA [130]. The nonlinear absorption of a device limits the achievable nonlinear

phase shifts, decrease the device’s throughput and increase the corresponding switching

threshold [38]. Examples include silicon, As2Se3 and GaAs whose TPA is stronger than

that of AlGaAs at a given optical intensity. As Al0.20Ga0.80As (the waveguide core’s

material) is operated at below the half-bandgap11, TPA is negligible, and thus will not

be measured in this thesis. However, 3PA could become the dominant nonlinear loss

mechanism in the waveguide. Although the 3PA coefficients of Al0.20Ga0.80As over the

C-band were measured by Aitchison [115] in 1997, the values of the 3PA coefficients

can be increased by defects or impurities introduced into the material during the wafer

growth. Thus, in this section, the 3PA coefficient at 1550 nm is measured using the

inverse transmission square curve for the 1-cm-long, 2-µm-wide AlGaAs waveguide.

6.2.1 Higher-order effective area

The nonlinear absorption reduces the intensity of the optical field propagating along the

device length, which can be described as

dI(z)

dz= −αI(z), (6.11)

where I is the spatial-dependent optical intensity coupled into the waveguide, α is the

overall loss coefficient. The total absorption can be expressed as a sum of the linear loss12

and the intensity-dependent nonlinear absorptions of the waveguide, such that

α = αo +

∆α2︷︸︸︷α2I +

∆α3︷︸︸︷α3I

2 + . . . , (6.12)

where αo is the linear loss coefficient, α2 and α3 are the two- and three-photon absorption

coefficients, respectively. The intensity-dependent changes of loss coefficient due to TPA

11Al0.20Ga0.80As has a bandgap of ∼ 1500 nm.12In this section, the linear loss is caused by scattering of light due to waveguide’s surface roughness.

As the photon energy is assumed to be much smaller than the material’s bandgap energy, the linearabsorption does not exist.


and 3PA are defined as

∆α2 = ∆α2(x, y, z) = α2I(x, y, z) (6.13a)

∆α3 = ∆α3(x, y, z) = α3I2(x, y, z), (6.13b)

where ∆α2 and ∆α3 are written as functions of both transverse and longitudinal coor-

dinates, as the optical intensity is not uniform across the transverse mode profile in a

waveguide structure and the amount of the nonlinear absorption depends on the intensity

along the waveguide. Eqn. (6.11) is then written as

dI(x, y, z)

dz= −[αo + ∆α2(x, y, z) + ∆α3(x, y, z)]I(x, y, z). (6.14)

The spatial dependence of the change of the loss coefficient due to TPA on the waveg-

uide mode profile can be eliminated by following the mathematical procedures shown in

Section 3.2.2, and the effective change of the loss coefficient due to TPA is

∆α2,eff = α2P (z)

A(3)eff

, (6.15)

where the optical power P is defined by Eqn. (3.10), while the third-order effective core

area A(3)eff is defined by Eqn. (3.11). Similarly, the spatial dependence of the change of

the loss coefficients due to 3PA on the waveguide mode profile can be eliminated by the

following averaging technique

∆α3 ,eff (z) =

∫ +∞−∞

∫ +∞−∞ ∆α3(x, y, z)I(x, y, z)dxdy∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy

(6.16a)

=

∫ +∞−∞

∫ +∞−∞ α3I

3(x, y, z)dxdy∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy

(6.16b)

= α3

∫ +∞−∞

∫ +∞−∞ I3(x, y, z)dxdy

[∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy]3

[

∫ +∞

−∞

∫ +∞

−∞I(x, y, z)dxdy]2 (6.16c)

=⇒ ∆α3 ,eff = α3P (z)2

(A(5)eff )

2, (6.16d)

where the fifth-order effective area is defined as

A(5)eff =

√√√√ [∫ +∞−∞

∫ +∞−∞ I(x, y, z)dxdy]3∫ +∞

−∞

∫ +∞−∞ I3(x, y, z)dxdy

. (6.17)


6.2.2 Inverse Trasmission Squared Method

Assuming that the free-carrier absorption is negligible, and 3PA is the main dominant

nonlinear absorption mechanism in the waveguide, Eqn. (6.11) becomes

dI(z)

dz= −αoI(z)− α3I

3(z). (6.18)

The solution of the above equation can be obtained from [134]. However, in order to

measure the 3PA coefficient, the inverse transmission squared curve is used [115], such

that

1

T 2=

1

(1−R)4η2e−2αoL+ α3

1− e−2αoL

αo(1−R)2e−2αoLI2in, (6.19)

where T is the intensity transmission of light through the waveguide, Iin is the input

intensity (corresponding to the fifth-order nonlinear effect) measured before coupling,

calculated as Eqn. (4.9c). The coupling coefficient η accounts for the coupling loss. By

measuring the transmission of light through the waveguide versus the input intensity, the

value of α3 can be estimated from the slope m of the inverse transmission squared curve

as follows:

α3 = mαo(1−R)2e−2αoL

1− e−2αoL. (6.20)

The above equation shows that the measurement of the 3PA coefficient of the waveguide

will be affected by the uncertainties in determining loss coefficients, device lengths, facet

reflectivities and the slope of the inverse transmission square curve.


Fig. 6.7 shows the experimental setup for the nonlinear optical characterization. The

high-power laser radiation was provided by the Coherent Mira laser system13 in which

an optical parametric oscillator (OPO) is responsible for converting the modelocked laser

pulses coming out from a tunable Ti:sapphire laser from 800 nm to some wavelengths

13The Coherent Mira laser system consists of a tunable Ti:sapphire laser and an optical parametricoscillator


between 1500 nm and 1560 nm. Gaussian-like pulses having a FWHM of 2 ps can be

found at the OPO output, with an average output power of 300 mW at a repetition

rate of 35.6 MHz. The polarization of the high-power pulsed laser (pump) was adjusted

by the half-wave plates (HWP) and the polarizing beam splitter cube (PBS). The non-

polarizing 50% beam splitter cube (NPBS) was used for XPM experiment. In order to

reduce the coupling loss of the pump into the waveguide under test, a telescope formed by

two different lenses L1 and L2, having focal lengths of 10 cm and 5 cm, respectively, was

used to halve the pump-beam diameter. A beam splitter was placed before the waveguide

input in order to obtain a reference power for calculating the intensity transmission. The

pump was then coupled into the waveguide under test using a 40X-diode objective lens,

and then out-coupled from the waveguide using a 20X objective. A piezoelectrically-

driven Elliot coupling unit consisting of 3D position stages was used for alignment. The

output was routed into an IR camera, a spectrum analyzer, or a power meter by the

corresponding flip mirrors (FM).


During the experiment, the intensity transmission of the 1-cm-long AlGaAs waveguide

for different input average powers at 1550 nm was recorded14. As the measured 3PA

coefficient using the inverse transmission squared curve is independent of coupling effi-

ciency, a beam splitter was placed before the waveguide input to reflect a part of the

input power for reference, as shown in Fig. 6.7. The reference power was then used to

calculate the input power before coupling. From Eqn. (4.9c), the input intensity was

estimated by using the input peak power of the 2-ps pump pulse from the OPO and

the fifth-order effective area of the 1-cm-long waveguide obtained from the simulated

mode field in Section 5. A linear fitting was used to find the slope m of to the inverse

14In this thesis, only the 3PA coefficient at 1550 nm will be considered. In the latter section, thepump pulse will be at ∼ 1550 nm.


Figure 6.7: Experimental setup for the nonlinear optical characterization of AlGaAswaveguide samples (from Dr. Ksenia Dolgaleva).

transmission squared curve (versus the input intensity), as shown in Fig. 6.8. The 3PA

coefficient of the 1-cm-long AlGaAs waveguide was found to be 0.08 ± 0.04 cm3/GW 2

at 1550 nm for the TM mode, which is on the same order of magnitude as that observed

in bulk AlGaAs waveguides [115].

Comprehensive error analysis of the 3PA measurement can be found in [138]. For

simplicity, detailed calculations of the errors will not be shown here. Generally, measure-

ment errors are introduced during the linear fitting processing of the inverse transmission

squared curve and the determination of waveguide length and the linear loss coefficients.

A significant amount of error can also be caused by the epitaxial growth of the AlGaAs

wafer that might have modified the refractive indices of the core and the cladding layers

in the wafer. In addition, the refractive index of the AlGaAs wafer may be modified

during the process of the AlGaAs etching, since the ion implantation was involved in

the fast etching process. These index changes will contribute to an error of 10 ∼ 20% in


Figure 6.8: Measured inverse transmission squared curve plotted as a function of thesquared intensity peak inside the waveguide at 1550 nm. The discrete data points repre-sent the experimental data. The dashed line is the best least-square fitting curve for theexperimental data (from Dr. Ksenia Dolgaleva).

determining higher-order effective areas of the AlGaAs waveguides.

6.3 Cross-Phase Modulation


For XPM, the experimental setup was similar to that for the nonlinear absorption. A

tunable CW laser whose tunable range covers the C-band was used to provide a maxi-

mum CW power of 1.5 mW . The CW probe was amplified by a 2-Watt erbium-doped

fiber amplifier (EDFA). The amplified CW was coupled from a single-mode fiber to free

space through a collimator. The polarizations of the pump and the probe were adjusted


separately by the half-wave plates (HWP) and the polarizing beam splitter cubes (PBS)

installed in each branch. The high-power pulsed laser beam (pump) and the CW probe

were combined through a non-polarizing 50% beam splitter cube (NPBS). In order to

allow more CW power coupled into the waveguide, optical filters15 were not used for sup-

pressing the (amplified spontaneous emission) ASE noise of the EDFA over the C-band.


Figure 6.9: The spectrum of XPM between 2-ps (FWHM) pump pulses at 1567 nm andthe CWs at different wavelengths (from Dr. Ksenia Dolgaleva).

In the experiment, the peak power of the pump and the average power of the CW

coupled into the 1-cm-long AlGaAs waveguide were 40 W 16 and 130 mW , respectively.

Fig. 6.9 shows the spectrum of XPM between pump pulses at 1567 nm and CWs at

different wavelengths. The pump wavelength was chosen to be 1567 nm in order to

observe the degenerated FWM product formed at between 1575 nm and 1585 nm where

15The insertion loss and the maximum allowed power of the available filters (JDSU) are ∼ 7 dB and24.7 dBm, respectively.

16Usually the peak power is of concern because the nonlinear phase shift can be estimated using thepeak power. The corresponding average power of the pump can be estimated by Paverage ∼ Ppeak ·τFWHM ·Rep; where τFHWM and Rep are the pulsewidth at FWHM and the repetition rate of the pulsetrain, respectively.


Figure 6.10: The spectrum of XPM between 2-ps (FWHM) pulses at 1500 nm and CWsat different wavelengths in a 1-cm-long AlGaAs waveguide (from Dr. Ksenia Dolgaleva).

the ASE noise was absent.

The nonlinear phase shift calculated using the peak power of the power, the simulated

effective core area of the waveguide (in Section 5.5), and the measured linear loss coeffi-

cient (in Section 6.1.5) is 1.67 ± 0.15 π radian, which is considered much larger than the

nonlinear phase shift (less than 0.5π) determined by using Fig. 6.9. Such difference can

be mainly attributed to the huge uncertainty in estimating the coupling loss from the

objective to the waveguide input facet as well as a significant amount of three-photon

absorption in Al0.20Ga0.80As at 1567 nm [94].

It has been found that the levels of the XPM-sidebands on the CWs and of the

degenerate FWM products reached their maxima when both the pump and the CW

were in the TM mode, which agrees with the calculated nonlinear coefficient Γ (13.3

/W/m for the TM mode and 12.3 /W/m for the TE mode at 1550 nm) using the mode

profiles simulated by Lumerical MODE Solutions in Section 4. In addition, the CW

power must be sufficiently high to increase the XPM-sidebands well-above the ASE noise

level. However, the ASE noise between 1535 nm and 1570 nm increased with higher CW

powers, and corrupted the XPM-induced sidebands significantly. It suggests that a low-


insertion-loss filter should be used to suppress ASE noise and to maintain a sufficiently

high CW power.

The pump wavelength was then detuned from 1567 nm to 1500 nm, as shown in Fig.

6.10. The XPM-sidebands still appeared on the CW, suggesting that XPM is a wideband

process that is not affected by the material dispersion of AlGaAs over the C-band. For

a 1-cm-long AlGaAs bulk waveguide with a dispersion parameter of 1000 ps/km/nm,

the wavelength separation between a 2-ps (FWHM)17 pump pulse and a CW is limited

by approximately 200 nm18. Therefore, in this thesis, the dispersion-induced walk-off

between a 2-ps (FWHM) pump pulse and a CW within the C-band is negligible.

6.4 Conclusion

In this chapter, both the linear and nonlinear properties of the 1-cm-long, 2-µm-wide

AlGaAs waveguide have been examined. The linear loss of a 1-cm-long AlGaAs waveguide

was measured using the Fabry Perot resonance technique. The estimated linear loss

coefficients of the 2-µm-wide AlGaAs waveguide were found to be 3 ± 0.9 dB/cm for

the TM mode and 3.5 ± 1.05 dB/cm for the TE mode at 1550 nm. The three-photon

absorption of the waveguide was measured using the inverse transmission squared curve.

The estimated 3PA coefficient is found to be 0.08 ± 0.04 cm3/GW 2 at 1550 nm for the

TM mode, which is on the same order of magnitude as that observed in bulk AlGaAs

waveguides [115]19 . It suggests that the AlGaAs wafer has a low impurity concentration,

and the corresponding two-photon absorption is negligible. Thus, the primary nonlinear

absorption mechanism is three-photon absorption, leading to a maximum output power

loss of approximately 15%.

Lastly, cross phase modulation between the pump (1567 nm, 1500 nm) and the CW

17The corresponding 1/e half-pulse width is 2/1.67 = 1.2 ps18200 nm refers to the 1/e full-width wavelength separation19In 1997, Aitchison obtained a 3PA coefficient of 0.055 cm3/GW2 from an Al0.18Ga0.76As waveguide

with very low impurity concentration.


(over the C-band), both in the TM modes, was examined. Sidebands were observed on

the CW, suggesting that XPM is a wideband process that is not affected by material dis-

persion of AlGaAs over the C-band. The wavelength separation between a 2-ps (FWHM)

pump pulse and a CW in a 1-cm-long AlGaAs bulk waveguide is limited by approximately

200 nm. Therefore, the dispersion-induced walk-off between a 2-ps (FWHM) pump pulse

and a CW within C-band is negligible.

Chapter 7

System Performance

7.1 Introduction

In this chapter, an experimental setup and the corresponding results for the fiber-based

nonlinear characterization for examining the bandwidth of XPM in a 1-cm-long AlGaAs

waveguide are presented in Section 7.2 and 7.3. Pulse-shape change of the wavelength-

converted signal with different filter offsets is discussed with experimental results in

detailed in Section 7.4 and 7.5. The three stages in offset filtering, XPM-sideband ex-

traction and carrier suppression are illustrated with the corresponding spectra in Section

7.6. Lastly, error-free XPM-AOWC at 10 Gb/s in the 1-cm-long AlGaAs waveguide is

demonstrated in Section 7.7.

7.2 Experimental Setup for the Fiber-based Nonlin-

ear Characterization

The experimental setup for the fiber-based nonlinear characterization is shown in Fig.

7.1. A Pritel actively-modelocked fiber laser at 1551 nm was used as a 2-ps (FWHM)

pump pulse source with a full spectral width of 8 nm. The repetition rate of the laser

101

Chapter 7. System Performance 102

Figure 7.1: Experimental setup for the fiber-based nonlinear characterization.

was set at 10 GHz (9.95328 GHz) by an external RF1 signal generator. An isolator

was placed at the laser output to avoid any backward reflection from the system. A

polarization controller (PC) was used to adjust the state of polarization of the pump.

The pump was amplified by a 30-dBm Erbium-Doped Fiber Amplifier (EDFA). The out-

of-band Amplified Spontaneous Emission (ASE) noise of the EDFA was suppressed by a

Fiber-Bragg Grating (FBG) as a transmission spectral filter with a flat-top bandwidth

of 8 nm and a tunable wavelength range of 2 nm near the center wavelength 1550 nm,

shown in Fig. 7.2. A 3-port circulator2 was used as an isolator to block the backward

reflection from the FBG as well as the Fresnel reflection from the AlGaAs waveguide

facet.

A tunable continuous wave (CW) source was used as a probe whose tunable wave-

length range covered the whole C-band. The state of polarization of the CW was adjusted

by the PC. Another 30-dBm EDFA was used to amplify the CW, followed by a com-

mercial JDSU TB9 filter, shown in Fig. 7.15, with a −3dB-bandwidth of 0.2 nm and a

tunability covering the entire C-band, to suppress the out-of-band ASE noise. An isolator

was placed before the filter to avoid any backward reflection from the filter and from the

waveguide facet.

1”RF” stands for radio frequency.2The measured insertion losses of a commercial isolator and of a circulator are 1 dB and 0.7 dB,

respectively. The maximum allowable input powers of an isolator and a circulator are ∼ 300 mW and∼ 2 W, respectively. In order to couple more power into the sample under test, a circulator instead ofan isolator was used in the experiment.


Figure 7.2: The spectral transmission of the 0.8-nm-wide FBG for suppressing the out-of-band ASE noise of the pump at 1550 nm.

Figure 7.3: The spectral transmission of the 0.2-nm-wide tunable filter for suppressingthe out-of-band ASE noise of the CW.


The pump and the CW were combined together using a 50/50 (3-dB) fiber coupler,

and then coupled into the waveguide under test through a tapered fiber from OZoptics

having a working distance of 14 µm, and a spot-size (mode field diameter) of 2.5 µm,

corresponding to an effective core area of approximately 5 µm2. Another identical tapered

fiber was used to out-couple the light from the waveguide. The input power before

coupling was monitored at the second output port of the 3-dB fiber coupler, with a

variable optical attenuator (VOA) to protect the 10-dBm-power meter. 2% of the light

coming out from the waveguide was measured by another 10-dBm-power meter, while

the rest 98% of the light was sent to the optical spectrum analyser (OSA) for observing

any changes in the spectrum.

The total insertion loss of the 1-cm-long AlGaAs waveguide in the TM mode in a

low-power operation was approximately 10 dB, taken as the difference between the input

power before coupling and the output power after coupling. As the linear loss of the

waveguide in the TM mode is ∼ 3 dB/cm (see Section 6.1.5), the coupling loss from

the tapered fiber to the waveguide was estimated to be ∼ 3.5 dB/facet, without using

index matching fluid. During the nonlinear characterization, the coupling efficiency at

the input was changed by the high-power pump within a few seconds, resulting in a

sudden increase in the total insertion loss of the waveguide. Mechanical drift of the

waveguide positioning stages also introduced a gradual coupling misalignment within a

few minutes. To solve the coupling misalignment in high-power operations, 2% of the

output power from the waveguide was being monitored during the experiment, followed

by hand re-alignment.


7.3 Experimental Results for the Fiber-based Non-

linear Characterization

Fig. 7.4 shows the experimental result of XPM in a 1-cm-long AlGaAs waveguide. When

the on-chip input power of the pump was 10 dBm (10 mW ) while that of the CW at

1537 nm was 12.7 dBm (18.6 mW ), the SPM-induced spectral broadening of the pump

pulse did not take place. Then, the on-chip input power of the pump at 1551 nm was

increased to 20 dBm (100 mW ), corresponding to a nonlinear phase shift of 0.16π, the

pump pulse experienced the SPM-induced spectral broadening. At the same time, two

additional sidebands were observed on the CW at 1537 nm via XPM.

Figure 7.4: Comparison of the spectra of XPM in a 1-cm-long AlGaAs waveguide whenthe pump power were varied from 10dBm (10 mW) to 20 dBm (100 mW) at 1551nm.The CW power was fixed at 12.7dBm (18.6mW) at 1537 nm.

The CW was tuned to 1535 nm, 1537 nm, 1539.5 nm, 1542 nm, 1558 nm, 1562

nm and 1568 nm, respectively. Sidebands of similar shapes were formed for all cases,

showing that XPM is independent of the dispersion of the AlGaAs waveguide over the

entire C-Band. In practice, the CW should be at least 7 nm always from the pump center

wavelength to avoid spectral overlap caused by SPM on the pump. Note that there was

an additional spectrum appeared beside the XPM-sideband when the CW was at 1562


Figure 7.5: The comparison of XPM spectra with the CWs at different wavelengths. Thepump power was maintained at 20dBm (100mW) at 1550 nm, while the CW powers werearound 20mW.

nm and at 1568 nm, which was the ASE noise included by the FBG filter3. A closer

look on the XPM-sidebands on the CW is shown in Fig. 7.6, showing fringes with equal

spacing of 0.08 nm, corresponding to a repetition rate of 10 GHz.

Figure 7.6: The XPM-sidebands appeared on the CW at 1558.6nm. The pump power at1551nm and the CW power were 20 dBm and 17.6 dBm respectively.

3The ASE noise was also present but not shown in Fig. 7.5 when the CW was at other wavelengths.During the experiment, the XPM spectra for the other CWs at shorter wavelengths (other than 1562nm and 1568 nm) were only recorded up to 1560 nm.


Figure 7.7: The experimental for the offset filtering with data modulation.

7.4 Experimental Setup for the Offsetting Filtering

with Data Modulation

Based on the experimental setup for the fiber-based nonlinear characterization, a 10-GHz

lithium-niobate Mach-Zehnder modulator (MZM) biased at the quadrature point was

used to carve 10-Gbit/s On-Off-Keying (OOK) data on the 10-GHz pulse-train coming

out from the Pritel modelocked fiber laser. The Bit-Error-Rate Tester (BERT) provided

a 10-GHz (9.95328-GHz) electrical clock to the Pritel modelocked fiber laser for active

modelocking and produced another 10-Gb/s (9.95328-Gb/s) electrical NRZ-OOK data to

the MZM for data modulation with a suitable electrical delay controllable from the BERT

digital control panel. A logic one, also called mark, of the electrical NRZ-OOK data

increased the transmission of the MZM from zero, and thus a NRZ switching window with

a time slot of 100 ps was created for the corresponding modelocked pulse to pass through.

As the lithium-niobate Mach-Zehnder modulator is highly polarization-dependent, an


additional PC was placed before the MZM to adjust the state of polarization of the

modelocked pulses in order to maximize the available output power. A low-power EDFA

was used to boost up the data to activate the 30-dBm EDFA.

For the offset filtering at the waveguide output, a commercial JDSU TB15 tunable

filter, with a -3-dB-bandwidth of 1.2 nm and with a tunable range from 1530 nm to

1565 nm was tuned to 1558.6 nm to block the pump wavelength. The filtered signal was

amplified by a 16-dBm-EDFA, and subsequently passed through the commercial JDSU

TB9 filter for the XPM-sideband extraction and the CW-carrier suppression (presented in

the next section). In practice, the offset filtering can be equivalently done by detuning the

CW wavelength instead of the filter’s center wavelength to avoid changing the composite

filter’s properties.

7.5 Change of Pulse Shape with Different Filter De-

tunings

The pump carries the RZ-OOK data, while the CW does not contain any information,

appeared as a logic one or a DC level. Via XPM, the strong pump induces two sidebands

on the CW spectrum. Temporally, the CW carrier component is shifted into the red side

(longer wavelength) due to a change in nonlinear refractive index caused by the pulse

rising edge, and then shifted into the blue side (shorter wavelength) due to an oppo-

site change in nonlinear refractive index caused by the pulse falling edge. By detuning

the filter to overlap either one of the XPM sidebands, a wavelength-converted data is

generated, with the same logic as the input pump.

Fig. 7.8 shows the temporal pulse shapes of the wavelength-converted signal changes

with different filter offsets, which were obtained based on the experimental setup shown

in Fig. 7.7. When the filter was detuned from the CW with the range of +0.4 nm to +0.9

nm, shown in Fig. 7.8 (a-c), the red XPM-sideband (longer wavelength) was extracted,


Figure 7.8: The temporal pulse shape of the wavelength-converted data observed on theDCA with different amounts of filter detuning (a) +0.9 nm (b) +0.5 nm (c) + 0.4 nm(d) +0.35 nm (e) +0.25 nm (f) 0 nm (g) -0.3 nm.

corresponding to the rising edge of marks, forming a wavelength-converted signal with

distinguishable marks and zeros.

When the filter was detuned from the CW by +0.35 nm, shown in Fig. 7.8(d), more

CW carrier and the red-XPM sideband were extracted, meaning that more energy of the

CW carrier was shifting into and out of the filter passband, causing a larger change of the

filtered energy compared with the previous filter offsets, and thus making the converted

pulse edge of marks more distinguishable. However, as more always-existing CW energy

was being filtered, the DC level of the converted signal increased, leading to a significant

amount of zero-noise.


When the filter was detuned from the CW by +0.25 nm, as shown in Fig. 7.8(e),

a larger amount of the CW carrier, compared to the previous detuning, and the red

XPM-sideband were extracted. As the filter obtained a substantial amount of the CW

carrier energy, the DC level of the wavelength-converted signal increased. The rising

edge of ”marks” induces a red chirp on the CW, and thus the CW carrier shifts into the

filter passband, forming a sudden temporal increase in the converted signal amplitude;

The falling edge of ”marks” induces a blue chirp on the CW, and thus the CW carrier

shifts out of the filter passband, forming a sudden temporal drop in the converted signal

amplitude.

When the filter center wavelength is on the CW, shown in Fig. 7.8(f), the CW carrier

as well as both of XPM-sidebands was filtered. The DC level of the converted signal

increased to maximum. There was still a slightly change in the converted signal amplitude

because the filter bandwidth was finite, meaning that the small amount of the CW carrier

shifted into or out of the filter passband.

When the filter was detuned from the CW by -0.3 nm, shown in Fig. 7.8(g), a

large amount of the CW carrier and the blue XPM-sideband (shorter wavelength) were

extracted. As the filter obtained a substantial amount of the CW carrier energy, the DC

level of the wavelength-converted signal increased. The rising edge of ”marks” induces a

red chirp on the CW, and thus the CW carrier shifts out of the filter passband, forming

a sudden temporal drop in the converted signal amplitude; The falling edge of ”marks”

induces a blue chirp on the CW, and thus the CW carrier shifts into the filter passband,

forming a sudden temporal increase in the converted signal amplitude.


7.6 XPM-Sideband Extraction and Carrier Suppres-

sion

The amplified CW plays two roles in XPM-AOWC. The first role is that the CW provides

a wavelength different from the pump wavelength so that the XPM process can be imple-

mented. The second role of the CW is that the sufficiently high-power CW can increase

the XPM-sideband level for achieving a good quality of the wavelength-converted signal.

The experimental results show that, by using 2-ps input pump pulses, XPM-sidebands

formed 35 dB below the peak of the CW carrier component as shown in Fig. 7.9. In the

following section, the signal-carrier-ratio (SCR) is defined as the contrast ratio of the

maximum XPM sideband level to the peak of the CW center carrier. The optical signal-

to-noise ratio (OSNR) is defined as the contrast ratio of the maximum XPM-sideband

level to the noise level.

As the OSA detection noise level is at -70 dBm while the EDFA noise level could be up

to -50 dBm, the XPM-sideband level should be high enough, say, 20 dB higher than the

noise level, for achieving a good signal quality. If the CW power is not sufficient, less CW

carrier energy is shifted into the two XPM-sidebands, resulting in a lower XPM-sideband

level with the same SCR.

Figure 7.9: Diagrams illustrating the differences of XPM-sideband levels with differentCW powers.


Figure 7.10: Three-stage filtering for XPM-AOWC.

Based on the experimental setup shown in Fig. 7.7, the offset filtering for blocking the

pump wavelength, extracting the XPM-sideband as well as suppressing the CW carrier

component was implemented by three cascading stages of filtering, as shown in Fig. 7.10,.

The on-chip input power of the pump at 1551 nm was 20 dBm (100 mW ), corresponding

to a nonlinear phase shift of 0.16π while that of the CW at 1558.6 nm was 17.67 dBm

(58.8 mW ).

In the first stage, a commercial WDM filter, whose transmission spectrum is shown

in Fig. 7.11, was used to block the pump wavelength as well as suppress the CW carrier

component by 30 dB. Since the pump power and the CW carrier component possessed

most of the power while the XPM-sideband contained a relatively small portion of the

overall input power, the output power of the WDM filter was only -28 dBm. The spec-

trum after the WDM filter was shown in Fig. 7.12, in which the CW level was suppressed

by 30 dB with a filter detuning of 1.2 nm from the CW carrier, corresponding to the 15th

- order XPM-sideband. The SCR of the resulting output spectrum was increased from

-35 dB to -5 dB.


In the second stage, the filtered sideband with a residual CW carrier component from

the first stage was amplified again by a channel amplification, in which a second 16-dBm-

EDFA and a 1.2-nm tunable filter were used as shown in Fig. 7.13, resulting in an output

power of -10 dBm. The spectrum after the 1.2-nm tunable filter was shown in Fig. 7.14,

in which the CW level was suppressed by 7 dB with a filter detuning of 1.1 nm from the

CW carrier, corresponding to the 14th - order XPM-sideband. The SCR of the resulting

output spectrum was increased from -5 dB to +2 dB.

In the third stage, the filtered output of the second stage was amplified again by

a channel amplification, in which a second 16-dBm-EDFA and a 0.2-nm tunable filter

were used shown in Fig. 7.15, resulting in an output power of 6 dBm. The overall output

spectrum is shown in Fig. 7.16, in which the CW level was suppressed by 40 dB with

a filter detuning of 1.2 nm from the CW carrier, corresponding to the 15th-order XPM-

sideband. The SCR of the resulting output spectrum was increased from +2 dB to +40

dB.

Figure 7.11: The spectral transmission of the WDM filter, detuned from the CW by 1.2nm.


Figure 7.12: The output of the WDM filter (the first stage)

Figure 7.13: The spectral transmission of the commercial tunable filter JDSU TB15,detuned from the CW by 1.1nm


Figure 7.14: The output of the commercial tunable filter JDSU TB15 (the second stage)

Figure 7.15: The spectral transmission of the commercial tunable filter JDSU TB9,detuned from the CW by 1.2nm

7.7 Error-free XPM-AOWC in a 1-cm-long AlGaAs

waveguide

By replacing the filter section in Fig. 7.7 with the three-stage composite filter in Fig. 7.10,

and adding a O-E receiver at the output of the AOWC, the system performance of the


Figure 7.16: The output of the commercial tunable filter JDSU TB9 (the overall outputof the AOWC).

Figure 7.17: Experimental setup of system measurement of the XPM-AOWC in a 1-cm-long AlGaAs waveguide.

XPM-AOWC in the 1-cm-long AlGaAs waveguide can be investigated. In this section,

receiver sensitivity and power penalty will be used to describe the output signal quality


of a system under test. Receiver sensitivity is defined as the minimum power that reaches

the receiver end that achieves an error-free detection at a bit-error-rate (BER) of 10−9.

The back-to-back receiver sensitivity is defined as the receiver sensitivity without the

system under test. The power penalty of a system under test is defined as the additional

amount of power required at the receiver end to achieve an error-free detection at the

BER of 10−9 in the presence of the system under test.

During the experiment, the output power of the AOWC was splitted by a 50/50 fiber

coupler, with 50% being sent to DCA or OSA for monitoring and with another 50% being

sent to the VOA. To measure the power penalty of the AOWC, the EDFA gains of the

composite filter were fixed to avoid any variation of ASE noise. The VOA was used to

attenuate the output power from the AOWC until the receiver sensitivity at the BER of

10−9 was reached.

Figure 7.18: The graph of the logarithm of the bit-error-rate versus receiver sensitivityof the wavelength-converted output signal at 1558 nm, with three different pump powerlevels at 1551 nm.


The back-to-back receiver sensitivity in Fig. 7.17 was measured to be -7.14 dBm

(0.193 mW ) for the 2-ps RZ-OOK data before entering the input fiber-to-waveguide

coupling. The receiver sensitivities of the whole AOWC system using the 1-cm-long

AlGaAs waveguide, shown in Fig. 7.18, tested with three different input pump powers

of 19.23 dBm (83.75 mW ), 19.61 dBm (91.4 mW ) and 20 dBm (100 mW ), were -

0.53 dBm (0.89 mW ), -1.02 dBm (0.79 mW ) and -1.44 dBm (0.72 mW ), respectively,

corresponding to power penalties of 6.61 dB, 6.12 dB and 5.7 dB, respectively.

The high power penalty, compared with 2 dB [69] and 1 dB [73, 131], is believed

to be caused by the thermal instability of the fiber-waveguide coupling when operating

at high powers, leading to an input-power fluctuation. The measured Q factor of the

2-ps-RZ-OOK pump at 1551 nm at the waveguide output was degraded from 14 dB to

11.5 dB when the input pump power was high (158.8 mW ). For the XPM-AOWC using

small nonlinear phase shift, the input amplitude noise is magnified at the output [132].

The extracted 14th- to 17th-order XPM-sidebands had a smaller OSNR compared to

the first 10th-order XPM sideband, showing a tradeoff between signal quality and filtering

high-order XPM-sideband in small-nonlinear-phase-shift XPM-AOWC. Fig. 7.6 shows the

XPM-sideband without data modulation, showing that the OSNR is decreasing as the

XPM-sideband is farther away from the CW. To improve the output signal quality, a

slight reduction in power penalty from 6.12 dB to 5.7 dB requires a larger power-level

increase (∼10 mW) at the waveguide input, while a slight increase in power penalty from

5.7 dB to 6.12 dB requires the lower power-level increase (∼0.1 mW) by the preamplifier

at the receiver end to have an error-free detection of the wavelength-converted signal.

7.8 Conclusion

In this chapter, the experimental setup for the fiber-based nonlinear characterization for

XPM in a 1-cm-long AlGaAs waveguide was explained in detail. Experimental results


Figure 7.19: Eye diagrams of the pump at 1551 nm before entering the waveguide (left) ,after passing through fiber-fiber (middle) and after passing through fiber-waveguide-fiber.

Figure 7.20: Eye diagrams of the pump at 1551 nm before entering the waveguide (left), and of the wavelength-converted signal at 1556.8 nm

show that the bandwidth of XPM between a strong 2-ps-pump pulse at 1551 nm and a

tunable CW both in the TM mode in the 1-cm-long AlGaAs waveguide covers the entire

C-band. The experimental setup for offset filtering has been built up, showing that the

pulse shape of the wavelength-converted output signal heavily depends on the amount

of filtering detuning. Pump blocking, carrier suppression and XPM-sideband extraction

were implemented with a three-stage filtering. The signal-carrier ratio (SCR) and the

optical signal-to-noise ratio (OSNR) of the XPM-sideband on the CW carrier component

should be maximized to achieve a wavelength-converted signal of high quality.

Lastly, we show the first demonstration of error-free XPM-AOWC at 10 Gbit/s in a 1-

cm-long AlGaAs waveguide with an estimated nonlinear phase shift was 0.16π. The 14th-

to 17th-XPM-sidebands (∼1.2-nm detuning from the CW) are extracted for generating

a wavelength-converted output with complete carrier suppression, with a power penalty


of 6 dB. A tradeoff has been found between achieving a good signal quality and easing

the filtering requirement. It has been experimentally shown that, to improve the output

signal quality, a slight reduction in power penalty from 6.12 dB to 5.7 dB requires a

larger power-level increase (∼10 mW) at the waveguide input, while a slight increase in

power penalty from 5.7 dB to 6.12 dB requires the lower power-level increase (∼0.1 mW)

by the preamplifier at the receiver end to have an error-free detection of the wavelength-

converted signal.

Chapter 8

Conclusion

This thesis covers the development of highly nonlinear Aluminum Gallium Arsenide (Al-

GaAs) waveguides and the demonstration of all-optical wavelength conversion via cross-

phase modulation in AlGaAs waveguides at telecommunication wavelengths.

During the 1990’s, AlGaAs operated within the C-band has been proven to have

ultrafast response, high Kerr nonlinearity and low nonlinear absorption. Its large tai-

lorable range of refractive index allows a strong light confinement within the waveguide

to further enhance the Kerr effect. The main idea of this thesis is simply to minimize the

effective core areas of AlGaAs waveguides in order to enhance the Kerr nonlinearity for

wavelength conversion, thus lowering the overall input power and shortening the device

length.

For wafer design and waveguide fabrication, a wafer was designed to have a 1.5-

µm-thick upper cladding, a 1-µm-thick guiding layer and a 4-µm-thick lower layer that

contain 50%, 20% and 24% of aluminum, respectively. The etch depth and the width

of the desired waveguide were chosen to be 1.2 µm and 2 µm, respectively, to assure

single-mode propagation with tolerance on fabrication error as well as with a minimum

effective core area. After waveguide design, a combination of standard photolithography

and RIE was used to transfer the waveguide pattern onto the top-cladding of the wafer.

121

Chapter 8. Conclusion 122

The finished AlGaAs waveguide has a length of 1 cm only. The effective core areas of

the finished waveguide are calculated to be ∼ 4.3 µm2 for the TM mode and ∼ 5 µm2

for the TE mode, corresponding to nonlinear coefficients of 13.3 /W/m and 12.3 /W/m

at 1550 nm, respectively.

For device characterization, both the linear and nonlinear properties of the 1-cm-

long, 2 µm-wide AlGaAs waveguide have been examined using the Fabry-Perot resonance

technique and the inverse transmission squared curve, respectively. The estimated linear

loss coefficients of the 2-µm-wide AlGaAs waveguide were found to be 3 ± 0.9 dB/cm for

the TM mode and 3.5 ± 1.05 dB/cm for the TE mode at 1550 nm. The nonlinear optical

characterization has shown that the primary nonlinear absorption mechanism is three-

photon absorption with the corresponding absorption coefficient of 0.08 ± 0.04 cm3/GW 2

at 1550 nm for the TM mode. The maximum output power loss due to the three-photon

absorption was around 15%. Cross phase modulation between the pump (1567 nm, 1500

nm) and the CW (over the C-band) , both in the TM modes, was examined. Sidebands

were observed on the CW, suggesting that XPM is a wideband process that is not affected

by material dispersion of AlGaAs over the C-band. The wavelength separation between

a 2-ps (FWHM) pump pulse and a CW in a 1-cm-long AlGaAs bulk waveguide is limited

by approximately 200 nm. Therefore, the dispersion-induced walk-off between a 2-ps

(FWHM) pump pulse and a CW within the C-band is negligible.

For system work, the 1-cm-long waveguide was tested in the fiber-based nonlinear

characterization setup. Experimental results show that the bandwidth of XPM between

a strong 2-ps-pump pulse at 1551 nm and a tunable CW both in the TM mode in

the 1-cm-long AlGaAs waveguide covers the entire C-band. It has been found that the

pulse shape of the wavelength-converted output signal heavily depends on the amount

of filtering detuning. Pump blocking, carrier suppression and XPM-sideband extraction

were implemented with a three-stage filtering. The signal-carrier ration (SCR) and the

optical signal-to-noise ratio (OSNR) of the XPM-sideband on the CW carrier component

Chapter 8. Conclusion 123

should be maximized to achieve a wavelength-converted signal of high quality. Lastly,

we show the first demonstration of error-free XPM-AOWC at 10 Gb/s in a 1-cm-long

AlGaAs waveguide with an estimated nonlinear phase shift was 0.16π. The 14th- to

17th-XPM-sidebands (∼1.2-nm detuning from the CW) are extracted for generating a

wavelength-converted output with complete carrier suppression, with a power penalty of

6 dB. A tradeoff has been found between achieving a good signal quality and easing the

filtering requirement. It has been experimentally shown that a slight reduction in power

penalty (from 6.12 dB to 5.7 dB) requires a larger power-level increase (∼10 mW) at the

waveguide input, compared to the power-level increase (∼0.1 mW) by the preamplifier

at the receiver end.

As a result of the work completed in this thesis, a conference paper will be published

by Dr. Ksenia Dolgaleva at the Conference of Frontiers in Optics, 2010 [143, 144], and

another conferencer paper will be published by myself at the 2010 Photonics Society

Annual Meeting [145, 146].

Table 8.1: Comparison of the effective core area and the Kerr nonlinearity among differenttypes of passive waveguides including AlGaAs waveguides (of this thesis) used in all-optical wavelength conversion

Material Nonlinear process Linear loss (dB/cm) Waveguide length n2 (m2/W ) Aeff (µm2) Γ (/W/km)

Silicon [63] FWM (40 Gb/s) 0.4 8 cm 900× 10−20 (∼ 400 nSiO22 ) 1.6 22800

As2S3 [69] XPM (10 Gb/s) 0.2 5 cm 300× 10−20 (∼ 136 nSiO22 ) 5.7 2080

As2S3 [70] XPM (40 Gb/s) 0.05 22.5 cm 300× 10−20 (∼ 136 nSiO22 ) 7.1 1700

As2S3 [72] FWM (40 Gb/s) 0.05 6 cm 300× 10−20 (∼ 136 nSiO22 ) 1.23 9800

GaAs [75, 73] XPM + FWM (10 Gb/s) 6 4.5 mm 2900× 10−20 (∼ 1300 nSiO22 ) 1.8 65000

AlGaAs [143, 145] XPM (10 Gb/s) 3 1 cm 1430× 10−20 (∼ 650 nSiO22 ) 4.3 13300

Remarks:



Appendix A

Nonlinear Absorption

In this chapter, the formulae of the inverse transmission curve for two-photon absorption

and of the inverse transmission squared curve for three-photon absorption are derived,

since most of the literature only show the corresponding equations only. The following

proof will allow readers (and future groupmates) to understand more about the nonlinear

absorption measurement.

A.1 Inverse Transmission Squared Curve

The spatial evolution of the optical intensity inside the waveguide where three-photon

absorption is the dominant absorption mechansim is governed by Eqn. (6.18):

dI

dz= −αoI − α3I

3. (A.1)

After separating variables, indefinite integrals are taken on both sides of the above equa-

tion, such that ∫1

αoI + α3I3dI =

∫(−1) dz. (A.2)

124

Appendix A. Nonlinear Absorption 125

To solve the integrand in Eqn. (A.2), the method of partial fraction is used:

1

αoI + α3I3=

1

αoI(1 + α3

αoI2)

(A.3a)

1

αoI + α3I3=

A

αoI+BI + C

1 + α3

αoI2

(A.3b)

After comparing the coefficients between the nominators of both sides in Eqn. (A.3b),

the constants A, B and C become:

A = 1, (A.4a)

B = −α3

α2o

, (A.4b)

C = 0. (A.4c)

Then, Eqn. (A.2) becomes

∫ [1/αoI

+(−α3

α2o)I

1 + α3

αoI2

]dI =

∫(−1) dz (A.5a)

1

αoln I + (− 1

2αo) ln(1 +

α3

αoI2) = z + c (A.5b)

ln I − ln

√1 +

α3

αoI2 = −αoz + αoc (A.5c)

I√1 + α3

αoI2

= K︸︷︷︸eαoc

e−αoz (A.5d)

I2

1 + α3

αoI2

= K2e−2αoz, (A.5e)

where K is an arbitary constant as a result of indefintie integration. K can be obtained,

as an initial condition, by setting z equal to zero:

K2 =I2(0)

1 + α3

αoI2(0)

. (A.6)


Then, Eqn. A.5e becomes

I2(z) = K2e−2αoz ·

[1 +

α3

αoI2(z)

](A.7a)

I2(z) =K2e−2αoz

1−K2e−2αoz(α3

αo

) (A.7b)

=

I2(0)

1+α3αoI2(0)

e−2αoz

1−

[I2(0)

1+α3αoI2(0)

]e−2αoz

(α3

αo

) (A.7c)

I2(z) =I2(0)e−2αoz[

1 + α3

αoI2(0)

]− I2(0)e−2αoz

(α3

αo

),

(A.7d)

where the spatial evolution of the optical intensity I(z) inside a waveguide depends on

the optical intensity entering the waveguide I(0), the linear loss coefficient αo, the three

photon absorption coefficient α3. Note that I(o) and I(z) refers to the on-chirp intensities.

Then, the inverse transmission squared curve for on-chip intensity is

1

T 2OC

=1

e−2αoz+

α3

αo

[1− e−2αoz

]I2(0)

e−2αoz(A.8)

where TOC = I(z)/I(0) is the on-chirp intensity tranmission of the waveguide.

In order to account for the objective-to-waveguide coupling loss η at the input and

the loss due to Fresnel reflection R at both waveguide facets, the input intensity before

coupling Iin and the output intensity after the waveguide Iout are introduced by Mr. Sean

Wagner (whom I asked for assistance to arrive the form in [115]):

I(0) = Iin · η(1−R), (A.9a)

Iout = I(z)(1−R). (A.9b)

(A.9c)

Note that Iout does not include the coupling coefficient η because the beamwidth of the

light coming out from the waveguide is much smaller than that of the objective, and thus


the output intensity from the waveguide is assumed to be completely collected by the

objective, i.e. η = 1. Then, the on-chip transmission becomes

TOC =I(z)

I(0)(A.10a)

=Iout/(1−R)

Iin · η(1−R)= T · 1

η(1−R)2, (A.10b)

where T is the transmission of the waveguide using the intensities before coupling at the

input and after coupling at the output, respectively. By substituting the above equation

into Eqn. (A.8), Eqn. (A.8) becomes

1

T 2· η2(1−R)4 =

1

e−2αoz+α3

αo

1− e−2αoz

e−2αozI2in · η2(1−R)2 (A.11a)

1

T 2=

1

η2(1−R)4e−2αoz+α3

αo

1− e−2αoz

(1−R)2e−2αozI2in (A.11b)

Eqn. (A.22a) shows that the 3PA coefficient α3 can be deduced by using the slope of

the plot of the inverse transmission squared verse the input intensity before coupling.

From the same plot, it is also possible to deduce the coupling coefficient by using the

y-intercept of the plot. Such a technique is of paramount importance especially for cross-

phase modulation in which the on-chip power must be accurately determined in order

to calculate the maximum nonlinear phase shift achieved in the waveguide under test.

Therefore, it is always recommended to measure the output powers for different input

powers during the experiment of cross-phase modulation or other nonlinear effects in

order to backward-calculate the corresponding coupling coefficients that might change

significantly during every alignment.

A.2 Inverse Transmission Curve

Starting from Eqn. (6.11), the spatial evolution of the optical intensity inside the waveg-

uide, in which two-photon absorption is the dominant absorption mechansim, is governed

by

dI

dz= −αoI − α3I

3. (A.12)


After separating variables, indefinite integrals are taken on both sides of the above equa-

tion, such that ∫1

αoI + α2I2dI =

∫(−1) dz. (A.13)

To solve the integrand in Eqn. (A.13), the method of partial fraction is used:

1

αoI + α2I2=A

I+

B

αo + α2I(A.14)

After comparing the coefficients between the nominators of both sides in Eqn. (A.14),

the constants A and B become:

A = 1/αo, (A.15a)

B = −α2

αo. (A.15b)

Then, Eqn. (A.13) becomes∫ [1/αoI

+(−α2/αo)

αo + α2I

]dI = =

∫(−1) dz (A.16a)

I

αo + α2I= Ke−αoz (A.16b)

I(z) =αoKe

−αoz

1− α2Ke−αoz, (A.16c)

where K is an arbitary constant as a result of indefintie integration. K can be obtained,

as an initial condition, by setting z equal to zero:

K =I(0)

αo + α2I(0)(A.17)

Then, Eqn. (A.16c) becomes

I(z) =

αo

[I(0)

αo+α2I(0)

]e−αoz

1− α2

[I(0)

αo+α2I(0)

]e−αoz

(A.18a)

I(z) =αoI(0)e−αoz

αo + α2I(0)− α2I(0)e−αoz(A.18b)

where the spatial evolution of the optical intensity I(z) inside a waveguide depends on the

optical intensity entering the waveguide I(0), the linear loss coefficient αo, the two-photon


absorption coefficient α2. Note that I(0) and I(z) refers to the on-chirp intensities. Then,

the inverse transmission for on-chip intensity is

1

TOC=

1

e−αoz+α2(1− e−αoz)αoe−αoz

I(0) (A.19)

where TOC = I(z)/I(0) is the on-chirp intensity tranmission of the waveguide.

In order to account for the objective-to-waveguide coupling loss η at the input and

the loss due to Fresnel reflection R at both waveguide facets, the input intensity before

coupling Iin and the output intensity after the waveguide Iout are introduced by Mr. Sean

Wagner (whom I asked for assistance to arrive the form in [115]):

I(0) = Iin · η(1−R), (A.20a)

Iout = I(z)(1−R). (A.20b)

(A.20c)

Note that Iout does not include the coupling coefficient η because the beamwidth of the

light coming out from the waveguide is much smaller than that of the objective, and thus

the output intensity from the waveguide is assumed to be completely collected by the

objective, i.e. η = 1. Then, the on-chip transmission becomes

TOC =I(z)

I(0)(A.21a)

=Iout/(1−R)

Iin · η(1−R)= T · 1

η(1−R)2, (A.21b)

where T is the transmission of the waveguide using the intensities before coupling at the

input and after coupling at the output, respectively. By substituting the above equation

into Eqn. (A.8), Eqn. (A.8) becomes

1

T=

1

η(1−R)2e−αoz+α2

αo

1− e−αoz

(1−R)e−αozIin (A.22a)

Appendix B

Scripts for Lumerical MODE

solutions

The plots of the effective core area as a function of waveguide width shown in Fig.5.4 and in Fig. 5.4 in Section 5 were plotted using Lumerical MODE Solution. Thescripts consist of two parts: Initialization.lsf and WidthScan.txt. Initialization.lsf isresponsible for setting the structure layout, changing the etch depth of the rib (or strip-loaded) waveguide, setting the number of cells for simulation as well as setting the rangeof effective indices for mode searching. WidthScan.txt is reponsible for sweeping thewaveguide width from 1 µm to 5 µm and calculating the corresponding effective core(third-order) areas for the TE and TM modes of the waveguide.

In the following code, the scripts are for Lumerical MODE solutions 3.0. ForLumerical MODE solutions 4.0 (new version), there are only some amendments inAnalysis window.

B.1 Initialization.lsf

#----- template for changing mesh cells number--------

switchtolayout; # layout window

#------ setting up rib structure--------------

structures; # structure window

etch_depth = 1e-6;

y_center_slab = 5e-6 + (1.5e-6-etch_depth)/2;

y_center_rib = 5e-6 + 1.5e-6 - etch_depth/2;

y_span_slab = 1.5e-6 - etch_depth;

y_span_rib = etch_depth;

setnamed("Rib", "y", y_center_rib);

setnamed("Slab", "y", y_center_slab);

130

Appendix B. Scripts for Lumerical MODE solutions 131

setnamed("Rib", "y span", y_span_rib);

setnamed("Slab", "y span", y_span_slab);

setnamed("Rib", "x", 0);

setnamed("Slab", "x", 0);

setnamed("Slab", "x", 0);

#------- simulation------

simulation; # simulation window

num_cells_x = 150;

num_cells_y = 150;

select("MODE");

setnamed("MODE", "mesh cells x", num_cells_x);

setnamed("MODE", "mesh cells y", num_cells_y);

#----- record x_span and y_span of the simulation area---

x_span=getnamed("MODE", "x span");

y_span=getnamed("MODE", "y span");

analysis; # analysis window

set("wavelength", 1.55e-6);

set("search in range", 1);

set("n1", 3.25); #the mode searching is done between n1 and n2.

set("n2", 3.22); # setting a smaller range helps reduce computational time

#analysis; #--- For Lumerical MODE solution 4.0

#setanalysis("wavelength", 1.55e-6);

#setanalysis("search in range", 1);

#setanalysis("n1", 3.25);

#setanalysis("n2", 3.22);

#?a=findmodes;

B.2 WidthScan.txt

width_max = 5;

width_min = 1;

num=19; # there are 19 simulation points between 1um and 5um

mode_name = "sdfs";

mode_index = 121;

neff_TE=linspace(width_min,width_max,num);

neff_TM=linspace(width_min,width_max,num);

Ex=linspace(width_min,width_max,num);

Ey=linspace(width_min,width_max,num);

Ez=linspace(width_min,width_max,num);


Hx=linspace(width_min,width_max,num);

Hy=linspace(width_min,width_max,num);

Hz=linspace(width_min,width_max,num);

E2_TE=linspace(width_min,width_max,num);

frequency_TE=linspace(width_min,width_max,num);

loss_TE=linspace(width_min,width_max,num);

Area_TE=linspace(width_min,width_max,num);

Aeff_TE=linspace(width_min,width_max,num);

TE_percent_TE=linspace(width_min,width_max,num);

E2_TM=linspace(width_min,width_max,num);

frequency_TM=linspace(width_min,width_max,num);

loss_TM=linspace(width_min,width_max,num);

Area_TM=linspace(width_min,width_max,num);

Aeff_TM=linspace(width_min,width_max,num);

TE_percent_TM=linspace(width_min,width_max,num);

TEfraction=linspace(width_min,width_max,num);

width=linspace(width_min,width_max,num);

spacing = (width_max-width_min)/(num-1);

message("Simulation start?");

TEfraction=linspace(0,0,6);

counter = 1;

# counter is the index for matrix generated by width scan

for (i=1:length(neff_TE))

j=(i-1)*spacing*1e-6+1e-6;

?"width=" + num2str(j);

switchtolayout;

structures;

select("Rib");

set("x span",j); # change the rib width of the waveguide

?a=findmodes;

#------ Starting capturing data-------------

# assume that the first six mode solutions already include

#fundamental TE and TM modes

TM_found=0;

for(index=1:6)

mode_name = "mode"+ num2str(index);

TEfraction(index) = getdata(mode_name, "TEfraction");

if ((TEfraction(index) < 0.5) and (TM_found==0)) ?TM_index=index;TM_found = 1;

#

#-----------choosing the fundamental TE/TM--------------------

#

#TM mode case

m2="mode"+num2str(TM_index);

E2_TM = getelectric(m2);


frequency_TM(counter) = getdata(m2, "f");

neff_TM(counter) = getdata(m2, "neff");

loss_TM(counter) = getdata(m2, "loss");

TE_percent_TM(counter) = getdata(m2, "TEfraction");

#

#----calculation of 3rd-order effective mode area------

denom = sum(sum(E2_TM^2));

nom= (sum(sum(E2_TM)))^2;

#matrix_x=linspace(1,length(E2_TE),length(E2_TE));

#matrix_y=linspace(1,length(E2_TE),length(E2_TE));

Area_TM(counter) = nom/denom;

?"TM mode area";

?Aeff_TM(counter) = Area_TM(counter)*(x_span/num_cells_x)*(y_span/num_cells_y);

#

#

#TE mode case

m1="mode1";

E2_TE = getelectric(m1);

frequency_TE(counter) = getdata(m1, "f");

neff_TE(counter) = getdata(m1, "neff");

loss_TE(counter) = getdata(m1, "loss");

TE_percent_TE(counter) = getdata(m1, "TEfraction");

#

#----calculation of 3rd-order effective mode area------

denom = sum(sum(E2_TE^2));

nom= (sum(sum(E2_TE)))^2;

Area_TE(counter) = nom/denom;

?"TE mode area";

?Aeff_TE(counter) = Area_TE(counter)*(x_span/num_cells_x)*(y_span/num_cells_y);

#

#

#-----------------------------------------

x = getdata(m1, "x");

y = getdata(m1, "y");

#

#filename_TE = "E2_TE_" + num2str(width(i), ) + "um";

#filename_TM = "E2_TM_" + num2str(width(i)) + "um";

#savedata(filename_TE, x, y, E2_TE);

#savedata(filename_TM ,x, y, E2_TM);

#ext_TE = "E2_TE_" + num2str(width(i)) + "um.ldf";

#ext_TM = "E2_TM_" + num2str(width(i)) + "um.ldf";

#lum2mat(ext_TE);

#um2mat(ext_TM);

counter=counter+1;


savedata("scan_width", width, frequency_TE, neff_TE, loss_TE, TE_percent_TE, Aeff_TE, frequency_TM, neff_TM, loss_TM, TE_percent_TM, Aeff_TM);

lum2mat("scan_width.ldf"); # change the format of the file into .mat for Matlab

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All-Optical Wavelength Conversion in Aluminum Gallium ... · nications Technology Institute for their introduction and safety training in cleanrooms. Discussion with Mr. Sean Wagner