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  • Planar Lightwave Circuits

    Employing Coupled Waveguides in

    Aluminum Gallium Arsenide

    by

    Rajiv Iyer

    A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

    Graduate Department of Electrical Engineering University of Toronto

    Copyright c© 2008 by Rajiv Iyer

  • Abstract

    Planar Lightwave Circuits

    Employing Coupled Waveguides in

    Aluminum Gallium Arsenide

    Rajiv Iyer

    Doctor of Philosophy

    Graduate Department of Electrical Engineering

    University of Toronto

    2008

    This dissertation addresses three research challenges in planar lightwave circuit (PLC)

    optical signal processing.

    1. Dynamic localization, a relatively new class of quantum phenomena, has not been

    demonstrated in any system to date. To address this challenge, the quantum system

    was mapped to the optical domain using a set of curved, coupled PLC waveguides in

    aluminum gallium arsenide (AlGaAs). The devices demonstrated, for the first time,

    exact dynamic localization in any system. These experiments motivate further mappings

    of quantum phenomena in the optical domain, leading toward the design of novel optical

    signal processing devices using these quantum-analog effects.

    2. The PLC microresonator promises to reduce PLC device size and increase optical

    signal processing functionality. Microresonators in a parallel cascaded configuration,

    called “side coupled integrated spaced sequence of resonators” (SCISSORs), could offer

    very interesting dispersion compensation abilities, if a sufficient number of rings is present

    to produce fully formed “Bragg” gaps. To date, a SCISSOR with only three rings has

    been reported in a high-index material system. In this work, one, two, four and eight-ring

    SCISSORs were fabricated in AlGaAs. The eight-ring SCISSOR succeeded in producing

    fully formed Bragg peaks, and offers a platform to study interesting linear and nonlinear

    ii

  • phenomena such as dispersion compensators and gap solitons.

    3. PLCs are ideal candidates to satisfy the projected performance requirements of

    future microchip interconnects. In addition to data routing, these PLCs must provide

    over 100-bit switchable delays operating at ∼ 1 Tbit/s. To date, no low loss optical device has met these requirements. To address this challenge, an ultrafast, low loss, switchable

    optically controllable delay line was fabricated in AlGaAs, capable of delaying 126 bits,

    with a bit-period of 1.5 ps. This successful demonstrator offers a practical solution for

    the incorporation of optics with microelectronics systems.

    The three aforementioned projects all employ, in their unique way, the coupling of light

    between PLC waveguides in AlGaAs. This central theme is explored in this dissertation

    in both its two- and multi-waveguide embodiments.

    iii

  • Acknowledgements

    I first and foremost express my sincere gratitude to Professor J. Stewart Aitchison for

    his mentorship over the past 5 years. Furthermore, I thank my research colleagues and

    mentors: Professor John E. Sipe, Professor Marc M. Dignam, Professor C. Martijn de

    Sterke, Professor Marc Sorel, Professor Peter W. E. Smith, Professor Henry M. van Driel,

    Professor Arthur L. Smirl, Dr. Jun Wan, Dr. Alan D. Bristow, Dr. Zhenshan Yang, Dr.

    Joachim Meier, Dr. Philip Chak, Dr. Francesca Pozzi and all my fellow students and

    staff in the Photonics Research Group.

    I also thank NSERC, the Ontario Centres of Excellence, the CCPE/Manulife Finan-

    cial, SPIE, and the AAPN for funding my research.

    I also thank Dr. Henry Lee and Yimin Zhou from the Emerging Communications

    Technology Institute for their assistance in fabricating my devices, and to Battista

    Calvieri and Steven Doyle from the Microscopy Imaging Lab for the use of their scanning

    electron microscopes. I also thank Andrew Bezinger and Dr. Margaret Buchanan from

    the Institute for Microstructural Sciences at the NRC for etching many of my devices.

    My thanks also extend to James Pond from Lumerical Inc. whose MODE Solutions

    served as an essential tool in my research.

    This PhD was only made possible thanks to my wife, Deepa, who supported my

    decision to return to school to continue my education. Her patience and friendship has

    been an invaluable resource of strength and advice.

    My sincere thanks to my parents, my niece, Mira, my nephew, Arjun, their parents,

    Tara and Vineet, their grandparents, Mana and Mavi, and all my friends, who helped

    me through the tough times, and celebrated with me during the high times. I also must

    specifically thank Arjun for helping me download my references, and our new baby who

    arrived just before final submission!

    Above all, I express my deepest gratitude to my Gurumatha Amma, for her unending

    guidance, love and support in all my endeavours.

    iv

  • Contents

    1 Introduction 1

    1.1 Planar Lightwave Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.1.1 Integrated versus Free-Space Optical Devices . . . . . . . . . . . . 2

    1.1.2 PLC Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.1.3 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.2 PLCs for Spatial Optical Signal Processing: Exact Dynamic Localization 5

    1.2.1 Mapping between Quantum and Optical Domains . . . . . . . . . 5

    1.2.2 Discrete Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    1.2.3 Bloch Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    1.2.4 Dynamic Localization . . . . . . . . . . . . . . . . . . . . . . . . . 8

    1.2.5 The Exact Dynamic Localization Challenge . . . . . . . . . . . . 9

    1.2.6 The Exact Dynamic Localization Solution . . . . . . . . . . . . . 9

    1.3 PLCs for Spectral Optical Signal Processing: SCISSORs . . . . . . . . . 10

    1.3.1 Microresonators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    1.3.2 Serial CROWs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    1.3.3 Parallel SCISSORs . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    1.3.4 The SCISSOR Challenge . . . . . . . . . . . . . . . . . . . . . . . 14

    1.3.5 The SCISSOR Solution . . . . . . . . . . . . . . . . . . . . . . . . 14

    1.4 PLCs for Temporal Optical Signal Processing: Optical Delay Lines . . . 15

    1.4.1 PLC Microchip Interconnects . . . . . . . . . . . . . . . . . . . . 15

    v

  • 1.4.2 Optical Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    1.4.3 PLC optical delays: Resonators versus Differing-Length

    Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    1.4.4 Optical Delay Switching . . . . . . . . . . . . . . . . . . . . . . . 18

    1.4.5 The Optical Delay Line Challenge . . . . . . . . . . . . . . . . . . 19

    1.4.6 The Optical Delay Line Solution . . . . . . . . . . . . . . . . . . . 20

    1.5 The Challenges and Solutions: Discussion . . . . . . . . . . . . . . . . . 20

    1.6 Light Coupling in Waveguides . . . . . . . . . . . . . . . . . . . . . . . . 21

    1.6.1 Light Confinement in a Single Waveguide . . . . . . . . . . . . . . 22

    1.6.2 Light Coupling in a Two-Waveguide System . . . . . . . . . . . . 23

    1.6.3 Light Coupling in a Multi-Waveguide System . . . . . . . . . . . 25

    1.6.4 The Nonlinear Directional Coupler Switch . . . . . . . . . . . . . 25

    1.7 Aluminum Gallium Arsenide . . . . . . . . . . . . . . . . . . . . . . . . . 26

    1.8 Summary and Thesis Organization . . . . . . . . . . . . . . . . . . . . . 28

    2 Light Coupling in Waveguides 29

    2.1 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

    2.2 Supermodes of the Directional Coupler . . . . . . . . . . . . . . . . . . . 33

    2.3 Hamiltonian Formulation of Coupled Mode Equations . . . . . . . . . . . 36

    2.3.1 Eigenmodes in a Restricted Basis . . . . . . . . . . . . . . . . . . 36

    2.3.2 Effective Fields and the Coupled Mode Equations . . . . . . . . . 39

    2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    3 Aluminum Gallium Arsenide 42

    3.1 AlGaAs Lattice Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    3.2 AlGaAs Material Index Dispersion . . . . . . . . . . . . . . . . . . . . . 44

    3.3 AlGaAs Optical Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . 45

    3.4 AlGaAs Wafers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

    vi

  • 3.4.1 AlGaAs Wafer: 24/18/24 . . . . . . . . . . . . . . . . . . . . . . . 47

    3.4.2 AlGaAs Wafer: 70/20/70 . . . . . . . . . . . . . . . . . . . . . . . 47

    3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    4 Exact Dynamic Localization 49

    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    4.2 Dynamic Localization in Curved Coupled Optical Waveguide Arrays . . . 52

    4.2.1 Paraxial Complex Vector Wave Equation . . . . . . . . . . . . . . 52

    4.2.2 Mapping of the Quantum System to Waveguide Arrays . . . . . . 54

    4.2.3 Straight Waveguide Array . . . . . . .