FM Mode-Locking and Coupled Optoelectronic Oscillation in a Composite-Cavity Electro-Optic Microchip Laser A Thesis Submitted to the Faculty of Drexel University by David K. Yoo in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2006 ii DEDICATIONS For Sam and Yifei, who always insisted that this day would come, And for my parents, who promised to watch over me until this day had come, And most of all for Steph, who was probably starting to wonder, “Will this day ever come?!” iii ACKNOWLEDGEMENTS Compiling even a partial list of the vast number of people who have advised and supported me throughout the years is an enormous undertaking. However, there are several individuals who I would like to thank by name. First and foremost, I thank my supervising advisor, Dr. Peter Herczfeld, for his trust, commitment, and a persistent guiding vision which involved not only lessons in science, but lessons in life as well. Secondly, I would like to express my gratitude to Dr. Robert Koerner and the Koerner family for their generous support of my graduate education as a Koerner Family Fellow; their direct encouragement and assistance quite literally made this achievement possible. Next, I thank Drs. Samuel Goldwasser, Yifei Li, and Arye Rosen, to whose camaraderie, wisdom, and professional expertise I credit my ability to persevere as a graduate student on a daily basis. Additionally, I give my heartfelt thanks to Renee Cohen for her enduring friendship and a willingness to assist me under the most unreasonable of expectations. I am also grateful to Drs. Allen Katz, William Jemison, Timothy Kurzweg, Tibor Berceli, and Ruifeng Zhang for their advice and support as members of my Candidacy and Thesis Examination Committees, as well as Dr. Mohana Shankar, who kindly served as Chairperson. I am indebted to Dr. Asher Madjar, Dr. Afshin Daryoush, Dr. Robert Fischl, Zygmund Turski, Dr. Lorenzo Narducci, Dr. Nihat Bilgutay, Dr. Mohammed-Reza “Soheil” Tofighi, Dr. Maja Bystrom, and Dr. Adam Fontecchio for their mentorship and technical advisement, as well as Dr. Anthony Siegman for a particularly helpful discussion regarding the effect of multiple reflections in mode-locked composite-cavity lasers. iv I acknowledge the following professional colleagues for their comradeship and vital insights at various junctures throughout my tenure as a graduate student: Michael Ermold (whose early accomplishments laying the groundwork for this thesis are neither unrecognized nor unappreciated), Prashant Poddar, Dr. Marcelo Franco and Linearizer Technology Incorporated, Ryan Spring, Steven Jenks, Dr. Amarildo Vieira, Usmah Kawoos, Hemang Shah, Liming Zhou, Vasileios Nasis, Shodhan Shetty, Chenpeng Mu, Thomas Krol, Joseph Petrella and IMET Corporation, Wayne Bitting and Micro- Electronics Assemblers, Long Xiao, Xiying Chen, Bernard Cohen, Amy Ji of Photop Technologies, Stacey Caiazzo, Megan Parker-Johnson, Tanita Chappelle, Kathy Bryant, Wayne Hill, Brian Kravitz, Jonathan Hoult, John MacDonald and Linear Photonics LLC, Michael Kubak, Kashma Rai, Ryan Michaluk, and Viktoriya Chekotun. I also affirm a particular appreciation for those friends who have patiently stood by me during this period, both in good times and in other times: Matthew Reddick, John “Duke” Munzer, Christopher Doody, Wesley Apgar, Vincent Dicaro, Eric Epstein, Dr. Brian Falcone, John and Donna Moffett, Jane Trent, Robert Marks, Robin Trent, Kevin Fisher, Stephen Manzo, Steven Moffett, Kurt Guenther, Lacey Swartz, Jonathan Botbyl, Alicia Lindsey, David Schmitt, and Regina Gunning. Furthermore, I thank Dr. Jorge Cham, creator of Piled Higher and Deeper Comics, for giving graduate students everywhere the laugh they need to make it through their week. Finally, and most importantly, I express my eternal gratitude and love to my entire family, including my parents Kyu Bong and Young Ock, my sister Marissa, Stephanie Marr, her brother Stephen, and their parents Frank and Sandra (who is remembered fondly), as well as Pete, Bob, and Margaret. (Well, maybe not Pete.) v TABLE OF CONTENTS List of tables.....................................................................................................................viii List of figures..................................................................................................................... ix Abstract............................................................................................................................ xvi Chapter 1 : Introduction...................................................................................................... 1 1.1 : The goal of this research effort....................................................................... 1 1.2 : Contributions .................................................................................................. 2 1.3 : Thesis organization......................................................................................... 3 Chapter 2 : Background and review of the literature.......................................................... 6 2.1 : Background and motivations .......................................................................... 6 2.1.1 : Microwave oscillator ....................................................................... 6 2.1.2 : Digital clock applications .............................................................. 10 2.1.3 : Sampler for photonic analog-to-digital conversion ....................... 12 2.2 : Review of the literature................................................................................. 14 2.2.1 : Laser mode-locking – AM and FM ............................................... 15 2.2.2 : Fundamental and harmonic mode-locking .................................... 19 2.2.3 : Optoelectronic oscillators .............................................................. 22 2.2.4 : Microwave resonant optical modulation........................................ 25 2.2.5 : Regenerative mode-locking ........................................................... 26 2.2.6 : Coupled optoelectronic oscillators................................................. 28 2.3 : A new approach to generating high speed, low noise optical pulses............ 30 2.3.1 : Electro-optic microchip laser......................................................... 31 2.3.2 : Material properties of interest........................................................ 35 vi 2.3.3 : Fundamental FM mode-locking..................................................... 39 2.4 : The objectives of this thesis work................................................................. 43 Chapter 3 : Optical mode control...................................................................................... 45 3.1 : Transverse mode confinement...................................................................... 46 3.1.1 : Paraxial ray propagation of pump beam........................................ 47 3.1.2 : Thermal lensing effects.................................................................. 49 3.1.3 : Optical resonator mode.................................................................. 50 3.1.4 : Physical observations..................................................................... 56 3.2 : Longitudinal mode control............................................................................ 62 3.2.1 : Experimental study ........................................................................ 66 3.2.2 : Analysis ......................................................................................... 70 3.2.3 : Revision of the analytical model ................................................... 73 Chapter 4 : Optimization of microwave/optical wave interaction.................................... 79 4.1 : Transverse optimization................................................................................ 79 4.1.1 : Resonator isotropic approximation with 5 magnetic walls............ 83 4.1.2 : Modal requirements for anisotropic case....................................... 86 4.1.3 : Improved formulation and analytical limitations........................... 88 4.1.4 : Coupling of rectangular waveguide into electro-optic medium .... 93 4.2 : Full-wave simulation study........................................................................... 97 4.3 : Longitudinal optimization........................................................................... 100 4.4 : Summary..................................................................................................... 106 Chapter 5 : FM mode-locking dynamics in a Fabry-Perot laser..................................... 108 5.1 : Formulation of the Maxwell-Bloch equations............................................ 111 vii 5.1.1 : Equations of motion..................................................................... 113 5.1.2 : Coordinate transform and scaling................................................ 115 5.1.3 : Boundary conditions.................................................................... 116 5.2 : Numerical solution strategy........................................................................ 119 5.3 : Numerical results ........................................................................................ 125 5.4 : Summary..................................................................................................... 136 Chapter 6 : Design and evaluation of laser prototype..................................................... 138 6.1 : Laser characterization................................................................................