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Transcript of LINEARIZED AND HIGH FREQUENCY ELECTROOPTIC Our technician, Reynold Johnson, helped me with numerous

  • LINEARIZED AND HIGH FREQUENCY ELECTROOPTIC MODULATORS

    Thesis by

    Uri Cummings

    In Partial Fulfillment of the Requirements for the

    degree of

    Doctor of Philosophy

    CALIFORNIA INSTITUTE OF TECHNOLOGY

    Pasadena, California

    2005

    (Defended April 27, 2005)

  • ii

    © 2005

    Uri Cummings

    All Rights Reserved

  • iii

    To the Memory of

    Francine Sachs Cummings (1940 - 1995)

    My mother,

    who encouraged me every day,

    always expressed spirited love,

    and wanted more for me than for herself.

  • iv ACKNOWLEDGEMENTS

    I thank Professor William B. Bridges, my graduate advisor. Bill taught me as an

    undergraduate, and then he invited me into his group for graduate studies. Bill took an active

    interest in my (and all of his students’) professional development and personal well-being.

    Whether on my behalf, or that of so many others, he sets a constant example of dedication and

    integrity. It was a pleasure to work for him. He has an incredible scientific intuition, a sense

    of humor, and a rich set of experiences that he shared from Caltech, Hughes, Berkeley, and

    many other places. After I took an extended leave to start Fulcrum Microsystems, Bill

    remained very supportive of my finishing my thesis. He spent a lot of time with me and

    invited me to his homes in Nevada City and Sierra Madre. No person in my professional life

    has had a larger impact.

    I thank Linda McManus, Bill’s spouse, who was also very eager to see me finish. She invited

    me to dinner many times and showed a keen interest in my well-being as well as that of all of

    Bill’s other students.

    This research was done under contract F30602-96-C-0020 from the U.S. Air Force Rome

    Laboratory and earlier under contract F30602-92-C-0005. I thank the late Brian Henderickson

    and the late Norman Bernstein who supported us both financially and morally.

    I thank all the people who helped in our laboratory. Our technician, Reynold Johnson, helped

    me with numerous experiments. His craft is first-rate, as is his humor. Lee Burrows, Bill’s

    other student, did a disproportionate amount of the laboratory setup.

    I thank our collaborators at Hughes Research Labs. Jim Schaffner worked closely with us,

    collaborating on modulator development and our peer publications. Joe Pikulski fabricated

    our modulators.

    I thank Axel Scherer for the generous use of his laboratory, and for help with difficult

    photolithographic tasks.

  • v I thank Charlie Cox at MIT Lincoln Labs who is a leader in the field and visited us many

    times and shared his insights.

    I thank and remember Ed Poser. Ed taught an insightful class, and did so with great wit. He

    gave me a Summer Undergraduate Research Fellowship (SURF) after just that one class. I was

    a transfer student, still learning my way around Caltech. On the first day of the SURF, Ed lost

    his life in a tragic accident. Bill offered to take me on, and gave me a new SURF project that

    eventually led to my graduate studies in his group.

    I thank Carolyn Ash who managed the SURF program. She matched contributions to support

    my SURF, and she showed interest in the details of research.

    I am happy with the formative years I spent at Caltech, 1992-1999. In particular I took many

    wonderful classes. Some professors taught so well that it seemed almost more important to

    take a class if taught by a particular professor then for the subject matter, as long as the class

    contributed to the department course requirements! Some, but not all of those professors, and

    in no particular order, are P.P. Vaidyanathan, David Rutledge, David Middlebrook, Alain

    Martin, R. J. McEliece, Amnon Yariv, Ed Posner, Joel Franklin, and of course Bill Bridges.

    I thank my colleagues at Fulcrum for being patient with me, when I had to reschedule work

    with them in order to work on my thesis, and for generally being supportive, in particular, Bob

    Nunn, Alain Gravel, Mike Zeile, and Andrew Lines.

    Many fellow students made Caltech a wonderful place, whether for intellectual excitement,

    social activities, or just silliness (pranks). I thank Andrew Lines, Ted Turocy, and Mika

    Nystrom, a core group of my friends.

    My family has been very supportive of me. I thank my father, Robert, my brother Theo, and

    my Aunt, Marguerite, and all of my father’s extended family. I thank and remember my

    mother Francine.

  • vi ABSTRACT

    An analysis is performed of many standard and linearized electrooptic modulators known in

    the industry. The transfer functions of these modulators are evaluated under a consistent set

    of performance figures of merit, which are gain and spur-free dynamic range, using a canonical

    set of optical link parameters. The tolerance of the needed precision of the parameters of the

    linearization mechanisms of all of these modulators is compared over the entire interesting

    range of noise bandwidth.

    A computer program was written to analyze the frequency dependence of any modulator

    transfer function under any set of functional inputs. The program is used to illustrate and

    compare the frequency dependence of the figures of merit of all of the modulators for which a

    d-c analysis was performed. Further analysis looks at the effect of greater noise-bandwidth

    and recovering the frequency-dependent degradation of gain and dynamic range through re-

    phasing techniques. The gain of directional couplers is analyzed in-depth.

    Two novel modulator schemes are produced. The first uses reflective wave techniques to

    retime the electrical and optical waves half way through the modulator. The second uses

    fabrication geometry and properties of the linearization technique to make a more robust

    modulator (applicable to three of the modulators analyzed).

    A 94 GHz antenna-coupled directional coupler modulator was initially demonstrated using an

    old modulator chip from Finbar Sheehy. A peculiar bug with the chip was uncovered. And a

    new modulator experiment was constructed and many aspects of the experimental apparatus

    were optimized. Though the revised experiment ultimately did not yield modulation side

    bands, it did couple a 94 GHz microwave signal into the optical waveguide, and many

    interesting challenges of high frequency electrooptic modulator fabrication were evaluated and

    improved upon.

  • vii TABLE OF CONTENTS

    Acknowledgements ............................................................................................................iv Abstract ................................................................................................................................vi Table of Contents..............................................................................................................vii List of Figures .....................................................................................................................ix List of Tables.......................................................................................................................xi Chapter I: Introduction.....................................................................................................1 Thesis Organization.........................................................................................................3 Chapter II: Electrooptic Modulator Fundamentals……………………………...5 The Electrooptic Effect..................................................................................................6 Electrooptic Modulation in Bulk Crystals ...................................................................7 Waveguide Phase Modulators......................................................................................10 Intensity Modulators Based on Mach-Zehnder Interferometers..........................11 Waveguide Electrooptic Modulators Based on Directional Couplers .................14 Fidelity in Electrooptic Modulators............................................................................17 Frequency and Bandwidth Limitations in Electrooptic Modulators....................19 Increasing Frequency Response of E-O Modulators by Velocity Matching......21 Chapter III: Distortion in Modulation Abstract............................................................................................................................25 Link Model ......................................................................................................................26 Analysis with One and Two Tones ............................................................................27 Linearized Modulators ..................................................................................................33 Super-Octave Modulators.........................................................................................33 The Ideal Limiter ........................................................................................................34 The Dual Parallel Mach-Zehnder Modulator.................................................