HOMODYNE DETECTION IN A LASER LOCKING SYSTEM by Aaron Bennett A senior thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Bachelor of Science Department of Physics and Astronomy Brigham Young University August 2010 Copyright (cid:13)c 2010 Aaron Bennett All Rights Reserved BRIGHAM YOUNG UNIVERSITY DEPARTMENT APPROVAL of a senior thesis submitted by Aaron Bennett This thesis has been reviewed by the research advisor, research coordinator, and department chair and has been found to be satisfactory. Date Dallin Durfee, Advisor Date Eric Hintz, Research Coordinator Date Ross L. Spencer, Chair ABSTRACT HOMODYNE DETECTION IN A LASER LOCKING SYSTEM Aaron Bennett Department of Physics and Astronomy Bachelor of Science I discuss a high speed, low noise homodyne photo-detector. This detector will be used to better implement laser locking techniques such as the Pound Drever Hall method or saturated absorption with lock-in amplification. I present a basic explanation of these methods and their benefits. I discuss aspects of the detector which allow it to operate with low noise over a high bandwidth. ACKNOWLEDGMENTS Most of all, I would like to acknowledge my wife whose constant support and unwavering loyalty makes all the difference in my life. I would also like to acknowledge my advisor who is possibly the only professor at BYU who would have the patience to advise me for over two years. Contents Table of Contents vii List of Figures ix 1 Introduction 1 1.1 Lock-In Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Locking to a Cavity . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Locking to an Atomic Absorption Line . . . . . . . . . . . . . 11 1.2.3 My Contribution to the Lock . . . . . . . . . . . . . . . . . . 19 2 Detector Layout 21 2.1 Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Transimpedance amplifier . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 Gain Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 Non-idealities in op amps 31 3.1 Back to the Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Gain Bandwidth Product . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1 What to be Aware of . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.2 Specific to my circuit . . . . . . . . . . . . . . . . . . . . . . . 35 3.3 Slew Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4 Load Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.5 Input Impedance and Capacitance . . . . . . . . . . . . . . . . . . . . 39 3.6 Voltage Swing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.7 DC Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.8 Parasitics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.9 Noise Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.10 Harmonic Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Results 53 4.1 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 vii viii CONTENTS 4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Bibliography 59 A Beer’s Law 61 B Saturated Absorption 65 C Computing Stray Capacitance 69 D Complex Analysis 73 List of Figures 1.1 Transmission through an optical cavity. . . . . . . . . . . . . . . . . . 7 1.2 Example of Poor Cavity Laser Lock. . . . . . . . . . . . . . . . . . . 8 1.3 The Pound Drever Hall Laser Lock. . . . . . . . . . . . . . . . . . . . 9 1.4 Transimpedance Amplifier. . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 Locking to an Atomic Absorption Line. . . . . . . . . . . . . . . . . . 15 2.1 Detector Schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Detector Block Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Photodiode Responsivity Curve. . . . . . . . . . . . . . . . . . . . . . 23 2.4 Reverse Biased Photodiode. . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 Transimpedance Amplifier. . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6 AD8015 Block Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.7 AD8099 Block Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1 Noninverting op amp. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 Inverting op amp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 AD8015 Bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4 AD8099 Bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.5 Schematic for Modeling Internal Resistance and Capacitance. . . . . . 40 3.6 Graphically Modeling Internal Resistance and Capacitance. . . . . . . 41 3.7 Exceeding the Voltage Swing of an op amp. . . . . . . . . . . . . . . 42 3.8 high-pass Filter Schematic. . . . . . . . . . . . . . . . . . . . . . . . . 44 3.9 Frequency Response of a High-Pass Filter. . . . . . . . . . . . . . . . 44 3.10 Noise Sources in a Non-inverting op amp. . . . . . . . . . . . . . . . . 49 4.1 Detector Bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.2 Detector Bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 B.1 Saturated Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 B.2 Saturated Absorption Graphs. . . . . . . . . . . . . . . . . . . . . . . 67 C.1 Stray Capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 D.1 Complex Analysis of Entire Circuit . . . . . . . . . . . . . . . . . . . 74 D.2 Complex Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . 75 ix x LIST OF FIGURES D.3 Mixer input vs. Mixer output . . . . . . . . . . . . . . . . . . . . . . 76