CHARACTERIZATION OF THE STRESS AND REFRACTIVE-INDEX DISTRIBUTIONS IN OPTICAL FIBERS AND FIBER-BASED DEVICES A Thesis Presented to The Academic Faculty by Michael R. Hutsel In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Electrical and Computer Engineering Georgia Institute of Technology December 2011 CHARACTERIZATION OF THE STRESS AND REFRACTIVE-INDEX DISTRIBUTIONS IN OPTICAL FIBERS AND FIBER-BASED DEVICES Approved by: Professor Thomas K. Gaylord, Professor Linda S. Milor Advisor, Committee Chair School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor John A. Buck Dr. Michael E. Knotts School of Electrical and Computer Signature Technology Laboratory Engineering Georgia Tech Research Institute Georgia Institute of Technology Dr. Donald D. Davis Date Approved: 3 November 2011 School of Electrical and Computer Engineering Georgia Institute of Technology ACKNOWLEDGEMENTS Trust in the LORD with all your heart, and do not lean on your own understanding. In all your ways acknowledge him, and he will make straight your paths. − Proverbs 3:5-6 (ESV) I thank God for His grace, His unmerited kindness, that He's shown me throughout my life and especially during my time at Georgia Tech. This is especially evident in the loving and supportive family, friends, and colleagues that He's brought into my life and allowed me to work alongside. My wife, Laura, made the completion of this degree possible with her uncon- ditional love demonstrated daily with encouraging words and in special ways like bringing a homemade dinner to the office on nights I worked late. Her daily support never declined, though she worked full time as a dedicated speech-language patholo- gist and most recently as a full-time, wonderful mother of our daughter, Katherine. Her commitment to me and to our family is my greatest motivation. My parents, Ross and Pat, enabled me to pursue and complete this degree in more ways than I'll ever know. Early in my life they fostered my engineering interests by allowing my brother, Brian, and me to dump gallons of Lego pieces across the living room floor and spend all day constructing whatever we could imagine. As I grew older, they continued to support my sometimes questionable technical pursuits like removing all of the seats, interior panels, consoles, and carpeting from my car to run wires to speakers that occupied nearly the entire trunk. iii It has been a privilege to have Dr. Tom Gaylord as an advisor. The work reported in this thesis is a direct result of his constant positive attitude and support at the deepest technical level. He is an example of a great leader in the Optics Lab, a thoughtful and thorough researcher, and a considerate gentleman. My committee members, Dr. John Buck, Dr. Don Davis, Dr. Linda Milor, and Dr. Michael Knotts helped me to refine this work and this thesis to a level that I could not achieve on my own. I am grateful for the interest they showed in this work and the time they took to discuss it in great detail. I am grateful for the students in the Optics Lab with whom I've been able to collaborate. My work is only a building block on top of the excellent work performed by Dr. Brent Bachim and Dr. Carole Montarou. Dr. Justin Stay, Jon Maikisch, Dr. Chien-I Lin, Matt Burrow, Matthieu Leibovici, and Micah Jenkins sacrificed great amounts of time and effort to work through difficult concepts, troubleshoot lab equipment and procedures, and help refine my writing and presentations in great detail. Gatherings of the Optics All Stars helped me remain balanced; Optics Lab cook-offs kept me well fed. I am also grateful for the assistance of Louis Boulanger in the machine shop and Rajib Acharya for computer support. The measurement apparatus developed as part of this work would not have been possible without Mr. Boulanger's excellent, careful work and Mr. Acharya's ability to solve the most obscure problems. I thank God for all of these family, friends, and colleagues and for many others that I have not acknowledged here. He has set straight my path, drawing me closer to Himself, through all of you. For that I am eternally thankful. Michael R. Hutsel Georgia Institute of Technology November 2011 iv TABLE OF CONTENTS ACKNOWLEDGEMENTS .......................... iii LIST OF TABLES ............................... ix LIST OF FIGURES .............................. x LIST OF ABBREVIATIONS ........................ xiv SUMMARY .................................... xv 1 INTRODUCTION ............................. 1 1.1 Motivation................................1 1.2 Background...............................4 1.2.1 Residual Stress in Optical Fibers................4 1.2.2 Refractive-Index Distribution in Optical Fibers........5 1.3 Existing Characterization Techniques.................5 1.3.1 Residual-Stress Characterization................5 1.3.2 Refractive-Index Characterization............... 11 1.4 CO2-Laser-Induced LPFGs....................... 18 1.4.1 Potential Applications...................... 19 1.4.2 Characterization Efforts..................... 22 1.5 Research Objectives and Accomplishments.............. 23 1.6 Thesis Overview............................. 25 2 RESIDUAL-STRESS CHARACTERIZATION ........... 27 2.1 Retardation Measurement with the BKC Technique......... 27 2.1.1 Theory.............................. 27 2.1.2 Measurement Procedure..................... 30 2.1.3 Image Analysis.......................... 34 2.2 Residual-Stress Characterization.................... 36 2.2.1 Relationship Between the Retardation and the Stress.... 36 2.2.2 Computed Tomography for the Determination of RSDs... 38 v 2.3 Measurement Issues........................... 43 2.3.1 Background Retardation Removal............... 43 3 REFRACTIVE-INDEX CHARACTERIZATION .......... 45 3.1 Phase-Shift Measurement with the QPM Technique......... 45 3.1.1 Theory.............................. 45 3.1.2 Measurement Procedure..................... 48 3.1.3 Image Analysis.......................... 49 3.2 Refractive-Index Characterization................... 50 3.2.1 Relationship Between the Phase Shift and the Refractive Index 50 3.2.2 Inverse Abel Transform for the Determination of RIPs.... 51 3.2.3 Computed Tomography for the Determination of RIDs.... 63 3.3 Measurement Issues........................... 65 3.3.1 Temperature Sensitivity..................... 65 3.3.2 Background Measurement.................... 66 4 MEASUREMENT APPARATUS ................... 70 4.1 Common Elements............................ 71 4.1.1 Light Source, Polarizer and Condenser............. 71 4.1.2 Microscope Stage Plate..................... 71 4.1.3 Fiber Rotation Apparatus................... 73 4.1.4 Objective............................. 73 4.1.5 CCD Camera.......................... 74 4.2 Elements and Issues Specific to the BKC Technique......... 75 4.2.1 Polarizer and Analyzer..................... 75 4.2.2 Compensator........................... 75 4.3 Elements and Issues Specific to the QPM Technique......... 77 4.3.1 Polarizer............................. 77 4.3.2 Defocusing Apparatus...................... 77 vi 5 PRELIMINARY MEASUREMENTS AND PERFORMANCE . 78 5.1 Residual-Stress Characterization.................... 78 5.1.1 Unperturbed Fiber....................... 78 5.1.2 Cleaved Fiber.......................... 87 5.1.3 Fiber Exposed to CO2-Laser Radiation............ 90 5.1.4 Performance and Accuracy................... 96 5.2 Refractive-Index Characterization................... 99 5.2.1 Determination of Optimal Imaging Parameters........ 99 5.2.2 Unperturbed Fiber....................... 106 5.2.3 Performance and Accuracy................... 107 5.3 Summary................................. 108 6 CHARACTERIZATION OF CO2-LASER-INDUCED LPFGS .. 110 6.1 Previous Efforts............................. 110 6.1.1 Theoretical Investigations.................... 110 6.1.2 Investigations of Changes in the Core............. 113 6.1.3 Investigations of Changes in the Cladding........... 115 6.1.4 Qualitative Investigations.................... 115 6.2 Characterization of an Incrementally Exposed Fiber......... 116 6.2.1 Incrementally Exposed Fiber.................. 116 6.2.2 Characterization Procedure................... 117 6.2.3 Overall Results......................... 118 6.3 Analysis of the Incrementally Exposed Fiber............. 124 6.3.1 Photoelastic Effect........................ 125 6.3.2 Overall Stress-Induced and Measured Index Changes..... 127 6.3.3 Changes in the Core....................... 128 6.3.4 Changes in the Cladding Facing the Exposure........ 134 6.3.5 Changes in the Cladding Opposite the Exposure....... 138 6.4 Summary................................. 141 vii 7 CONCLUSIONS .............................. 146 7.1 Summary of Results........................... 146 7.1.1 Review of Existing Characterization Techniques....... 146 7.1.2 Residual-Stress Characterization with the BKC Technique.. 147 7.1.3 Refractive-Index Characterization with the QPM Technique. 148 7.1.4 Measurement Apparatus for the Concurrent Characterization of the RSD and RID....................... 149 7.1.5 Experimental Verification.................... 150 7.1.6 Characterization of CO2-Laser-Induced LPFGs........ 151 7.2 Future Work............................... 152 7.2.1 RSD and RID Characterization Techniques.......... 152 7.2.2 CO2-Laser-Induced LPFGs................... 154 7.2.3 Other Optical Fibers and Fiber-Based Devices........ 155 7.3 Concluding Remarks..........................