Photonic crystals: Analysis, design and biochemical sensing applications A Thesis Presented to The Academic Faculty by Hamza Kurt In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Electrical and Computer Engineering Georgia Institute of Technology August 2006 Copyright © 2006 by Hamza Kurt Photonic crystals: Analysis, design and biochemical sensing applications Approved by: Dr. Ali Adibi, Committee Chair Dr. Paul Voss School of ECE School of ECE Georgia Institute of Technology Georgia Institute of Technology Dr. David S. Citrin, Advisor Dr. Christopher Summers School of ECE School of MSE Georgia Institute of Technology Georgia Institute of Technology Dr. John Papapolymerou School of ECE Georgia Institute of Technology Date Approved: June 22, 2006 This dissertation is dedicated to my mother Seniye and my father Ali ACKNOWLEDGEMENTS The end of one journey means the beginning of another one. After two-year of study at the University of Southern California while exploring the west side of the US, I started my PhD program on the east side at Georgia Institute of Technology in 2002. During the last year of my study, I had a chance to move to the Georgia Tech Lorraine, France. Throughout all these years, I was lucky meeting with precious people; friends, instructors and advisors. It is impossible to mention all of the people whom I would like to thank but first I want to express my sincere gratitude towards my advisor, Prof. David S. Citrin, for making my study at Georgia Tech stimulating and enjoyable one while giving me the full freedom to explore this research topic. I would like to thank to my dissertation committee members Prof. Ali Adibi and Prof. John Papapolymerou for taking the time to read and comment on both my proposal and dissertation and Prof. Christopher Summers for willing to serve in my committee. I gratefully acknowledge the financial support of the Turkish Education Foundation (TEV) for my master study at the University of Southern California. I would like to thank all my friends in Atlanta, California, and everywhere for the joy they brought in my life. My big gratitude goes to every member of my family for everything especially believing in me, for their never ending love, encourages and patience. Last but not least, I am grateful to my fiancée, Özlem, for her love and support. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS ............................................................................................ iv LIST OF TABLES.......................................................................................................... vii LIST OF FIGURES....................................................................................................... viii SUMMARY ...................................................................................................................... xi CHAPTER I INTRODUCTION ............................................................................................................ 1 1.1 Photonic crystals: Past, present and future ................................................................ 1 1.2 Outline of the thesis................................................................................................. 16 CHAPTER II THE STUDY OF PHOTONIC CRYSTALS................................................................ 17 2.1 Introduction to the numerical methods.................................................................... 17 2.2 The plane wave expansion method.......................................................................... 18 2.2.1 The theory of band structures............................................................................ 18 2.2.2 The formulation of PWM ................................................................................. 20 2.2.3 Two-dimensional PWM .................................................................................... 22 2.2.4 Two-dimensional photonic crystals .................................................................. 24 2.2.5 Three-dimensional photonic crystals ................................................................ 25 2.2.6 Photonic crystal parameters .............................................................................. 30 2.3 Finite-difference time-domain method.................................................................... 32 2.3.1 The formulation of FDTD ................................................................................ 32 2.3.2 One-dimensional FDTD method ...................................................................... 33 2.3.3 Two-dimensional FDTD method ...................................................................... 36 2.3.4 There-dimensonal FDTD method .................................................................... 39 2.4 Boundary conditions................................................................................................ 43 2.4.1 Perfectly matched layer .................................................................................... 43 2.4.2 PML loss parameters ........................................................................................ 44 2.4.3 Periodic boundary conditon ............................................................................. 45 2.5 Finite-difference time-domain with recursive convolution..................................... 47 v CHAPTER III PHOTONIC CRYSTALS FOR BIOCHEMICAL SENSING (I) .............................. 55 3.1 Introduction ............................................................................................................. 55 3.2 Photonic crystal waveguide sensors ........................................................................ 57 3.3 Results and discussions ........................................................................................... 61 3.4 Photonic crystal waveguide sensors in the microwave regime ............................... 67 3.5 Conclusions ............................................................................................................. 69 CHAPTER IV PHOTONIC CRYSTALS FOR BIOCHEMICAL SENSING (II)............................. 72 4.1 Introduction ............................................................................................................. 72 4.2 Coupled-resonator optical waveguide sensors ........................................................ 73 4.3 Results and discussions ........................................................................................... 74 4.4 Conclusions ............................................................................................................. 82 CHAPTER V ANNULAR PHOTONIC CRYSTALS ......................................................................... 85 5.1 Introduction ............................................................................................................. 85 5.2 The structure............................................................................................................ 87 5.3 Results and discussions ........................................................................................... 88 5.4 Conclusions ........................................................................................................... 105 CHAPTER VI PHOTONIC-CRYSTAL HETEROSTRUCTURES ................................................. 106 6.1 Introduction ........................................................................................................... 106 6.2 Design of photonic crystal heterostructure waveguides........................................ 108 6.3 Calculation of bending efficiency.......................................................................... 116 6.4 Results and discussions of 300 PCW bend ............................................................ 119 6.5 Conclusions ........................................................................................................... 126 CHAPTER VII CONCLUSIONS AND FUTURE RESEARCH......................................................... 128 REFERENCES.............................................................................................................. 134 vi LIST OF TABLES Table 4.1: Design parameters of CROW. ..................................................................... 78 Table 5.1: Comparison of square lattice PC and APC. .................................................. 97 Table 5.2: Comparison of triangular lattice PC and APC. ............................................. 97 vii LIST OF FIGURES Figure 1.1: Energy plot of an electron. ........................................................................... 3 Figure 1.2: One dimensional periodic layers. ................................................................. 4 Figure 1.3: Band diagram of 1D periodic layer. ............................................................. 6 Figure 1.4: Schematics of photonic crystals. .................................................................. 7 Figure 1.5: Defect modes of a photonic crystal. ........................................................... 11 Figure 1.6: 900 waveguide band. .................................................................................... 12 Figure 1.7: T-junction and splitter. ............................................................................... 13 Figure 2.1: Schematics of 2D photonic crystals. ......................................................... 24 Figure 2.2: Band daigram of 2D square lattice photonic crystal. ................................. 26 Figure 2.3: Band