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Negative Refraction in Photonic Crystals and Metamaterials for Transformation Optics

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Negative Refraction in Photonic Crystals and Metamaterials for Transformation Optics Negative Refraction in Photonic Crystals and Metamaterials for Transformation Optics A Dissertation Presented by Yongjian Huang to The Department of Physics In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy In the field of Physics Northeastern University Boston, Massachusetts April, 2011 1 Copyright © 2011 by Yongjian Huang ALL RIGHTS RESERVED. 2 Negative Refraction in Photonic Crystals and Metamaterials for Transformation Optics by Yongjian Huang ABSTRACT OF DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate School of Arts and Sciences of Northeastern University, April, 2011 3 Abstract This thesis is about metamaterials and its application in negative refraction, slow light and transformation optics. Metamaterials have properties not available in nature and are typically man-made. They have exciting applications such as invisible cloaking, modulators, band-pass filters, perfect lenses, subwavelength resolution, beam compressors, slow-light devices and so on. We demonstrated one-dimensional, two-dimensional photonic crystals negative lenses, prisms, flat lens theoretically and experimentally at both microwave and optical frequency. We proposed a new mechanism on surface grating to realize negative refraction in photonics crystals. This approach can be used to image large and/or far way objects. We studied the slow light effect in extremely anisotropic nano-wire and planar waveguide consisting of conventional dielectric cladding with single-negative materials. Super-resolution imaging in three-dimensional metamaterial nanolens consisting of nanowires template is also demonstrated. We also studied the optical transmission at the interface of two transformation optics media or between a transformation optics medium and free space. We derived the generalized reflectionless boundary condition for the interface, which makes possible to guide and focus light without reflection. Flat lens and non-magnetic beam concentrator are two examples of this new design. They showed great advantage to previous research results in literature. 4 Acknowledgements It is a great pleasure to thank all people who helped me to make this thesis possible. Foremost, I would like to express my sincere gratitude to my advisor Prof. Srinivas Sridhar for encouragement, guidance and support of my PhD study and research, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis. I am especially grateful to Dr. Wentao Lu for his inspiration, and his great efforts to explain things clearly in theory. His familiarity in theory and simulation was very helpful during the research. It was a pleasure and a great opportunity to work with such a brilliant mind. I am also very grateful to thank the members of my thesis committee, Prof. Latika Menon and Prof. Jeffrey Sokoloff, for their valuable input and comments on my thesis. My sincere thanks also go to Dr. Bernard Didier F. Casse and Dr. Plarenta Vodo for their valuable experimental skills. I greatly benefited from collaborating with Dr. Dong Xiao and his excellent comments on my thesis. I also thank Dr. Ravinder Banyal and Dr. Salvatore Savo for the stimulating discussions and for all the fun we have had. I would to thank Miss Rita Kaderian for her consideration and to host group discussion each week. I would also like to thank my parents Jimin Huang and Meihua Huang for giving birth to me at the first place and supporting me spiritually throughout my life. 5 I owe my loving thanks to my wife Ding Wang for her understanding and love during last few years. Her support and encouragement was so important for me to finish this thesis. 6 Table of Contents Abstract .......................................................................................................................................... 3 Acknowledgements ....................................................................................................................... 5 Table of Contents .......................................................................................................................... 7 Introduction ................................................................................................................................. 11 Chapter 1 Negative Refraction in Photonic Crystals ............................................................. 17 I. Negative Refraction and Plano-Concave Lens Focusing in One-Dimensional Photonic Crystals ... 17 II. Optical Experiment of 2D PC Plano-concave Lens ......................................................................... 26 III. Subwavelength Imaging by 1D Photonic Crystals ......................................................................... 35 IV. Subwavelength Imaging by Superlens at Infrared Wavelengths .................................................... 41 Appendix: FDTD Simulation ............................................................................................................... 47 Chapter 2 New Mechanism of Negative Refraction ............................................................... 49 I. A New Mechanism for Negative Refraction and Focusing using Selective Diffraction from Surface Corrugation ..................................................................................................................... 49 A. Introduction .............................................................................................................................................. 49 B. Negative refraction with visible light and microwave............................................................................... 50 C. Focusing by a plano-concave grating lens ............................................................................................... 56 D. All-angle negative refraction and negative lateral shift through grating multilayered structure ............ 59 E. Discussion and conclusion ........................................................................................................................ 62 II. Alternative Approach to All-angle Negative Refraction in Two-dimensional Photonic Crystals ... 64 A. Introduction .............................................................................................................................................. 65 7 B. Another Approach to AANR ...................................................................................................................... 66 C. Flat Lens with Large σ ............................................................................................................................. 70 D. Discussion and Conclusion ...................................................................................................................... 76 III. Nanoengineering of a Negative-index Binary-staircase Lens for the Optics Regime ................... 77 Chapter 3 Slow Light of Extremely Anisotropic Nanowire .................................................. 85 I. Introduction ....................................................................................................................................... 85 II. Wave Propagation and Energy Flow on Anisotropic Cylindrical Waveguides ............................... 86 A. TE modes .................................................................................................................................................. 90 B. TM modes .................................................................................................................................................. 91 C. Hybrid modes .......................................................................................................................................... 102 III. Slow and Trapped Light ............................................................................................................... 110 IV. Realization of Extremely Anisotropic Nanowires ........................................................................ 112 V. Conclusions ................................................................................................................................... 116 Appendix: PADÉ Approximant of fn ()x ......................................................................................... 117 Chapter 4 Storing Light in Active Optical Waveguides with Single-Negative Metamaterials ............................................................................................................................ 121 I. Introduction ..................................................................................................................................... 121 II. Waveguide geometry and transverse wave modes ........................................................................ 122 A. Delay Bandwidth Product ....................................................................................................................... 131 B. Effect of gain saturation .......................................................................................................................... 131 C. TE modes ................................................................................................................................................ 132 III. Realizability of the waveguides .................................................................................................... 133 IV. Conclusion ...................................................................................................................................
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