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Transformation Optics Applied to Plasmonics Imperial College London Department of Physics Transformation Optics Applied to Plasmonics Yu Luo Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of Imperial College London and the Diploma of Imperial College London Condensed Matter Theory Group Department of Physics, Blackett Laboratory Imperial College London London SW7 2BZ, UK August 2012 1 Abstract Lately, transformation optics (TO) has driven the development of metamaterial science, providing a direct link between a desired electromagnetic phenomenon and the material response required for its occurrence. However, this powerful framework is not restricted to the metamaterial design, and it has recently been exploited to study surface plasmon assisted phenomena. In this thesis, we mainly focus on the general strategy based on TO to design and study analytically plasmonic devices capable of efficiently harvesting light over a broadband spectrum and achieving considerable field confinement and enhancement. Using TO, we show that a finite nanoparticle with sharp geometrical features can behave like an infinite plasmonic system, thereby allowing simultaneously a broad- band interaction with the incoming light as well as a spectacular nanofocusing of its energy. Various plasmonic structures are designed and studied, such as 2D crescents, groove/wedge like nanostructures, overlapping nanowires, and rough metal surfaces. Comprehensive discussions are also provided on practical issues of this problem. First, we discuss how the edge rounding at the sharp boundary affects the local field enhancement as well as the energy and bandwidth of each plasmonic resonance. In particular, the necessary conditions for achieving broadband light harvesting with blunt structures are highlighted. The TO approach is then applied to study the interaction between plasmonic nanoparticles. We demonstrate that the energy and spectral shape of the localized surface plasmon resonances can be precisely controlled by tuning the separation between the nanoparticles. Finally, we consider the extension of the TO framework to 3D geometries, and show that the 3D structure is more robust to radiative loss than its 2D counterpart. The physical insights into sharp and blunt plasmonic nanostructures presented in this thesis may be of great interest for the design of broadband light-harvesting devices, invisible and non-invasive biosensors, and slowing-light devices. 2 Declaration I hereby certify that the material presented in this thesis, which I now submitted for the award of Doctor of Philosophy of Imperial College London, is my own work unless otherwise cited or acknowledged within the body of the text. Yu Luo 3 Acknowledgement In the summer of 2009 I left my home country for the first time to study at Imperial College. Time flies and now I am about to get my PhD degree. This three years' time is full of fond memories. This thesis would not have been possible without the help and support of the kind people around me, to only some of whom it is possible to give particular mention here. First and foremost I want to give my deepest gratitude to my supervisor, Prof. Pendry. It is his help, support and encouragement that make my Ph.D research productive and stimulating. I am also thankful for his openness and the time he spent on listening to my ideas, some of which even sound crazy. The advice he gave me was always helpful and inspiring, and I was always overwhelmed by his unsurpassed knowledge of physics. His enthusiasm and commitment for his work has also made profound impact on me. Prof. Pendry has provided an example of being a great scientist and professor, making me eager to follow in his footsteps. It is always an honour to be his student. Many colleagues provided generous help during my study, and I am grateful to all of them for their assistance and support. In particular, I would like to thank Dr. Alexandre Aubry, Dr. Antonio Fernández-Domínguez, Dr. Wei Hsiung Wee, Dr. Rongkuo Zhao, and Dr. Kosmas Tsakmakidis for discussions and collaborations. My thanks also go to Prof. Stefan Maier who brought unique perspectives to my work. I appreciate the contributions of time and administrative support from Prof. Matthew Foulkes and Prof. Adrian Sutton throughout the years. I acknowledge Lee Family Scholarship for the financial support for my PhD study. I am appreciative of my fellow graduate students, Tristan West, James Varley, Aeneas Wiener for making my time at Imperial a more enjoyable experience. I'm most grateful to my parents who raised me with a love of science and supported me in all my pursuits, as always, for which my mere expression of thanks does not suffice. Last, but by no means least, I would like to thank my girlfriend Jingjing Zhang, to whom this thesis is dedicated. I appreciate the good times and hard times we spent together, and the tremendous support you have provided in the past three years. Thank you for always being there for me. You are the apple of my eye. Yu Luo 4 Contents LIST OF FIGURES................................................................................................................................7 LIST OF TABLES ................................................................................................................................17 LIST OF ABBREVIATIONS...............................................................................................................18 LIST OF PUBLICATIONS..................................................................................................................19 CHAPTER 1: INTRODUCTION .......................................................................................................21 1.1 THEORY OF SURFACE PLASMONS ...................................................................................................21 1.1.1 Surface Plasmon polaritons at metal/dielectric interfaces....................................................22 1.1.2 Excitation of surface plasmon polaritons..............................................................................29 1.1.3 Localized surface plasmons ..................................................................................................31 1.2 THEORY OF TRANSFORMATION OPTICS...........................................................................................36 1.2.1 Geometrical view of transformation optics ...........................................................................36 1.2.2 Principle of transformation optics approach ........................................................................38 1.2.3 Application of transformation optics.....................................................................................39 1.2.4 Conformal transformation.....................................................................................................41 1.3 THESIS OVERVIEW.........................................................................................................................43 CHAPTER 2: SINGULAR PLASMONIC STRUCTURES FOR BROADBAND LIGHT HARVESTING .....................................................................................................................................45 2.1 EXAMPLES OF TWO TYPICAL SINGULAR STRUCTURES ....................................................................46 2.2 GENERAL SINGULAR STRUCTURES.................................................................................................49 2.2.1 Transformation of geometries ...............................................................................................49 2.2.2 The surface plasmon excitations ...........................................................................................52 2.2.3 The divergent electric field....................................................................................................58 2.2.4 Coupling of a dipole to a metallic wedge..............................................................................61 2.2.5 Light harvesting properties of crescents with a nonzero vertex angle...................................62 2.3 SURFACE ENHANCED RAMAN SCATTERING FROM ROUGH METAL SURFACES ..................................64 2.3.1 Broadband Raman scattering responses ...............................................................................64 2.3.2 Raman signal enhancements .................................................................................................66 2.4 CONCLUSIONS................................................................................................................................70 CHAPTER 3: PLASMONIC NANOSTRUCTURES WITH BLUNT EDGES/CORNERS..........71 3.1 THE CONFORMAL TRANSFORMATION APPROACH ...........................................................................72 3.2 THE NANOCRESCENT CONTAINING BLUNT TIPS ..............................................................................74 3.2.1 The quantization of surface plasmon modes..........................................................................74 3.2.2 Designing blunt plasmonic structures for broadband light absorption.................................77 3.2.3 Nanofocusing with blunt nanostructures...............................................................................80 3.3 THE OVERLAPPING NANOWIRE DIMER WITH BLUNT CORNERS........................................................81 3.3.1 The analytical solution ..........................................................................................................82 3.2.2 The absorption property........................................................................................................84
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