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TRAVIS-DISSERTATION.Pdf Copyright by Kort Alan Travis 2010 The Dissertation Committee for Kort Alan Travis certifies that this is the approved version of the following dissertation: Optical Scattering from Nanoparticle Aggregates Committee: Ernst-Ludwig Florin, Supervisor Konstantin V. Sokolov, Supervisor Michael C. Downer Michael Marder Gennady Shvets Optical Scattering from Nanoparticle Aggregates by Kort Alan Travis, B.S.; M.A. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN December 2010 Acknowledgments My supervisors and committee, for guidance and patience: • Konstantin Sokolov and Ernst-Ludwig Florin, at the University of Texas at Austin; • Mike Downer, Mike Marder, and Gennady Shvets, at the University of Texas at Austin; • Jochen Guck at the University of Leipzig. My mentors and professors, for excellent teaching and inspiration: • Marshall F. Onellion, Kirk W. McVoy, and Edward E. Miller, at the University of Wisconsin at Madison; • John Wilkerson, Marjorie A. Olmstead, Frederick C. Brown, and Hong Qian, at the University of Washington at Seattle; • Vadim Kaplunovski, Takeshi Udagawa, and Thomas A. Griffy, at the Univer- sity of Texas at Austin. My research colleagues and fellow students, for assistance and friendship: • Zhengui Wang at Seattle; • Timo Betz, Bryan Lincoln, Florian Rückerl and Dorothea Schön at Leipzig; iv • Kelly Rodibaugh, Dmitry Culcur, Wendy Chih-Wen Kan, Ryna Karnik, Tim Larson, and Justina Tam at Austin. My parents and siblings, for encouragement and love. And the many others who have enriched and elevated my life and education in innumerable ways. v Optical Scattering from Nanoparticle Aggregates Kort Alan Travis, Ph.D. The University of Texas at Austin, 2010 Supervisors: Ernst-Ludwig Florin Konstantin V. Sokolov Nanometer-scale particles of the noble metals have been used for decades as con- trast enhancement agents in electron microscopy. Over the past several years it has been demonstrated that these particles also function as excellent contrast agents for optical imaging techniques. The resonant optical scattering they exhibit en- ables scattering cross sections that may be many orders of magnitude greater than the analogous efficiency factor for fluorescent dye molecules. Biologically rele- vant labeling with nanoparticles generally results in aggregates containing a few to several tens of particles. The electrodynamic coupling between particles in these aggregates produces observable shifts in the resonance-scattering spectrum. This dissertation provides a theoretical analysis of the scattering from nanoparticle ag- gregates. The key objectives are to describe this scattering behavior qualitatively and to provide numerical codes usable for modeling its application to biomedical engineering. Considerations of the lowest-order dipole-dipole coupling lead to sim- ple qualitative predictions of the behavior of the spectral properties of the optical cross sections as they depend on number of particles, inter-particle spacing, and aggregate aspect ratio. More comprehensive analysis using the multiple-particle T- matrix formalism allows the elaboration of more subtle cross-section spectral fea- tures depending on the interactions of the electrodynamic collective-modes of the vi aggregate, of individual-particle modes, and of modes associated with groups of particles within the aggregate sub-structure. In combination these analyses and the supporting numerical code-base provide a unified electrodynamic approach which facilitates interpretation of experimental cross section spectra, guides the design of new biophysical experiments using nanoparticle aggregates, and enables optimal fabrication of nanoparticle structures for biophysical applications. vii Table of Contents Acknowledgments iv Abstract vi List of Tables xxii List of Figures xxiii Chapter 1. Introduction 1 Chapter 2. Single-particle electrodynamics 7 2.1 The material permittivity function . 7 2.1.1 Asimplemodel ...................... 9 2.1.2 Empirical measurement . 11 2.2 T-matrix formalism . 13 2.2.1 Vector spherical wave (VSW) basis . 14 2.2.2 T-matrix for a sphere: Mie scattering theory . 18 2.2.2.1 Truncation criterion . 22 2.2.3 Extinction and scattering cross sections . 24 2.2.3.1 Small radius limit . 28 2.2.4 Arbitrary boundary surfaces . 30 2.2.5 Limitations of the boundary conditions . 33 2.2.6 Core-shell composite particles . 35 Chapter 3. Phenomenology 38 3.1 Introduction............................. 38 3.2 Qualitative features of the scattering cross section . ....... 42 3.2.1 Definition of an aggregate . 42 viii 3.2.2 Widely-spaced particles; coherent structure factor .... 45 3.2.3 Closely-spaced particles . 45 3.2.3.1 Total number of particles . 46 3.2.3.2 Aspectratio ................... 49 3.2.3.3 Particle packing . 51 3.3 Approximation formulas . 52 3.3.1 A numerical experiment . 55 3.4 Summary .............................. 60 Chapter 4. Multiple-particle systems 62 4.1 Introduction............................. 62 4.2 T-matrixasanabstraction. 63 4.3 Translation operator for the VSW basis . 64 4.3.1 Closed-form expressions . 67 4.3.2 Recurrence relations . 67 4.3.3 Limitations of matrix representations . 69 4.4 Multiple-particle T-matrix . 69 4.4.1 Redundant multipole basis . 72 4.4.2 Cluster-centered approach . 73 4.4.2.1 Mackowski-Mishchenko formulation . 74 4.4.3 Multi-centered approach . 75 4.4.3.1 Full fields calculation . 75 4.4.3.2 Partial cross sections . 76 4.4.3.3 Recursive formulation . 77 4.5 Summary .............................. 79 Chapter 5. Computational methods 82 5.1 Overview .............................. 82 5.1.1 Designgoals ........................ 83 5.1.2 Dependencies........................ 84 5.2 Keyfeatures............................. 84 5.2.1 Arbitrary-precision number classes . 84 ix 5.2.2 Numerical functor class . 85 5.2.2.1 Spherical Bessel functions . 88 5.2.2.2 Legendre functions and transforms . 90 5.2.2.3 Jacobi functions . 92 5.2.2.4 Gaussian-Lobotto quadrature . 93 5.2.2.5 Gaunt, Wigner-3J, and Clebsch-Gordan coef- ficients...................... 95 5.2.2.6 Vector Spherical Harmonics . 97 5.2.3 Linearalgebraclasses . 98 5.2.4 Parallel processing support . 99 5.2.4.1 Thread-level parallelism . 99 5.2.4.2 Process-level parallelism . 102 5.3 Problem-spacespecifics. 105 5.3.1 Indexing on the vector multipole basis . 105 5.3.2 Translation operator for the VSW basis . 106 5.3.3 Representations of the T-matrix: single-particle, multi- centered,andcluster-centered . 107 5.3.4 Recursive, multi-centered implementation . 108 5.3.5 Cluster-centered implementation . 110 5.3.6 Full-fields calculation . 112 5.4 Futuredirections .......................... 113 Chapter 6. Advanced phenomenology 117 6.1 Introduction............................. 117 6.2 Collective mode interactions . 118 6.3 Per-particle interactions . 123 6.3.1 Constructive superposition . 124 6.3.1.1 A simple structure . 124 6.3.1.2 A more realistic structure . 128 6.3.1.3 Implications of constructive superposition . 135 6.3.2 Destructive superposition . 135 6.3.2.1 An example structure . 138 x 6.3.2.2 Statistical effects . 142 6.3.2.3 Dependence on particle size and inter-particle spacing...................... 142 6.3.2.4 Implications of destructive superposition . 143 6.4 Size dependence, near-field considerations . 144 6.4.1 High-order symmetry: implication of the Debye criterion 145 6.4.2 Limitations of the partial cross-section analysis . .... 148 6.5 Summary .............................. 151 Chapter 7. Conclusion 154 Appendix 1. Abridged documentation of numerical codes 162 1.0.1 Overview of the appendix . 162 1.1 ModuleIndex ............................ 165 1.1.1 Modules .......................... 165 1.2 NamespaceIndex .......................... 166 1.2.1 NamespaceList ...................... 166 1.3 ClassIndex ............................. 167 1.3.1 ClassHierarchy ...................... 167 1.4 ClassIndex ............................. 175 1.4.1 ClassList.......................... 175 1.5 Module Documentation . 183 1.5.1 arbitrary precision . 183 1.5.1.1 Detailed Description . 183 1.5.2 T-matrix .......................... 184 1.5.2.1 Detailed Description . 184 1.5.3 parallel programming . 184 1.5.3.1 Detailed Description . 185 1.6 NamespaceDocumentation. 186 1.6.1 commUtil Namespace Reference . 186 1.6.1.1 Detailed Description . 196 1.6.2 distributed_solver_module Namespace Reference . 196 xi 1.6.2.1 Detailed Description . 196 1.6.3 geometry Namespace Reference . 197 1.6.3.1 Detailed Description . 197 1.6.4 linalg Namespace Reference . 198 1.6.4.1 Detailed Description . 211 1.6.4.2 Function Documentation . 211 1.6.4.3 ND_deref .................... 211 1.6.4.4 ND_deref .................... 212 1.6.4.5 quadraticDiscriminant . 213 1.6.4.6 quadraticFormula . 213 1.6.5 linalg::sparse Namespace Reference . 214 1.6.5.1 Detailed Description . 215 1.6.6 mereNamespaceReference . 215 1.6.6.1 Detailed Description . 223 1.6.7 number Namespace Reference . 223 1.6.7.1 Detailed Description . 233 1.6.7.2 Function Documentation . 233 1.6.7.3 setDefaultPrecision . 233 1.6.8 numerical_functor Namespace Reference . 233 1.6.8.1 Detailed Description . 235 1.6.9 parallelUtil Namespace Reference . 235 1.6.9.1 Detailed Description . 237 1.6.10 TMatrix Namespace Reference . 237 1.6.10.1 Detailed Description . 239 1.6.11 TMatrix::constants Namespace Reference . 240 1.6.11.1 Detailed Description . 240 1.7 ClassDocumentation
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