by Tong Shiu Sing Dominic. / Parallel title in Chinese characters. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 236-241). / Acknowledgements --- p.iv / Abstract --- p.v / Chapter 1 --- Open Systems and Quasinormal Modes --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Non-Hermitian Systems --- p.1 / Chapter 1.1.2 --- Optical Cavities as Open Systems --- p.3 / Chapter 1.1.3 --- Outline of this Thesis --- p.6 / Chapter 1.2 --- Simple Models of Open Systems --- p.10 / Chapter 1.3 --- Contributions of the Author --- p.14 / Chapter 2 --- Completeness and Orthogonality --- p.16 / Chapter 2.1 --- Introduction --- p.16 / Chapter 2.2 --- Green's Function of the Open System --- p.19 / Chapter 2.3 --- High Frequency Behaviour of the Green's Function --- p.24 / Chapter 2.4 --- Completeness of Quasinormal Modes --- p.29 / Chapter 2. 5 --- Method of Projection --- p.31 / Chapter 2.5.1 --- Problems with the Usual Method of Projection --- p.31 / Chapter 2.5.2 --- Modified Method of Projection --- p.33 / Chapter 2.6 --- Uniqueness of Representation --- p.38 / Chapter 2.7 --- Definition of Inner Product and Quasi-Stationary States --- p.39 / Chapter 2.7.1 --- Orthogonal Relation of Quasinormal Modes --- p.39 / Chapter 2.7.2 --- Definition of Hilbert Space and State Vectors --- p.41 / Chapter 2.8 --- Hermitian Limits --- p.43 / Chapter 2.9 --- Numerical Examples --- p.45 / Chapter 3 --- Time-Independent Perturbation --- p.58 / Chapter 3.1 --- Introduction --- p.58 / Chapter 3.2 --- Formalism --- p.60 / Chapter 3.2.1 --- Expansion of the Perturbed Quasi-Stationary States --- p.60 / Chapter 3.2.2 --- Formal Solution --- p.62 / Chapter 3.2.3 --- Perturbative Series --- p.66 / Chapter 3.3 --- Diagrammatic Perturbation --- p.70 / Chapter 3.3.1 --- Series Representation of the Green's Function --- p.70 / Chapter 3.3.2 --- Eigenfrequencies --- p.73 / Chapter 3.3.3 --- Eigenfunctions --- p.75 / Chapter 3.4 --- Numerical Examples --- p.77 / Chapter 4 --- Method of Diagonization --- p.81 / Chapter 4.1 --- Introduction --- p.81 / Chapter 4.2 --- Formalism --- p.82 / Chapter 4.2.1 --- Matrix Equation with Non-unique Solution --- p.82 / Chapter 4.2.2 --- Matrix Equation with a Unique Solution --- p.88 / Chapter 4.3 --- Numerical Examples --- p.91 / Chapter 5 --- Evolution of the Open System --- p.97 / Chapter 5.1 --- Introduction --- p.97 / Chapter 5.2 --- Evolution with Arbitrary Initial Conditions --- p.99 / Chapter 5.3 --- Evolution with the Outgoing Plane Wave Condition --- p.106 / Chapter 5.3.1 --- Evolution Inside the Cavity --- p.106 / Chapter 5.3.2 --- Evolution Outside the Cavity --- p.110 / Chapter 5.4 --- Physical Implications --- p.112 / Chapter 6 --- Time-Dependent Perturbation --- p.114 / Chapter 6.1 --- Introduction --- p.114 / Chapter 6.2 --- Inhomogeneous Wave Equation --- p.117 / Chapter 6.3 --- Perturbative Scheme --- p.120 / Chapter 6.4 --- Energy Changes due to the Perturbation --- p.128 / Chapter 6.5 --- Numerical Examples --- p.131 / Chapter 7 --- Adiabatic Approximation --- p.150 / Chapter 7.1 --- Introduction --- p.150 / Chapter 7.2 --- The Effect of a Varying Refractive Index --- p.153 / Chapter 7.3 --- Adiabatic Expansion --- p.156 / Chapter 7.4 --- Numerical Examples --- p.167 / Chapter 8 --- Generalization of the Formalism --- p.176 / Chapter 8. 1 --- Introduction --- p.176 / Chapter 8.2 --- Generalization of the Orthogonal Relation --- p.180 / Chapter 8.3 --- Evolution with the Outgong Wave Condition --- p.183 / Chapter 8.4 --- Uniform Convergence of the Series Representation --- p.193 / Chapter 8.5 --- Uniqueness of Representation --- p.200 / Chapter 8.6 --- Generalization of Standard Calculations --- p.202 / Chapter 8.6.1 --- Time-Independent Perturbation --- p.203 / Chapter 8.6.2 --- Method of Diagonization --- p.206 / Chapter 8.6.3 --- Remarks on Dynamical Calculations --- p.208 / Appendix A --- p.209 / Appendix B --- p.213 / Appendix C --- p.225 / Appendix D --- p.231 / Appendix E --- p.234 / References --- p.236
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_318332 |
| Date | January 1995 |
| Contributors | Tong, Shiu Sing Dominic., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, v, 241 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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