內容大鋼
This book is devoted to the spectral theory of localized resonances including surface plasmon/polariton resonances, atypical resonances, anomalous localized resonances and interior transmission resonances. Those resonance phenomena arise in different physical contexts, but share similar features. They form the fundamental basis for many cutting-edge technologies and applications including invisibility cloaking and superresolution imaging. The book presents a systematic and comprehensive treatment on these resonance phenomena and the associated applications in a unified manner from a mathematical and spectral perspective, covering acoustic, electromagnetic and elastic wave scattering.
The book can serve as a handy reference book for researchers in this field and it can also serve as a textbook or an inspiring source for postgraduate students who are interested in entering this field.
目錄
1 Introduction and Preliminaries
1.1 Overview
1.2 Layer Potentials in Electro-Magnetic System
1.3 Layer Potentials in Elastic System
1.4 Bessel and Neumann Functions
2 Mathematical Theory of Plasmon/Polariton Resonances in Quasi-Static Regime
2.1 Maxwell's Problem
2.1.1 Introduction to Plasmonic Resonances
2.1.2 Drude's Model for the Electric Permittivity and Magnetic Permeability
2.1.3 Boundary Integral Operators and Resolvent Estimates
2.1.4 Layer Potential Formulation
2.1.5 Derivation of the Asymptotic Formula
2.1.6 Numerical Ilustrations
2.1.7 Concluding Remarks
2.2 Elastic Problem
2.2.1 Layer Potential Techniques
2.2.2 Asymptotics for the Integral Operators
2.23 Far Field Expansion
2.2.5 Resolvent Analysis
2.2.6 Polariton Resonance for Elastic Nanoparticles
3 Anomalous Localized Resonances and Their Cloaking Effect
3.1 Elastostatic Problem
3.1.1 Mathematical Setup of Elastostatics Problem
3.1.2 Preliminaries on Layer Potentials
3.1.3 Spectral Analysis of N-P Operator in Spherical Geometry
3.1.4 Anomalous Localized Resonances and Their Cloaking Effect
3.1.5 Cloaking by Anomalous Localized Resonance on a Coated Structure in Two Dimensional Case
3.2 Electrostatic Problem
3.2.1 Background
3.2.2 Layer Potential Formulation and Spectral Theory of a Neumann Poincare -Type Operator
3.2.3 Analysis of Cloaking Due to Anomalous Localized Resonance
4 Localized Resonances for Anisotropic Geometry
4.1 Conductivity Problem
4.1.1 Some Auxiliary Results
4.1.2 Quantitative Analysis of the Electric Field
4.13 Application to Calderon's Inverse Inclusion Problem
4.2 Helmholtz Problem
4.2.1 Asymptotic and Quantitative Analysis of the Scattering Field
4.2.2 Resonance Analysis of the Exterior Wave Field
4.2.3 Resonance Analysis of the Interior Wave Field
4.2.4 Conclusion
5 Localized Resonances Beyond the Quasi-Static Approximation
5.1 Spectral System of Neumann Poincare Operators in Helmoholtz System and Its Asymptotic Behavior
5.1.1 Layer Potential and Spectral Properties of Neumann Poincare Operator in R
5.1.2 Asymptotic Behavior of Spectral System of Ncumann-Poincare Operator
5.1.3 Two Dimensional Case
5.2 Helmboltz System
5.2.1 Atypical Resonance and ALR Results in Three Dimensions
5.2.2 Spectral System of the N-P Operalor and IIs Application to Atypical Resonance in R
5.2.3 Atypical Resonance and ALR Results in Two Dimensions
5.3 Maxwell's Problem
5.3.1 Integral Formulation of the Maxwell System
5.3.2 Spectral Analysis of the Integral Operators
5.3.3 Atypical Resonance and Its Cloaking Effect
5.3.4 Invisibility Cloaking
5.4 Elastic Problem
5.4.1 Preliminaries
5.4.2 Spectrum System of the Neumann-Poincare Operator
5.4.3 Atypical Resonance Beyond the Quasi -Static
5.4.4 CALR Beyond the Quasi-Static Approximation
6 Interior Transmission Resonance
6.1 Introduction
6.2 Scalar Case (Helmholtz Equations)
6.2.1 Boundary-Localized Transmission Eigenstates
6.2.2 Super-Resolution Wave Imaing
6.2.3 Numerical Example
6.2.4 Pseudo Surface Plasmon Resonances and Potential
6.2.5 Concluding Remarks and Discussions
6.3 Vectorial Case (Maxwell Equations)
6.3.1 Background
6.3.2 Boundary-L ocalized Transmission Eigenmodes
6.3.3 Numerics
6.3.4 Application of Boundary-Localized Transmission Eigenfunctions: Artificial Mirage
6.4 Concluding Remarks
References
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