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「SpectraI Theory of Localized Resonances and Applications(局域共振谱理论及其应用)


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「SpectraI Theory of Localized Resonances and Applications(局域共振谱理论及其应用)
  • 书号:9787030775436
    作者:邓又军,刘宏宇
  • 外文书名:
  • 装帧:平装
    开本:B5
  • 页数:362
    字数:466000
    语种:zh-Hans
  • 出版社:科学出版社
    出版时间:2024-05-01
  • 所属分类:高等数学
  • 定价: ¥168.00元
    售价: ¥126.00元
  • 图书介质:
    纸质书

  • 购买数量: 件  可供
  • 商品总价:

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本书致力于局域共振的光谱理论,包括表面等离子体/极化子共振,非典型共振,异常局域共振和内部传输共振。这些共振现象出现在不同的物理环境中,但具有相似的特征。它们构成了许多尖端技术和应用的基础,包括隐形斗篷和超分辨率成像。本书从数学和频谱的角度,以系统全面的方式对这些共振现象及其相关应用进行了统一的处理,涵盖了声波、电磁波和弹性波散射。
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目录

  • Contents
    1 Introduction and Preliminaries 1
    1.1 Overview 1
    1.2 Layer Potentials in Electro-Magnetic System 2
    13 Layer Potentials in Elastic System 4
    1.4 Bessel and Neumann Functions 6
    2 Mathematical Theory of Plasmon/Polariton Resonances in Quasi-Static Regime 9
    2.1 Maxwell's Problem 9
    2.1.1 Introduction to Plasmonic Resonances 9
    2.1.2 Drude's Model for the Electric Permittivity and Magnetic Permeability 12
    2.1.3 Boundary Integral Operators and Resolvent Estimates 15
    2.1.4 Layer Potential Formulation 24
    2.1.5 Derivation of the Asymptotic Formula 25
    2.1.6 Numerical Ilustrations 46
    2.1.7 Concluding Remarks 48
    2.2 Elastic Problem 48
    2.2.1 Layer Potential Techniques 51
    2.2.2 Asymptotics for the Integral Operators 53
    2.23 Far Field Expansion 57
    2.2.5 Resolvent Analysis 67
    2.2.6 Polariton Resonance for Elastic Nanoparticles 69
    3 Anomalous Localized Resonances and Their Cloaking Effect 77
    3.1 Elastostatic Problem 77
    3.1.1 Mathematical Setup of Elastostatics Problem 77
    3.1.2 Preliminaries on Layer Potentials 79
    3.1.3 Spectral Analysis of N-P Operator in Spherical Geometry 81
    3.1.4 Anomalous Localized Resonances and Their Cloaking Effect 90
    3.1.5 Cloaking by Anomalous Localized Resonance on a Coated Structure in Two Dimensional Case 97
    3.2 Electrostatic Problem 115
    3.2.1 Background 115
    3.2.2 Layer Potential Formulation and Spectral Theory of a Neumann Poincare -Type Operator 117
    3.2.3 Analysis of Cloaking Due to Anomalous Localized Resonance 121
    4 Localized Resonances for Anisotropic Geometry 129
    4.1 Conductivity Problem 129
    4.1.1 Some Auxiliary Results 130
    4.1.2 Quantitative Analysis of the Electric Field 135
    4.13 Application to Calderon's Inverse Inclusion Problem 144
    4.2 Helmholtz Problem 145
    4.2.1 Asymptotic and Quantitative Analysis of the Scattering Field 150
    4.2.2 Resonance Analysis of the Exterior Wave Field 169
    4.2.3 Resonance Analysis of the Interior Wave Field 176
    4.2.4 Conclusion 181
    5 Localized Resonances Beyond the Quasi-Static Approximation 183
    5.1 Spectral System of Neumann Poincare Operators in Helmoholtz System and Its Asymptotic Behavior 184
    5.1.1 Layer Potential and Spectral Properties of Neumann Poincare Operator in R3 184
    5.1.2 Asymptotic Behavior of Spectral System of Ncumann-Poincare Operator 187
    5.1.3 Two Dimensional Case 191
    5.2 Helmboltz System 196
    5.2.1 Atypical Resonance and ALR Results in Three Dimensions 200
    5.2.2 Spectral System of the N-P Operalor and IIs Application to Atypical Resonance in R3 210
    5.2.3 Atypical Resonance and ALR Results in Two Dimensions 213
    5.3 Maxwell's Problem 219
    5.3.1 Integral Formulation of the Maxwell System 220
    5.3.2 Spectral Analysis of the Integral Operators 225
    5.3.3 Atypical Resonance and Its Cloaking Effect 233
    5.3.4 Invisibility Cloaking 240
    5.4 Elastic Problem 248
    5.4.1 Preliminaries 251
    5.4.2 Spectrum System of the Neumann-Poincare Operator 257
    5.4.3 Atypical Resonance Beyond the Quasi -Static 267
    5.4.4 CALR Beyond the Quasi-Static Approximation 273
    6 Interior Transmission Resonance 281
    6.1 Introduction 281
    6.2 Scalar Case (Helmholtz Equations) 285
    6.2.1 Boundary-Localized Transmission Eigenstates 285
    6.2.2 Super-Resolution Wave Imaing 311
    6.2.3 Numerical Example 321
    6.2.4 Pseudo Surface Plasmon Resonances and Potential 324
    6.2.5 Concluding Remarks and Discussions 325
    6.3 Vectorial Case (Maxwell Equations) 328
    6.3.1 Background 328
    6.3.2 Boundary-L ocalized Transmission Eigenmodes 329
    6.3.3 Numerics 348
    6.3.4 Application of Boundary-Localized Transmission Eigenfunctions: Artificial Mirage 351
    6.4 Concluding Remarks 356
    References 357
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