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周期結構中的Maxwell方程組(英文版) 版權信息
- ISBN：9787030669995
- 條形碼：9787030669995 ; 978-7-03-066999-5
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
周期結構中的Maxwell方程組(英文版) 本書特色
適讀人群 ：It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics,and engineering disciplines as well.本書關于麥克斯韋爾方程組理論和計算方法這一主題的數學理論是嚴格而深刻的。麥克斯韋爾方程組的計算方法是該書的亮點。
周期結構中的Maxwell方程組(英文版) 內容簡介
本書系統地闡述周期性結構中的正、反散射理論，它涵蓋了周期結構中麥克斯韋方程組正、反散射問題的幾乎所有主題，包括數學模型、物理原理、數學分析以及計算方法。該書首先介紹了電磁場和光柵的基本理論。對于正散射問題，本書詳細介紹變分方法來研究解的適定性以及自適應有限元的數值計算方法。對于反散射問題，本書討論了解的專享性、穩定性以及光柵界面重構的數值方法。此外，本書也介紹了此領域中的重要近期新發展，例如近場成像、時域散射問題、非線性光學和很優設計問題等。該書可以為攻讀碩士和博士學位的研究生提供初步的材料，以介紹周期性結構中麥克斯韋方程的正、反散射理論。它還為應用和計算數學的研究人員以及不同相關學科，例如電磁學和光學的工程人員提供了近期新的深刻的數學結果和具有挑戰性的問題。
周期結構中的Maxwell方程組(英文版) 目錄
Contents
1 Maxwell’s Equations 1
1.1 Electromagnetic Waves 1
1.2 Jump and Boundary Conditions 6
1.3 Two Fundamental Polarizations 9
References 12
2 Diffraction Grating Theory 13
2.1 Perfectly Conducting Gratings 14
2.2 Dielectric Gratings 22
2.3 Biperiodic Gratings 32
2.3.1 Perfect Electric Conductors 33
2.3.2 Dielectric Media 38
References 42
3 Variational Formulations 45
3.1 The Dirichlet Problem 46
3.2 The Transmission Problem 53
3.3 Biperiodic Structures 59
3.3.1 Function Spaces 60
3.3.2 The Transparent Boundary Condition 68
3.3.3 The Variational Problem 76
References 84
4 Finite Element Methods 87
4.1 The Finite Element Method 89
4.1.1 Finite Element Analysis for TE Polarization 90
4.1.2 Finite Element Analysis for TM Polarization 94
4.2 Adaptive Finite Element PML Method 98
4.2.1 The PML Formulation 99
4.2.2 Transparent Boundary Condition for the PML Problem 102
4.2.3 Error Estimate of the PML Solution 105
4.2.4 The Discrete Problem 108
4.2.5 Error Representation Formula 109
4.2.6 A Posteriori Error Analysis 111
4.2.7 Numerical Results 114
4.3 Adaptive Finite Element DtN Method 118
4.3.1 The Discrete Problem 120
4.3.2 A Posteriori Error Analysis 122
4.3.3 TM Polarization 125
4.3.4 Numerical Results 126
4.4 Adaptive Finite Element PML Method for Biperiodic Structures 130
4.4.1 The PML Formulation 132
4.4.2 Transparent Boundary Condition for the PML Problem 135
4.4.3 Convergence of the PML Solution 140
4.4.4 The Discrete Problem 145
4.4.5 A Posteriori Error Analysis 148
4.4.6 Numerical Results 153
References 158
5 Inverse Diffraction Grating 163
5.1 Uniqueness Theorems 164
5.1.1 The Helmholtz Equation 165
5.1.2 Maxwell’s Equations 170
5.2 Local Stability 175
5.2.1 The Helmholtz Equation 176
5.2.2 Maxwell’s Equations 182
5.3 Numerical Methods 193
References 200
6 Near-Field Imaging 205
6.1 Near-Field Data 208
6.1.1 The Variational Problem 210
6.1.2 An Analytic Solution 215
6.1.3 Convergence of the Power Series 219
6.1.4 The Reconstruction Formula 224
6.1.5 Error Estimates 228
6.1.6 Numerical Results 232
6.2 Far-Field Data 233
6.2.1 The Reduced Problem 236
6.2.2 Transformed Field Expansion 238
6.2.3 The Reconstruction Formula 242
6.2.4 A Nonlinear Correction Scheme 243
6.2.5 Numerical Results 244
6.3 Maxwell’s Equations 245
6.3.1 The Reduced Model Problem 248
6.3.2 Transformed Field Expansion 249
6.3.3 The Zeroth Order Term 253
6.3.4 The First Order Term 254
6.3.5 The Reconstruction Formula 256
6.3.6 Numerical Results 258
References 261
7 Related Topics 267
7.1 Method of Boundary Integral Equations 267
7.1.1 Model Problems 268
7.1.2 Quasi-periodic Green’s Function 270
7.1.3 Boundary Integral Operators 273
7.1.4 Boundary Integral Equations 277
7.1.5 Integral Formulas for Rayleigh’s Coefficients 280
7.2 Time-Domain Problems 282
7.2.1 Problem Formulation 282
7.2.2 Time-Domain Transparent Boundary Condition 286
7.2.3 The Reduced Problem 291
7.2.4 A Priori Estimates 297
7.3 Nonlinear Gratings 302
7.3.1 SHG Model 303
7.3.2 TE-TE Polarization 305
7.3.3 TM-TE Polarization 310
7.4 Optimal Design Problems 315
7.4.1 The Model Problem 316
7.4.2 The Optimal Design Problem 318
7.4.3 Homogenization of the Design Problem 320
7.4.4 The Relaxed Problem 323
References 326
Appendices 331
Tndex 351
Book list of the Series in Information and Computational Science 357
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周期結構中的Maxwell方程組(英文版) 節選
Chapter 1 Maxwell’s Equations Since Maxwell established a foundation of the modem electromagnetic theory in 1873 [1]，electromagnetics has undergone a rapid development and has been one of the most important research areas in engineering and science. It demands the study of Maxwell's equations and their application to the analysis and design of devices and systems. Maxwell’s equations represent one of the most concise statements of the fundamentals of electricity and magnetism. They are essential in describing the propagation of electromagnetic waves. Maxwell’s equations have marked a unification of electromagnetic theory， and enabled many modem developments， such as in radar and antennas， optics， remote sensing， wireless communication， medical imaging， and etc. This chapter provides a brief introduction to the electromagnetic theory. The focus is on the differential form of Maxwell’s equations and some commonly used boundary conditions， which are needed to specify boundary value problems. When the structure is invariant along a certain direction， the electromagnetic fields may exhibit some polarization. We discuss two fundamental polarizations for the time-harmonic Maxwell equations and the corresponding boundary conditions. For more details on the electromagnetic theory， the reader can consult the monographs of Harrington [2]， Kraus [3]，Jackson [4]，and Stratton [5]. 1.1 Electromagnetic Waves Maxwell’s equations are a set of fundamental equations that govern all electromagnetic phenomena. For general time dependent electromagnetic fields， Maxwell’s equations in differential form are given by where E is the electric field intensity， H is the magnetic field intensity， D is the electric flux density， B is the magnetic flux density， J is the electric current density， and p is the electric charge density. Taking the divergence on both sides of (1.2)， using (1.3) and the identity we obtain the equation of continuity Maxwell’s equations (1.1)-(1.4) are in indefinite form since the number of equations is less than the number of unknowns. They become definite when constitutive relations between the field quantities are specified. The constitutive relations describe macroscopic properties of the medium being considered. For a linear medium， they are (1.5) where e is the electric permittivity， μ is the magnetic permeability， and a is the electrical conductivity. The electric permittivity of free space (a vacuum) is denoted as eo， which is also called the electric constant. The permittivity of a dielectric medium is often represented by the ratio of its absolute permittivity to the electric constant， This dimensionless quantity is called relative permittivity and is commonly referred to as the dielectric coefficient. The parameters e，
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