Generalized Multipole Techniques for Electromagnetic and Light Scattering (eBook)

Front Cover 1
Generalized Multipole Techniques for Electromagnetic and Light Scattering 4
Copyright Page 5
Contents 6
Chapter 1. Introduction 10
References 13
Chapter 2. Review of the Generalized Multipole Technique Literature 14
2.1. Point matching method 15
2.2. Extended boundary condition method (EBCM) 16
2.3. Multiple multipole method (MMP) 17
2.4. Yasuura's methods 19
2.5. Discrete sources method (DSM) 20
2.6. Method of auxiliary sources (MAS) 21
2.7. Analytical continuation of solutions of boundary problems 22
2.8. Conclusion 23
References 23
Chapter 3. The Multiple Multipole Program (MMP) and the Generalized Multipole Technique (GMT) 30
3.1. Introduction 31
3.2. From CHA to MMP expansions 31
3.3. Matrix methods 34
3.4. Special MMP features 36
3.5. Example: Scattering at a particle on a planar structure 42
References 47
Chapter 4. Models of Electromagnetic Scattering Problems Based on Discrete Sources Method 48
4.1. Introduction 49
4.2. Mathematical models for the Helmholtz equation 51
4.3. Mathematical models for the Maxwell equations 64
4.4. Conclusion 87
References 88
Chapter 5. Singularities of Wave Fields and Numerical Methods of Solving the Boundary-Value Problems for Helmholtz Equations 90
5.1. Introduction 91
5.2. Basic analytical representations of wave fields 91
5.3. Singularities of a wave field and their localization 96
5.4. Utilization of the information about wave field singularities when solving the boundary value problems for the Helmholtz equation 104
References 117
Chapter 6. Yasuura's Method, its Relation to the Fictitious-Source Methods, and its Advancements in the Solution of 2D Problems 120
6.1. Introduction 121
6.2. Formulation of a sample problem 122
6.3. Modal functions 123
6.4. An approximate solution 125
6.5. Integral representation of the solution 125
6.6. Method of solution 1: the CYM 125
6.7. Method of solution 2: the YMSP 127
6.8. Method of solution 3: the YMSSP 130
6.9. Method of numerical analysis and examples 133
6.10. Miscellanea 143
6.11. Conclusion 145
6.12. Appendix A 145
6.13. Appendix B 146
6.14. Appendix C 147
References 149
Chapter 7. The Method of Auxiliary Sources in Electromagnetic Scattering Problems 152
7.1. Introduction 153
7.2. Problem formulation 154
7.3. Construction of the solution by the method of auxiliary sources 155
7.4. Choice of auxiliary parameters 159
7.5. Application to particular problems 167
7.6. Conclusions 178
References 179
Chapter 8. Numerical Solution of Electromagnetic Scattering Problems of Three Dimensional Nonaxisymmetrical Bodies on the Foundation of Discrete Sources Method 182
8.1. Introduction 183
8.2. Perfectly conducting scatterer 184
8.3. Impedance scatterer 187
8.4. Magneto-dielectric scatterer 188
8.5. Chiral scatterer 191
8.6. Coated scatterer 193
8.7. Some ideas towards the solution of dense ill-posed linear algebraic equation systems of discrete sources method 197
8.8. Numerical results 199
8.9. Conclusion 211
References 211
Chapter 9. Hybrid GMT–MoM Method 214
9.1. Introduction 215
9.2. Formulation 217
9.3. On the location of GMT and MoM sources 223
9.4. Regularization of the GMT–MoM method 227
9.5. Conclusions 234
References 235
Chapter 10. Null-Field Method with Discrete Sources 238
10.1. Introduction 239
10.2. Transmission boundary-value problem 240
10.3. Null-field equations 242
10.4. Complete systems of functions 243
10.5. Null-field method 255
10.6. Numerical results 257
10.7. Conclusions 260
References 261
Author Index 264
Subject Index 270