The book has a dual purpose. The first is to expose a general methodology to solve problems of electromagnetism in geometries constituted of angular regions. The second is to bring the solutions of some canonical problems of fundamental importance in modern electromagnetic engineering with the use of the Wiener-Hopf technique. In particular, the general mathematical methodology is very ingenious and original. It is based on sophisticated and attractive procedures exploiting simple and advanced properties of analytical functions. Once the reader has acquired the methodology, she/he can easily obtain the solution of the canonical problems reported in the book. The book can be appealing also to readers who are not directly interested in the detailed mathematical methodology and/ or in electromagnetics. In fact the same methodology can be extended to acoustics and elasticity problems. Moreover, the proposed practical problems with their solutions constitute a list of reference solutions and can be of interests in engineering production in the field of radio propagations, electromagnetic compatibility and radar technologies.
Vito G.Daniele, Ecole Polytechnique of Turin, Italia Lombardi Guido, Ecole Polytechnique of Turin, Italia
Preface ix
Introduction xiii
Chapter 4. Exact Solutions for Electromagnetic Impedance Wedges 1
4.1. Introduction 1
4.2. A list of the impedance wedge problems amenable to exact WH solutions 9
4.3. Cases involving classical WH equations 10
4.3.1. WH formulation of the diffraction by an impedance half-plane 11
4.3.2. Exact solutions of the diffraction by an impedance half-plane 18
4.3.3. Exact solution for the full-plane junction at skew incidence 37
4.3.4. Exact solution of the penetrable half-plane problem (the jump) 39
4.3.5. Exact solution of the right-angled wedge scattering problem 40
4.4. Exact solutions for impedance wedge problems with the GWHE form of section 3.5 form #1 51
4.4.1. The WH solution of the Malyuzhinets problem 52
4.4.2. Diffraction at skew incidence (o 0) by a wedge with a PEC and a PMC face 58
4.4.3. Diffraction at skew incidence (o0) by a wedge with a PEC face and the other face with diagonalZbwith one null element 60
4.5. Exact solutions for the impedance wedge problems with the GWHEs written in an alternative form form #2 62
4.5.1. Exact factorization with diagonal polynomial matricesPa,b(m) 64
4.5.2. Anisotropic symmetric impedance wedges at normal incidence 67
4.5.3. Non-symmetric wedges at normal incidence with commuting Pa and Pb 68
4.5.4. Non-symmetric wedges at skew incidence 70
4.5.5. Two particular wedge problems amenable to exact solutions 72
4.6. A general form of the GWHEs to study the arbitrary face impedance wedges form #3 76
Appendix 4.A. Some important formulas of decomposition for wedge problems 79
Chapter 5. Fredholm Factorization Solutions of GWHEs for the Electromagnetic Impedance Wedges Surrounded by an Isotropic Medium 87
5.1. Introduction 87
5.2. Generalized Wiener-Hopf equations for the impenetrable wedge scattering problem of an electromagnetic plane wave at skew incidence 88
5.3. Fredholm factorization solution in the plane of GWHEs 92
5.4. Fredholm factorization solution in thewplane of GWHEs 95
5.5. Approximate solution of FIEs derived from GWHEs 97
5.6. Analytic continuation of approximate solutions of GWHEs 101
5.7. Far-field computation 103
5.8. Criteria for the examples 110
5.9. Example 1: Symmetric isotropic impedance wedge at normal incidence with Ez polarization 111
5.10. Example 2: Non-symmetric isotropic impedance wedge at normal incidence with Hz polarization and surface wave contribution 119
5.11. Example 3: PEC wedge at skew incidence 121
5.12. Example 4: Arbitrary impedance half-plane at skew incidence 124
5.13. Example 5: Arbitrary impedance wedge at skew incidence 126
5.14. Example 6: Arbitrary impedance concave wedge at skew incidence 128
5.15. Discussion 132
Appendix 5.A. Fredholm properties of the integral equation (5.3.1) 132
Chapter 6. Diffraction by Penetrable Wedges 135
6.1. Introduction 135
6.2. GWHEs for the dielectric wedge at normal incidence (Ez-polarization) 140
6.3. Reduction of the GWHEs for the dielectric wedge at Ez-polarization to Fredholm integral equations 142
6.4. Analytic continuation for the solution of the dielectric wedge at Ez-polarization 154
6.5. Some remarks on the Fredholm integral equations (6.3.24), (6.3.26) and numerical solutions 159
6.6. Field evaluation in any point of the space 162
6.7. The dielectric wedge at skew incidence 165
6.8. Criteria for examples of the scattering by a dielectric wedge at normal incidence (Ez-polarization) 176
6.9. Example: the scattering by a dielectric wedge at normal incidence (Ez-polarization) 177
6.10. Discussion 186
Appendix 6.A. Fredholm factorization applied to (6.3.2)(6.3.5) 186
Appendix 6.B. Source termi() 188
References 199
Index 205
Summary of Volume 1 209
