This book is intended for university students who specialize in the acoustic and electromagnetic wave scattering by deterministic obstacles in plane-layered mediua, or by discrete random perturbations in the statistically layered random media. The approach of this book is based on the formulation of the corresponding scattering problems in the form of volume integral equations. The main ingredient of such an approach is the Green's functions for the appertaining regular boundary value problems. Special attention is paid to the analysis of Green's functions as generalized functions, and of their singularities in the source region. The deterministic problems are solved for small scatterers using a low-frequency approximation. In the analysis of randomly perturbed media, the main attention is focused on the derivation of the effective permittivity operators which describe the properties of such media with respect to the statistically mean field. The main effects on the mean field (deporarization, perturbation of spatial distribution, emergence of a waveguding layer and of "new" eigenmodes) are considered.
Author(s): Николай Михайлович Богомолов, Николай Петрович Жук [Nikolai Mikhailovich Bogomolov, Nikolai Petrovich Zhuck]
Edition: 1
Publisher: Харьковский государственный университет
Year: 1992
Language: Russian
City: Харьков [Kharkov]
INTRODUCTION - p. 5.
CHAPTER 1. GREEN's FUNCTIONS FOR BOUNDARY VALUE PROBLEMS OF WAVE THEORY - 18.
Section 1.1. Green's functions of Maxwell's equations in a plane-layered uniaxial medium - 19.
Article 1. Scalarization of Green's functions - 19.
Article 2. Regularization of Green's functions of Maxwell's equations - 24.
Article 3. Expansion over the eigenwaves - 29.
Section 1.2. Green's functions for Euler's equations in a spatially inhomogeneous medium - 36.
Article 1. Representation in terms of scalar potentials - 36.
Article 2. Regularization of Green's functions for Euler's equations - 38.
Article 3. Expansion over the eigenwaves - 40.
Section 1.3. Integral equations for boundary value problems of wave theory in an inhomogeneous medium - 42.
Article 1. Integral equations of electrodynamics in a plane-layered medium - 43.
Article 2. Low-frequency approximation - 47.
Article 3. Expansion of scattered field over the eigenwaves - 49.
Article 4. Integral equations of acoustics in an inhomogeneous medium - 52.
Problems and exercises - 54.
CHAPTER 2. SCATTERING OF WAVES FROM DETERMINISTIC OBSTACLES IN A PLANE-LAYERED MEDIUM - 56.
Section 2.1. Induced electromagnetic field of an obstacle buried in an inhomogeneous medium - 58.
Article 1. Transition operators - 58.
Article 2. The induced field inside a small obstacle - 63.
Article 3. Particular cases of obstacle's orientation - 67.
Section 2.2. Scattered electromagnetic field of a small obstacle in an inhomogeneous medium - 70.
Article 1. The near-field zone - 71.
Article 2. The far-field zone - 74.
Article 3. Resonance scattering - 84.
Section 2.3. Low-frequency scattering of acoustic waves in an inhomogeneous medium - 88.
Article 1. The induced field inside an obstacle - 89.
Article 2. The near-field zone - 91.
Article 3. The far-field zone - 92.
Problems and exercises - 94.
CHAPTER 3. MEAN FIELD IN A RANDOM STATISTICALLY LAYERED MEDIUM - 96.
Section 3.1. Effective permittivity of a discrete medium with uncorrelated scatterers - 98.
Article 1. Perurbation theory for a discrete medium - 100.
Article 2. General properties of effective permittivity - 103.
Article 3. "Mild" scatterers - 110.
Section 3.2. Effective permittivity of a discrete medium with correlated scatterers - 119.
Article 1. Change of field variables - 122.
Article 2. Effective permittivity of the "continuous" medium - 123.
Article 3. Emergence of a waveguiding layer - 129.
Section 3.3. Eigenewaves in a statistically layered medium with disrete perurbations - 132.
Article 1. Depolarization and distortion of spatial distribution - 133.
Article 2. Attenuation and shift of phase velocity - 138.
Article 3. Emergence of new eigenwaves - 142.
Problems and exercises - 143.
SUMMARY - 145.
APPENDIX 1 - 146.
APPENDIX 2 - 149.
APPENDIX 3 - 150.
APPENDIX 4 - 122.
REFERENCES - 161.
