Возбуждение и рассеяние волн в плоско-слоистых средах [Excitation and Scattering of Waves in Plane-layered Media]

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.