Asymptotic methods in electromagnetism
type: Item
instance of: scholarly article
title: Asymptotic methods in electromagnetism
zbMATH Open document ID: 0817.35110
author: D. Bouche
author: Frédéric Molinet
published in: Mathématiques \& Applications (Berlin)
publication date: 1994-10-10T00:00:00Z
review text: The object of this book is to discuss problems in the field of diffraction of high frequency electromagnetic waves and to consider the relationship between the boundary layer approach and the geometrical optics approach. There are eight chapters. The first is concerned with the geometrical theory of diffraction and sets out the concepts involved. The second considers the idea of solutions in the form of asymptotic expansions and introduces the concept of the eikonal. The third chapter is entitled the boundary layer method. Amongst the topics discussed are creeping waves, whispering-gallery waves, caustics, diffraction by wedges and the matching of fields. The fourth, on the spectral theory of diffraction, introduces the idea of building up fields by means of integrating a spectrum of plane waves. The fifth chapter, on uniform solutions, is a long one, comprising about a third of the main portion of the book. After a discussion of the principles of uniform expansions, there follow treatments of subjects such as diffraction by a wedge, the problem of a sudden change in curvature of the surface of a diffracting object, the shadow region, creeping waves on curved wedges, and caustics. The sixth chapter, integral methods, is mainly concerned with Maslov's method, which provides solutions in the form of integrals, valid in the neighbourhood of caustics. The seventh chapter deals with surface fields and physical diffraction theory. In this approximations to diffracted fields are developed by using radiation from current elements on the illuminating part of the surface of the diffracted object. The eighth and final chapter, a short one, is concerned with the idea of surface impedance of a diffracting object, and the effect upon the diffraction fields. The main portion of the book is followed by six appendices: canonical problems, differential geometry, asymptotic developments of integrals, complex rays, Fock functions and the reciprocity principle. These appendices provide …
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78-02
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 35-02
zbMATH DE Number: 651724
zbMATH Keywords: diffraction of high frequency electromagnetic waves
zbMATH Keywords: boundary layer approach
zbMATH Keywords: geometrical optics approach
zbMATH Keywords: creeping waves
zbMATH Keywords: Whispering-gallery waves
zbMATH Keywords: caustics
zbMATH Keywords: diffraction by wedges
zbMATH Keywords: matching of fields
zbMATH Keywords: spectral theory of diffraction
zbMATH Keywords: integral methods
zbMATH Keywords: Maslov's method
zbMATH Keywords: surface impedance
zbMATH Keywords: reference source
reviewed by: Ll. G. Chambers
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 651724