Green's functions for composite media

Abstract

A method is given on construction of Green's functions for finding field excited by a point (or line) source in a layered composite medium. The concept of Green's function for a composite medium as a whole is introduced in a rigorous manner by showing that it possesses all properties of the Green's function for an uniform medium. The appropriate Green's function for the whole composite medium is constructed through two solutions of the corresponding homogeneous equation over the whole multiregion. The method enables one to write down, directly, the explicit expression for the field in an arbitrary region produced by a point (or line) source located in another arbitrary region without resort to images, Fourier-Bessel integrals, integral transforms of quasi-orthogonal functions. It is an extension of the existing method, which constructs the Green's functions for uniform media through the generalized Fourier expansions and two solutions of the corresponding homogeneous equations, to cases heretofore beyond its scope.