Generalized Fourier Transform for Stratified Media

Abstract

A Fourier-type transform is derived for functions satisfying the scalar wave equation in stratified media. Using this transform, the function is expressed as a sum of two infinite integrals and a discrete term. In electromagnetic theory, the infinite integrals correspond to the radiation and the lateral wave terms and the discrete term corresponds to the surface wave.The transform provides a suitable basis for the expansion of electromagnetic fields when the height of the interface between two semi-infinite media and their electromagnetic parameters vary along the propagation path. Exact boundary conditions are employed here rather than the restricted surface impedance condition. The expansion is particularly appropriate for problems in which the source and the observation point are not in the same medium.