On the eigenfunction expansion of dyadic Green's function in planarly stratified media

Abstract

Using the eigenfunction expansion, a terse expression of the scattering dyadic Green's function is presented for defining electromagnetic fields in a planarly stratified medium with a current source arbitrarily located in one of the layers. The scattering dyadic Green's function for each layer is constructed in terms of the cylindrical vector wave functions by applying the method of scattering superposition. The general but succinct expression of the coefficients of the scattering dyadic Green's function for each layer of the multilayers is derived directly from the boundary conditions of the dyadic Green's function. To demonstrate how to apply this method, the coefficients of the scattering Green dyads for a three-layered medium, as an example, are reduced from the general expression for the cases where the current source is located in the first, the intermediate, and the last layers. The complete agreement of such coefficients derived in this article and obtained in the previous published papers asserts the applicability of these general formulae.