The mean Green's dyadic for a half-space random medium: A nonlinear approximation

Abstract

The vector problem of a source embedded in a halfspace random medium is considered, and a zeroth-order solution for the mean Green's dyadic in the nonlinear approximation is derived. This is done by applying a two-variable expansion method to obtain a perturbation solution of the Dyson equation for the mean Green's dyadic. The final results of the dyadic are given in closed form as a corrected effective propagation constant, including terms of the order k_{a}^{2}\sigma^{2}l^{2} where k_{a} is the wavenumber in the average medium, l is the correlation length, and \sigma^{2} is the variance of the permittivity fluctuations. These results show a significant difference from those of the one-dimensional problem considered by Tsang and Kong [4]. Whereas the scalar solution gives different effective propagation constants for the component waves in the Green's function, the vector solution derived contains only a single propagation constant for all of the components in the Green's dyadic.