Electromagnetic scattering from buried inhomogeneities - a general three-dimensional formalism

We will in the present paper derive a general three-dimensional formalism for electromagnetic scattering from buried inhomogeneities. We will exploit the transition matrix formalism, originally given by Waterman, to electromagnetic scattering in the presence of an infinite surface and a buried bounded inhomogeneity. The analysis explicitly assumes that the sources are located above the ground, but this restriction can easily be relaxed and a parallel derivation can be made for sources located in the ground or inside the buried obstacle. No explicit symmetry assumptions are made for the bounded inhomogeneity or the interface between the halfspaces, except that the interface be bounded by two parallel planes. The scattered field above the ground is calculated in terms of an expansion where the expansion coefficients are solutions of a matrix equation. The expression for the scattered field is separated into a directly scattered term, as if no scatterers were present, and the so called anomalous field, reflecting the presence of the inhomogeneity. We give some numerical examples for a flat interface and an inhomogeneity consisting of one or two buried spheres or a perfectly conducting spheroid.