Scattering of a plane wave from a perfectly conducting sphere buried in a conducting dielectric

A rigorous method has been developed to determine the scattering of a linearly polarized plane wave above a conducting ground, in which a perfect electrically conducting sphere is buried. The method is based on expressing the fields alternately as the integrals of plane waves and in terms of spherical modes in imposing the boundary conditions on the ground and on the sphere, respectively, and transforming one representation into the other as required. Using this method, an infinite linear system of equations is obtained for the back-scattered field involving the unknown scattering coefficients of the field components, which is then truncated for numerical evaluation. Truncation criteria and its impact on the accuracy of the calculated results are established via comparisons with the analytical and numerical results reported in the literature for problems that correspond to special choices of parameters in our case. Numerical results are presented to demonstrate the effects of some parameters such as conductivity and permittivity of the soil, radius of the sphere and of the signal frequency on the back-scattered field.