Formal solution to the electromagnetic scattering by buried dielectric and metallic spheres

The canonical problem of electromagnetic scattering by a buried dielectric or metallic sphere is studied in this paper. Two expansions are presented, of which one is the expansion of the vector plane waves into the vector spherical waves. The other is its converse, the expansion of the vector spherical waves into the vector plane waves. The use of two expansions is to facilitate matching the boundary conditions at the planar ground surface and the sphere surface. A general full-wave analytic solution is given in which not only the high-order multipoles but also the multiple reflections between the sphere and the ground surface are considered. Oblique plane wave and vertical magnetic dipole are considered as sources, though the illumination can be of arbitrary form with the use of Weyl identity.