Electromagnetic scattering by a sphere above a plane interface

The study the electromagnetic scattering by a sphere above a plane interface provides a proper theoretical model in many applications, thus we present an exact semi-analytical solution in this paper. This technique utilizes appropriate spherical vector wave functions to expand the scattered field by and internal field within the sphere, and to treat the coupling scattering between the sphere and plane interface, and the transformation relations of spherical vector wave functions to cylindrical ones are applied. The reflected wave off the interface and scattered field by the sphere are both calculated with a projection scheme. By taking incident plane wave, Gaussian beam and Laguerre-Gaussian beam on a polystyrene sphere above a silicon substrate as three typical examples, normalized differential scattering cross sections are evaluated. Numerical results show that for a plane wave and Gaussian beam the maximum scattering occurs in the angle regions around the direction of reflection, and the forward scattering becomes larger with the increase of the distance between the sphere and plane interface.