Electromagnetic scattering by a multilayer elliptic cylinder under transverse-magnetic illumination: series solution in terms of Mathieu functions

An exact solution to the electromagnetic scattering by a dielectric multilayer infinite cylinder of elliptic cross section is proposed. The interfaces between different media, which are assumed to be lossless and nonmagnetic, are confocal elliptic cylinders. Starting from the series expansions in terms of Mathieu functions, an efficient recursive procedure for the computation of fields and radar cross sections per unit length under a transverse-magnetic illumination is developed. The mathematical formulation is detailed and some numerical results are provided.