Closed-form solution for electromagnetic scattering by a dielectric spheroid coating a metallic sphere

A closed-form solution for the electromagnetic scattering of a plane wave by a dielectric lossless or lossy prolate spheroid coating a concentric metallic sphere is studied in this work. The problem is solved using two independent methods: first, asymptotic expansions are applied on the spheroidal eigenvectors, allowing a closed-form solution which is valid for small eccentricities of the spheroid. Second, the full wave exact solution is constructed using the separation of variables in terms of the spheroidal eigenvectors.