Fast Solution of the Electromagnetic Scattering by Composite Spheroidal–Spherical and Spherical–Spheroidal Configurations

The electromagnetic scattering of a plane wave by composite spheroidal-spherical and spherical-spheroidal configurations is studied in this work. The spheroidal-spherical configuration consists of a spheroidal dielectric shell coating a spherical metallic core, while the spherical-spheroidal configuration consists of a spherical dielectric shell coating a spheroidal metallic core. Initially, the formal series solution is constructed by using analytical expansions connecting the spheroidal with the spherical eigenvectors. The solution of the problem is then obtained following two independent paths: first, asymptotic expansions are applied on all related quantities leading to a solution for the fields and the scattering cross sections, which is given by closed-form expressions, and is valid for small eccentricities of the spheroid. Second, the formal full-wave series solution is solved numerically by truncation. Both the full-wave and the closed-form solutions are validated by numerous comparisons with numerical simulations. The accuracy of the closed-form solution is then compared to the full-wave solution. The closed-form solution has very low computational cost. The spheroid can be one of prolate or oblate type. Both TE and TM incidence are studied and numerical results are given for various values of the parameters.