Scattering of a plane electromagnetic wave by a spherical shell with an elliptical aperture

The vector spherical multipole expansion is applied to determine the electromagnetic field of a perfectly conducting spherical shell with an elliptical aperture, which is illuminated by a plane wave. Using problem-adapted sphero-conal coordinates the authors are able to treat this diffraction problem mostly analytically. They solve the electric field integral equation (EFIE) by Galerkin´s method with entire domain expansions and a bilinear spherical multipole expansion of the dyadic Green´s function as the integral equation kernel. Numerical results such as the scattering cross section and the energy density at the center of the spherical shell with an elliptical aperture are computed both as functions of frequency and/or of the aperture ellipticity. From the numerical data it is seen that the resonance frequencies of the energy density at the center are identical to those appearing in the backscattering cross section