Spherical-multipole analysis of electromagnetic scattering by an elliptic cone

Abstract

The scattering of a plane electromagnetic wave by a perfectly electrically conducting (PEC) semi-infinite elliptic cone is treated by means of the spherical-multipole technique in sphero-conal coordinates. The total field in the space outside the elliptic cone is determined as an eigenfunction expansion, and the scattered far field is obtained by a single integration over the induced surface currents. The final free-space-type expansion is not converging in the usual sense but a linear series transformation due to Cesàro is applied to obtain a meaningful and consistent limiting value. The eigenvalues of the underlying two-parametric eigenvalue problem with two coupled Lame´ equations belong to the Dirichlet- or the Neumann condition and can be arranged as so-called eigenvalue curves. It has been found that the eigenvalues can be separated into a first type, where the eigenfunctions look very similar to free-space modes and do not contribute to the scattered field and into a second type relevant for the scattered field. Similar non-contributing parts also occur in the Physical-Optics approximate solution of the scattering problem. As shown in this paper these observations allow to significantly improve the accuracy of the calculated scattering coefficients.