Electromagnetic scattering by semi-infinite circular and elliptic cones

The scattering of a plane electromagnetic wave by a perfectly conducting semi-infinite cone with an elliptic or a circular cross section is treated by means of a multipole analysis in sphero-conal coordinates, in which the elliptic (including the circular) cone is one of the coordinate surfaces. Starting from the dyadic Green's function of the elliptic cone given in terms of periodic and nonperiodic Lamé functions, first the exact surface current on the cone is obtained. This surface current is the source of the scattered far field which is completely analytically found by means of the dyadic Green's function of the free space in sphero-conal coordinates. The finally obtained infinite series do not converge by a straight-forward summing-up procedure; however, a simple linear (consistent) sequence transformation technique is sufficient to come to stable and physically correct asymptotic results.