Impact of a hollow spheroidal cylinder on electric dipole radiation features

The development and testing of numerical and other approximate methods for calculating the diffraction and scattering by complex shapes depends strongly upon comparison with solutions to canonical problems which are as rigorously analytical as possible. A thin perfectly conducting spheroidal shell with two circular holes provides a canonical example of considerable complexity, with several interacting scattering mechanisms including coupling via apertures into closed regions, and scattering from open surfaces having edges and non-trivial geometry. Moreover, whilst the limiting geometries such as a hollow cylindrical tube possess intrinsic interest, this class of scatterers provides insight into the relative importance of the various scattering mechanisms as the hole size and spheroidal aspect ratio changes. This paper considers the wave diffraction problem associated with an electric dipole source in the presence of a hollow spheroidal cylinder. Based on the rigorous formulation of the problem, a regularisation method is applied to obtain an essentially analytic solution. Regarding the dipole-spheroidal shell structure as a surface-wave antenna we can also compute the radiation resistance and radiation patterns as functions of frequency. The results provide an accurate “benchmark” solution for the validation of general numerical codes