Electromagnetic scattering of a complex-source beam by semi-infinite sectors and cones

A perfectly conducting semi-infinite elliptic cone is illuminated by an arbitrarily directed complex source beam (CSB). The boundary-value problem is solved by means of the corresponding spherical-multipole expansion of the electric field in sphero-conal coordinates. The CSB is realized by assigning a suitable complex value to the source coordinate of a Hertzian dipole. The CSB which asymptotically represents a Gaussian beam, that is a localized plane wave, can be used to probe any desired area of the elliptic cone. Besides, the resulting multipole expansion does not suffer from convergence problems as observed in case of an incident full plane wave.