Creeping waves on a perfectly conducting cone

The rigorously formulated scalar and vector Green´s functions for a perfectly conducting semi-infinite cone are approximated asymptotically to furnish the high-frequency creeping wave contributions when the source and observation points are both located on the cone surface. The results are expressed in the ray-optical format of the geometrical theory of diffraction and thus provide another canonical solution for verification of the postulates of that theory. The analytical procedure for isolating the creeping waves from other high-frequency phenomena such as tip diffraction is motivated by the methodology for the simpler circular cylinder problem, to which the present solution reduces when the cone-to-cylinder transition is performed. The results are of interest for calculation of source-induced surface currents, and of mutual coupling between slot array elements, on conical surfaces.