Radiation from ring sources in the presence of a semi-infinite cone

A rigorous formulation for ring source Green's functions for a semi-infinite cone, carried out in terms of images in an infinitely extended angular transmission line, is evaluated asymptotically in the short-wave length range to yield geometric-optical, diffracted, and transition effects. Both scalar problems with Neumann or Dirichlet type boundary conditions, and electromagnetic problems appropriate to a perfectly conducting cone, are treated. The results are applied to calculate approximately the radiation pattern for a prescribed magnetic current distribution on the cone surface which can be taken to represent the excitation due to certain leaky wave type antenna arrays.