High-Frequency Asymptotic Solution for the Electromagnetic Scattering From a Small Groove Around a Conical or Cylindrical Surface

The electromagnetic scattering from a small circumferential groove around an electrically large conical surface is found in closed form using the method of stationary phase. The fields at every point along the groove are found from the two-dimensional analytic solution for the TE and TM scattering from a small rectangular cavity in a ground plane, defining an equivalent groove current radiating in the presence of the curved surface. The stationary phase evaluation of the three-dimensional radiation integral reduces the solution to two scattering points along the groove on opposite sides of the cone, one of which may be in the shadow region depending on the incidence angle. The asymptotic cone solution extends trivially to the cylinder solution, and is validated with numerical data for a finite cone with a circumferential groove.