A uniform GTD solution for the radiation from sources on a convex surface

TLDR

The study develops a compact approximate asymptotic solution for the field radiated by an antenna on a perfectly conducting smooth convex surface. The high‑frequency solution uses geometrical theory of diffraction ray coordinates, modeling shadow‑region propagation along Keller’s surface‑diffracted rays and lit‑region propagation along geometrical‑optics rays, with fields expressed via Fock functions and a torsion factor accounting for surface ray torsion. Calculated radiation patterns for slots and monopoles on cylinders, cones, and spheroids match measured patterns and exact solutions closely.

Abstract

A compact approximate asymptotic solution is developed for the field radiated by an antenna on a perfectly conducting smooth convex surface. This high-frequency solution employs the ray coordinates of the geometrical theory of diffraction (GTD). In the shadow region the field radiated by the source propagates along Keller's surface diffracted ray path, whereas in the lit region the incident field propagates along the geometrical optics ray path directly from the source to the field point. These ray fields are expressed in terms of Fock functions which reduce to the geometrical optics field in the deep lit region and remain uniformly valid across the shadow boundary transition region into the deep shadow region. Surface ray torsion, which affects the radiated field in both the shadow and transition regions, appears explicitly in the solution as a torsion factor. The radiation patterns of slots and monopoles on cylinders, cones, and spheroids calculated from this solution agree very well with measured patterns and with patterns calculated from exact solutions.