A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

TLDR

The study builds on Keller’s canonical wedge diffraction method applied to perfectly conducting wedges illuminated by plane, cylindrical, conical, and spherical waves. The authors aim to derive a compact dyadic diffraction coefficient for electromagnetic waves incident obliquely on a curved edge of a perfectly conducting surface. They extend Keller’s canonical wedge theory by introducing a ray‑fixed coordinate system, yielding a dyadic diffraction coefficient that is the sum of two dyads—soft and hard—whose Fresnel‑integral expressions guarantee field continuity and can be applied to curved edges. The resulting coefficient remains valid in transition regions adjacent to shadow and reflection boundaries where Keller’s theory fails, and it shows that for all edge illuminations the coefficient has the same form—only the Fresnel‑integral arguments differ—ensuring continuous total fields even with varying polarizations and wavefront curvatures.

Abstract

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.