Wave Scattering By Periodic Surface At Low Grazing Angles: Single Grazing Mode - Abstract

Abstract

We examine wave scattering by a perfectly conducting periodic surface, and demonstrate that for vertical polarization, conventional perturbation theory is invalid in the presence of a low-grazing scattered mode. We develop a new perturbation expansion that is valid when one of the scattered modes propagates at a low grazing angle. For this expansion, scattering amplitude is nonlinear in height. We find that the surface is conveniently characterized by effective impedance and corresponding Brewster angle. Conventional perturbation theory is valid only when all scattering grazing angles are larger than the effective Brewster angle, and new perturbation formulas are accurate when one mode is below the effective Brewster angle. This development resolves any contradiction between low-grazing scattering results by Barrick [1] and Tatarskii/Charnotskii [2, 3], for a periodic surface case. We propose a uniform perturbation approximation which combines the conventional and low-grazing-angle perturbation results and incorporates the effective surface impedance. In particular, this theory describes the sign change of the reflection coefficient when the incidence angle approaches zero.