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

Abstract

We examine wave scattering by a perfectly conducting periodic surface in the presence of two diffraction modes propagating at low grazing angles. This scenario includes a backscatter case that has practical importance. For TM polarization, conventional perturbation theory is shown to be invalid in the limit of small grazing angles. We develop a new perturbation expansion that is valid when two of the scattered modes propagate at low grazing angles. We find that there is a critical scattering angle associated with the surface profile. Conventional perturbation theory is valid only when all scattering grazing angles are larger than the critical angle, and new perturbation formulas are accurate when two modes are below the critical angle. This development resolves the existing contradiction between low-grazing backscattering 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 critical angle. This theory accurately describes the sign change of the reflection coefficient when the incidence angle approaches zero as well as a sharp decrease in the reflection coefficient at the critical angle.