Scattering by a rectangularly corrugated surface: an approximate theory

We address the problem of the scattering of a plane, TM-polarized electromagnetic wave by a two-dimensional rectangularly corrugated surface. The height of the corrugation is measured by a characteristic length D and its period by /spl Lambda/. We take the ordering of these scales to be D/spl sim//spl Lambda//spl sim//spl lambda/ where /spl lambda/ is the wavelength of the incident wave. We apply a radiation condition (strictly valid only in the far-field) in the aperture above a rectangular notch. This approximation allows the determination of an explicit representation of the reflection coefficients, the scattered field, and the field within a corrugation. Numerical results are presented which are in excellent agreement with a published finite difference approximation for diffraction gratings.