Grating diffraction and Wood's anomalies at two-dimensionally periodic impedance surfaces

We address the problem of plane-wave scattering and Wood's anomalies at two-dimensional (2-D) periodic surfaces by employing a simplified grating model given by a planar surface whose impedance varies sinusoidally along two orthogonal directions. We obtain a rigorous solution to the corresponding boundary-value problem in terms of an infinite set of coupled recurrence equations. When truncated for computational purposes, this solution is in the form of a banded matrix, which we solve by direct methods and also by a highly efficient iterated matrix procedure. Numerical results are presented for symmetric and nonsymmetric incidence cases, and we show that certain diffracted fields do not depolarize in the former case. The expected Wood's anomalies of both Rayleigh and leaky-wave types are confirmed, and their location in wavelength space is numerically demonstrated for 2-D periodic configurations.