Modal method for scattering by arbitrarily shaped multivalued surfaces

We present a modal method to calculate the electromagnetic fields scattered by a perfectly conducting surface with a finite number of grooves described by non-single-valued functions. The surface can be illuminated by s-or p-polarized Gaussian beams with propagation directions perpendicular to the grooves. The method, based on the multilayer approximation and the R-matrix propagation algorithm, is numerically stable even for deep cavities. We give numerical results which show an important influence of the grooves′ concavity on the far-field pattern.