Scattering from a periodic surface: comparison of the numerical techniques

Summary form only given. Many numerical techniques have been proposed for solving the problem of the diffraction by a periodic surface (diffraction grating). But, up to now there are only partial studies, dealing with the comparison of their features. In this report the results of numerical experiments, testing and comparing different techniques, are discussed. We examine several features of the methods, such as the convergency velocity, the accuracy, the simplicity of the implementations, the efficiency and others. We consider both several novel methods (the adaptive collocation technique, the pattern equation method and the auxiliary currents method) and the well known methods (the point matching technique, the integral equation method and others). A new approach for the analysis of the plane wave diffraction by a periodic surface is also considered. The approach suggested by the authors is based on the fact that scattered fields can be represented as potentials whose densities are distributed on some auxiliary surfaces (auxiliary currents method)