WATERMAN AND RAYLEIGH METHODS FOR DIFFRACTION GRATING PROBLEMS - EXTENSION OF THE CONVERGENCE DOMAIN

We show that the Waterman method, a classical and rigorous method of e lectromagnetics for scattering by surfaces or objects, can be signific antly improved. In a first step, it is shown, in the case of scatterin g by gratings, that the origin of the instabilities encountered in the numerical implementation of the method must be found in the ill condi tioning of the equations. A well-adapted regularization process allows us to extend the domain of convergence of the method by a factor of a pproximately 40% in the range of groove depth for one-dimensional grat ings and s polarization. Finally, we show that the same kind of regula rization can extend the domain of convergence of the Rayleigh method. (C) 1998 Optical Society of America.