We show that the Waterman method, a classical and rigorous method of electromagnetics for scattering by surfaces or objects, can be significantly improved. In a first step, it is shown, in the case of scattering by gratings, that the origin of the instabilities encountered in the numerical implementation of the method must be found in the ill conditioning of the equations. A well-adapted regularization process allows us to extend the domain of convergence of the method by a factor of approximately 40% in the range of groove depth for one-dimensional gratings and s polarization. Finally, we show that the same kind of regularization can extend the domain of convergence of the Rayleigh method. (C) 1998 Optical Society of America. [References: 20]
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