Regularized Waterman and Rayleigh methods: extension to two-dimensional gratings

The origin of the instabilities of the Waterman method was studied previously and an improvement in the method was developed for one-dimensional gratings and s polarization [J. Opt. Soc. Am. 15, 1566 (1998)]. Later, the same kind of regularization was used to improve Rayleigh's expansion method. We show that the same well-adapted regularization process can be generalized to two-dimensional (2D) gratings. Numerical implementations show that the convergence domain of the Waterman method is extended by a factor of similar to 40% in the range of groove depth. In the same way, the convergence domain of the Rayleigh expansion method is extended by a factor of similar to 35% for 2D sinusoidal gratings. As a consequence, the new versions of Waterman and Rayleigh methods become simple and efficient tools for use in investigating the properties of 2D gratings that have ratios of groove depth to period up to unity. (C) 1999 Optical Society of America [S0740-3232(99)01102-3].