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Wavelet element method for lamellar gratings.

A wavelet element method is developed for analyzing lamellar diffraction gratings or grating stacks. The eigenmodes of the grating layers are accurately calculated by this method, and then the diffraction efficiencies of the gratings are calculated by the S-matrix algorithm. The method proposed in this paper consists in mapping each homogeneous layer to a wavelet element, and then matching them according to the boundary conditions between the layers. By this method the boundary conditions are satisfied rigorously and the Gibbs phenomenon in the Fourier modal method (FMM) can be avoided. The method performs better than the standard FMM for gratings involving metals. It can also be applied to analyze other discontinuous structures.