Diffraction of electromagnetic waves by dielectric crossed gratings: a three-dimensional Rayleigh-Fourier solution

We present a solution based on the Rayleigh hypothesis. The calculation lea ds to a matrix system that can be computed to yield the efficiencies of a t wo-dimensional dielectric grating. The results are compared with previously reported numerical results obtained both with exact theories and with pert urbation methods. We show that our method can treat rougher surfaces than c an classic perturbation methods. (C) 1999 Optical Society of America [S0740 -3232(99)02406-0].