CLASSICAL DIFFRACTION BY DEEP RECTANGULAR GRATINGS USING THE LEGENDREEXACT EIGENFUNCTION METHOD

A rigorous numerical electromagnetic method, based on the use of a pie cewise description of the field inside a lamellar grating using Legend re polynomials, is discussed. This method allows the accurate calculat ion, for both TE and TM polarized incident light, of the eigenvalues o f lossless and highly conducting lamellar gratings using simple eigenv alue-eigenvector algorithms. The resulting eigenfunctions can then be used in conjunction with appropriate projections of the boundary condi tions to stably calculate the diffracted field from extremely deep rec tangular surface relief structures. The convergence of this method is tested and results are compared to those available in the literature. The method also allows non implicit power conservation to be used as a test of convergence for both dielectric and conducting gratings. Some comments regarding the use of this method for multi-layer structures with slanted edges are also made.