Fast Fourier factorization method applied to modal analysis of slanted lamellar diffraction gratings in conical mountings

A new formulation of the Fourier modal method that applies fast Fourier factorization [J. Opt. Soc. Am. A 17 (2000) 1773] is presented for slanted lamellar gratings in conical mountings. A new eigenvalue problem in the grating region is derived, and used to study metallic gratings. Comparison of the convergence speed of the numerical results given by the conventional methods and the new one shows a spectacular improvement. The fast Fourier factorization method can be also applied to various volume slanted-fringe gratings with discontinuous permittivity variations.

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