Group-theoretic approach to the enhancement of the Fourier modal method for crossed gratings: C2 symmetry case.

A new formulation of the Fourier modal method for crossed gratings with symmetry considerations is established by using the group-theoretic approach that we have developed recently. Considering crossed gratings with the C2 symmetry (invariance after rotation about the normal of the mean grating plane through angle pi), we present in detail the construction of the new algorithm, illustrate the improved computation efficiency, and discuss its application. It is shown theoretically and numerically that when the grating is Littrow mounted and the truncated reciprocal lattice of the diffracted field also has the C2 symmetry, the maximum effective truncation number of the algorithm is doubled and the computation time is reduced by a factor of 4. The time saving factor is increased to 8 for the special case of normal incidence.

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