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In this paper we propose a new formulation of the Fourier Modal Method basedon an alternative treatment of interface conditions allowing us to overcome theeffect of the Gibbs phenomenon. Explicit consideration of the interfaceconditions for the discontinuous part of the field leads to an equation for theeigenvalue problem, which can be written in an inversion-free form. The resultsof the method are in good agreement with the results for the classical approachbased on the Li factorization rules both for dielectric and metallic gratings.Moreover, the developed method allows calculating the near field much moreaccurately, and may find its applications in sensing and nonlinear optics.

Reformulated Fourier Modal Method with improved near field computations