Reformulated Fourier Modal Method with improved near field computations

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