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On error estimation in the fourier modal method for diffractive gratings

The Fourier Modal Method (FMM, also called the Rigorous Coupled Wave Analysis, RCWA) is a numerical discretization method which is often used to calculate a scattered field from a periodic diffraction grating. For 1D periodic gratings in FMM the electromagnetic field is presented by a truncated Fourier series expansion in the direction of the grating periodicity. The grating’s material properties are assumed to be piece-wise constant (called slicing), and next per slice the scattered field is approximated by a truncated Fourier series expansion. The truncation representation of the scattered field and the piece-wise constant approximation of the grating’s material properties cause the error in FMM. This paper presents an analytical estimate/bound for the FMM error caused by slicing.