Coupled wave method with modified boundary conditions for diffraction grating calculations

Abstract

The Fourier modal method for grating diffraction calculations is reformulated to improve its numerical performance, which is then studied on a rectangular aluminium grating. The Fourier coefficients of the rectangular permittivity function are calculated by the discrete Fourier transform from equidistant sample points rather than from the Fourier integral, which partially suppresses the Gibbs phenomenon. The continuous field components are treated in the Fourier space analogously to the conventional algorithm, whereas the discontinuous components are calculated in the direct space. The lateral component of the electric field, which is discontinuous inside the periodic medium but continuous on horizontal interfaces, is used for the boundary conditions in the direct space, which improves the convergence of diffraction efficiencies and considerably suppresses field fluctuations in the vicinity of sharp corners.