Efficient technique for the numerical solution of diffraction by a Fourier grating

A numerical implementation in the mode-matching method with a smoothing procedure is developed for solving the problem of plane-wave diffraction by a Fourier grating. The technique presented here enables us to evaluate rapidly an approximate solution in terms of a truncated plane-wave expansion. It is made clear that the technique is an economical and accurate method for exploring the physical phenomena associated with Fourier gratings. As a numerical example, dependence of the efficiency on the groove profile of a Fourier grating is investigated for both E-and H-polarized incident plane waves.