A combination of up- and down-going plane waves used to describe the field inside grooves of a deep grating

The purpose of the present research is to extend the range of application of Yasuura's method in solving the problem of diffraction by a grating. To accelerate the convergence of solutions, Yasuura's method is equipped with a smoothing procedure. It has been shown that in the above problem, we can obtain a solution with 1% error using 17-41 modal functions (the number depending on the order of the smoothing procedure and on the polarization). Hence, Yasuura's method with the smoothing procedure is effective in handling problems with complicated boundaries, e.g. Fourier gratings.