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.