ABSTRACT
This paper deals with one of the important aspects of grating theory in optics—the scattering of a plane wave by a periodical structure in the high frequency approximation (the period of grating is far greater than the wavelength). The well-known traditional numerical methods face difficulties in calculating characteristics of the reflected field with high frequency oscillations since the order of the corresponding system of complex linear equations becomes very high and the calculations are quite time-consuming. Under these conditions it is natural to employ the asymptotic methods of the geometric theory of diffraction (GTD), that is, ray-optical analysis (see [1] and [2]), to investigate the problem of short wave scattering by a diffraction grating. The methods we refer to are the uniform asymptotic theory of diffracted waves and the summation of multiple diffracted fields (MDF).
