Ray optical analysis of a plane wave scattering by an echelette diffraction grating

The two-dimensional problem of scattering of a nearly grazing plane wave by a diffraction grating, echelette with right angle is considered for the case of high-frequency approximation (when period of grating is far greater than the wavelength). The two classical boundary conditions, transverse electric (TE) and transverse magnetic (TM) cases in electromagnetic theory, are implied. The ray optical solution of the problem (short-wave asymptotic result) is derived on the basis of the method of summation of multiple diffracted fields, which is well known in the geometric theory of diffraction. Numerical results are presented and compared with calculations based on the rigorous method of integral equation.