Shortwave scattering by echelette diffraction grating

The two-dimensional problem of a plane wave scattering by a periodic perfectly conducting grating – an echelette with a right angle is considered in the case of high-frequency approximation (the wave length is assumed to be small compared with the period of grating). The situation where the incident plane wave glides along one of the faces of a wedge is discussed. The ray optical solution to the problem (short-wave asymptotic result) is derived on the basis of the method of summation of multiple diffrated fields, which is well known in the geometric theory of diffraction. The main result of the paper is simple formulas for the efficiency of diffraction order with maximum value derived in the short-wave approximation. Numerical results are presented and important optical properties resulted from asymptotic analysis are described.