Diffraction of high-frequency grazing wave on grating with screens of different height

A 2D problem of diffraction by a periodic diffraction grating composed of absorptive screens is studied. A period of the grating comprises two screens having different heights. The incident wave is assumed to have wavelength short comparatively to the period of the grating, and the incidence angle is assumed to be small. High diffraction orders are neglected, and the parabolic approximation is used to describe the wave process. The embedding formula, which expresses reflection coefficients in terms of the directivity of the edge Green´s functions is proven. A spectral equation, which is an ordinary differential equation for the directivities of the edge Green´s function is derived. The coefficient of the spectral equation is found by solving an Ordered Exponential (OE) equation numerically.