Diffraction by grating consisting of screens with different height: new equations

A 2D problem of diffraction of a plane wave by a grating consisting of screens of different heights is studied. The incident wave travels at a grazing incidence angle. The consideration is held in the parabolic approximation. Screens are supposed to be perfectly absorbing. Edge Green's functions of the problem are introduced. Embedding formula and a spectral equation are proven. An OE-equation for the unknown coefficient of spectral equation is derived. An evolution equation which describes dependence of the edge Green's functions on geometrical parameter of problem(screen height) is derived. An asymptotic estimation of the reflection coefficient is obtained by using the evolution equation.