Operator method in the problem of wave diffraction by flat semi-infinite strip grating

The electromagnetic (EM) wave scattering by a flat semi-infinite grating (SIG) of metal strips is studied by the operator method. The nonlinear equation in terms of the operator of reflection from SIG is built using the translation property of a periodical SIG. The approximate analytical solution at the assumption that strips are narrow and spaced sparsely is obtained by the steepest-descent method. This representation can be used as the initial approach for an iteration procedure of the numerical solution in general case.