Analytical-numerical method of studying the diffraction of waves by periodic structures with a noncoordinate shape of the period

A new analytical-numerical method is described which enables problems of wave diffraction by periodic structures with a noncoordinate shape of the boundary surface of a periodicity element to be solved efficiently. The method is based on reducing the original diffraction problem of a boundary-value problem for an infinite system of ordinary differential equations and regularizing it by means of a semi-inversion of a convolution-type matrix operator in the boundary conditions. A justification of the method is given along with a numerical example.