Generalized model of TE- and TM-polarized light diffraction on periodical structures of different types

In this investigation we would like to show that the problem of diffraction on all types of gratings and on two-dimensional crystals, except pure reflecting gratings, can be brought to an infinitely-dimensional system of linear differential equations of the first order in general case with variable coefficients, besides that the character of coefficient variation is being determined by grating type and polarization of the wave propagating inside the periodical structure. Such equation system can be brought to a matrix view, and its properties are studied well by mathematicians. Here, relief grating and two-dimensional phonon crystal are considered. Dielectric constant of periodical structures is presented.