Application of Krylov-Bogolyubov averaging method to the problem of periodic perturbations in the layered medium

Influence of small periodic perturbation in periodic dielectric medium on propagation of TM-polarized waves is investigated by the Krylov-Bogolyubov averaging method. As a result of periodic perturbation inside the allowed bands of unperturbed medium forbidden bands appear. The appearance of forbidden bands is conditioned by a parametric resonance between spatial harmonics of perturbation and plane waves, on which the solution of the wave equation in periodic medium is decomposed. The location, number and width of these bands are determined