Investigation of the influence of periodic disturbances in the layered medium by the method of averaging of Krylov-Bogolyubov

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