Electromagnetic waves in a waveguide with a space-time multiperiodic dielectric filling

We obtain analytic solutions to the problem of propagation of TE waves (H_z≠0) in a regular waveguide of arbitrary transverse cross section with multiperiodically nonuniform dielectric fillings under the assumption of small modulation indices m₁ and m₂ of the medium. The investigation of such a multiperiodically modulated dielectric medium has both theoretical and experimental interest because it can be used in multifrequency distributed feedback lasers, filters, etc