The propagation of electromagnetic waves in the waveguide with space-time periodic insert

The review of theoretical researches of the author, devoted to propagation of electromagnetic waves in the waveguide of arbitrary cross section, filled with space-time periodically modulated medium is given. The analytical method of solving of electrodynamics problems, developed by the author in similar medium, is resulted. The propagation of transverse-electric (TE) and transverse-magnetic (TM) waves in the waveguide, mentioned above, is investigated. The peculiarities of physical phenomena of electrodynamics of periodically modulated mediums in the waveguide in the region of “weak” and “strong” interactions between the signal wave and the modulation wave are studied.