On the Electrodinamics of Space-Time Periodic Mediums in a Waveguide of Arbitrary Cross Section

Abstract

Theoretical investigations of parametric interaction between the electrodynamics waves and space-time periodic filling of the waveguide of arbitrary cross section are reviewed. The cases of dielectric, anisotropic and magnetodielectric periodically modulated filling are considered. The analytical method of solution of the problems of electrodynamics of spacetime periodic mediums in a waveguide is given. The propagation of transverse-electric (TE) and transverse-magnetic (TM) waves in the waveguide mentioned above are investigated. Physical phenomena of electrodynamics of space-time periodic mediums in the region of “weak” and “strong” interactions between the travelling wave in the waveguide and the modulation wave are studied. Propagation of electromagnetic waves in the medium whose permittivity and permeability are modulated in space and time with help of pump waves of various nature (electromagnetic wave, ultrasonic wave, etc.) under the harmonic law, represents one of the basic problem of the electromagnetic theory. In the scientific literature the most part of such researches concerns to electrodynamics of periodically non-stationary and non-uniform mediums in the unlimited space [1-15], while the same problems in the limited modulated mediums, for example, in the waveguides of arbitrary cross section remain still insufficiently studied and there is no strict analytical theory of the propagation of electromagnetic waves in similar systems (although in the scientific literature already appeared the articles on the problems, mentioned above [16-25]. Meanwhile the investigation of the propagation of electromagnetic waves in the waveguides with space-time periodically modulated filling represents a great interest not only from point of view of development of theory but also from point of view of possibility of practice application of similar waveguides in the ultrahigh frequency electronics. For example, the waveguides with periodically non-stationary and non-uniform filling can be applied for designing of multifrequency distributing back-coupling lasers (DBS lasers), Bragg reflection lasers (DBR lasers), mode transformers, parametric amplifiers, multifrequency generators, transformers of low and higher frequency, Bragg resonators and filters, prismatic polarizer, diffraction lattices, oscillators, mode converters, wave-channeling devices with a fine periodic structure, etc [14], [26-30].