Electromagnetic waves in a waveguide with a magnetoactive anisotropic periodically modulated filling

Interaction of transverse-electric (TE) waves with magneto-active anisotropic periodically modulated in space and time filling of the waveguide with arbitrary cross section is considered. The wave equation for the potential of TE field is derived from the Maxwell equations. The method of solving of the wave equation is developed. Under the assumption that the modulation indexes are small, analytical expressions for the TE field are found in the region of weak interaction between the signal wave and the modulation wave.