Electromagnetic Waves in a Waveguide with Periodically Modulated Magnetodielectric Filling.

The propagation of electromagnetic waves in an ideal regular waveguide with the magnetodielectric filling periodically modulated in space and time is studied. It is assumed that the modulation depths are small, so the modulation of waveguide filling does not lead to the interaction between different waveguide modes. Wave equations are obtained for transverse electric (TE) and transverse magnetic (TM) fields in the waveguide with respect to the longitudinal components of the magnetic and electric vectors, respectively. They are second order partial differential equations with periodic coefficients. By changing the variables, these equations are reduced to ordinary differential equations of the Mathieu–Hill type with periodic coefficients. Solutions to these equations for small modulation depths in the region of weak interaction between the signal and modulation waves (the Wolfe–Bragg condition is not satisfied) are found in the first approximation. The results obtained in the above approximation show that the TE and TM fields in the waveguide can be expressed as the sum of three space–time harmonics (the zero harmonics and the first harmonics with the plus and minus signs) with complex amplitudes and frequencies. [ABSTRACT FROM AUTHOR]