Abstract
In this article the interaction of transverse-electric (TE) and transverse-magnetic (TM) waves with space-time nonmagnetic multiperiodically modulated filling of the waveguide is considered under the assumption of small modulation indexes. TE and TM fields in the waveguide are described by the longitudinal components of magnetic and electric vectors, respectively. The wave equations for the specified components are received from Maxwell equations, which are reduced to the Mathieu-Hill equations by changing variables. The solutions of these equations in the frequency domain of weak interaction of signal wave with modulation wave (the Wulff-Bragg condition is not satisfied) was found with an accuracy of terms proportional to in the first degree of modulation indexes. It is shown, that TE and TM fields in the waveguide in the approximation, indicated above, consist of the sum of three space-time harmonics with different amplitudes. An analytical expression is also found for the frequency around which a strong interaction between the signal wave and the waveguide modulation wave can occur.
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