On the Theory of Resonant Interaction of Electromagnetic Waves with Periodically Modulated Dielectric Filling of a Waveguide

In this article the peculiarities of the propagation of a signal transverse electric (TE) wave in a waveguide with periodically modulated dielectric filling in the frequency region of “strong” (resonant) interaction between the signal wave and the modulation wave (the first-order Wulff-Bragg condition is satisfied between reflected from filling inhomogeneities harmonics) are investigated. It is assumed that the modulation depth of the waveguide filling is much less than unity. Calculations are carried out with an accuracy up to a small parameter to the first power. A physical explanation of the strong interaction effect is given. An analytical expression for the frequency of strong interaction was obtained in three ways. It is shown that the width of the frequency region of the strong interaction is small (it is proportional to the modulation depth). It is also shown that when the directions of propagation of the signal wave and the modulation wave coincide, a strong interaction occurs between the minus first and zero harmonics reflected from the filling inhomogeneities. In this case the amplitude at the minus first harmonic does not depend on the modulation depth, while at the plus first harmonic it depends on the modulation depth to the first power. When the above waves propagate in opposite directions the minus first and plus first harmonics change roles.