I. Introduction

II. Statement of the Problem and its Solution

Conclusions

References

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.

INTRODUCTION

The propagation of electromagnetic waves in periodically modulated media has been considered in many articles [1-5]. In the articles [6] and [7] were discussed the features of the propagation of electromagnetic waves in a waveguide with two-periodic modulated dielectric filling. In this article the propagation of the signal TE and TM waves in the waveguide of arbitrary cross section filled with a multiperiodically modulated in space and time filling is considered. As noted in the articles [8] and [9] multiperiodically modulated media can represent the certain interest at carrying out of researches in various fields of science and in designing various radio engineering devices.