Interaction of Electromagnetic Waves with Multi Periodic Modulated Dielectric Filling of a Regular Waveguide |
| E. Gevorkyan
Plekhanov Russian University of Economics, Department of Higher Mathematics, 117997 Moscow, Russia |
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| The propagation of transverse electric (TE) and transverse magnetic (TM) signal waves in the waveguide with arbitrary cross-section is considered. It is assumed that the dielectric filling of the waveguide is modulated on z coordinate (the axis Oz is the axis of the waveguide) under multi periodic law with small modulation indexes mqε ≪ 1 (q=1, 2, 3, 4, 5). The wave equations for Hz and Ez describing TE and TM fields in the waveguide are received. With the help of change of variables these differential equations are reduced to the Mathieu-Hill equations with periodic coefficients. Analytic solutions of these equations are found up to small modulation indexes in the first degree in the region of ``weak'' interaction between the signal wave and the modulation wave, when the first-order Wolf-Bragg condition for the waves reflected from seals at their interference is not satisfied. The results show that TE and TM fields in the waveguide represent the sum of spatial harmonics (zero, plus, and minus one) with various amplitudes. |
DOI:10.12693/APhysPolA.135.650 topics: waveguide, electromagnetic waves, modulated filling, signal wave, modulation wave, Mathieu-Hill type differential equation |