Wave Propagation Part 9

Tham khảo tài liệu 'wave propagation part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 272 Wave Propagation The analysis of these dispersion equations show that under the following conditions 33 1 -Ớ0n 8n 1 -Ớ0n Sn 1 we become to the region of weak interaction between the signal wave and the modulation wave where the characteristic indexes Lin and LL are real and then the Mathie-Hill equations have the stable solutions. With help of obtained solutions of dispersion equations An 2 7 n 2 7 and the expressions for the coefficients 2n 2 n nil s-m C n 71 C0 cn 71 C0 1 4 1 1 4 1 where Cj and C0 are defined from the conditions of normalizing we obtained the analytical expressions for the Hz and Ez of TE and TM fields in the waveguide in the region of weak interaction. They have a form 33 where n I Hz -1 Ê n X y e P0 z-m f cj X V kn eikk0 z-ut M0 n 0 k -1 Ez ẾS 0 n 0 1 z . Cn X yn eikk0 t Cn - m 2 C0 An CJ V k .Al c1 k 9 rn V 2 C0 ms 2 - A0 Mm M - An Mm M - 0 2 k0 u 0 2 e k u - 2 an _ 7 1 k02 p b L - Ạb X 2 m. 2 7 wpib 2 8 1 - xn 2 m- Pn 2 ưu c u 82. m 2 ffl0_ . 1 0 c2 e0 0 8 n P 0 c 2 S0M0 An . As is seen from the expressions and TE and TM fields in the waveguide with modulated filling are represented as the set of space-time harmonics with different 273 On the Electrodinamics of Space-Time Periodic Mediums in a Waveguide of Arbitrary Cross Section amplitudes. At that time the amplitude of the zero fundamental harmonic are independent of small modulation indexes while the amplitudes of the plus and minus first harmonics side harmonics are proportional to the small modulation indexes in the first degree. At the realization the following condition 31 33 where 0 sũ 1 -Ớ0n ỈĨT7 1 c 0 - 2 - p a0 2 u 0 b E 1 - Pl c n2 - Pl - Ôn Wp e n 4 1 7 k22 b m p here are shown the results for the TE field when ịi 1 the strong resonance interaction between the signal wave and the modulation wave takes place when occurs the considerable energy exchange between them. The analytical expression .