tailieunhanh - Electromagnetic Waves Propagation in Complex Matter Part 6

Tham khảo tài liệu 'electromagnetic waves propagation in complex matter part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Nonlinear Propagation of Electromagnetic Waves in Antiferromagnet 87 f _ A 1 S 1 exp -ikyd __ cos kyd A A iS A - A sin kyd - i 1 A A 1 - S2 sin kyd where d is the film thickness A ky Iụvk0y and A kyIụvk ữy . The wave amplitudes R0 and T0 of R and T are not necessary for seeking the SHG so they are given up solve the output amplitudes of SHG Rs and Ts we should look for the solution of the SH wave equation in the film. In fact there are three component equations but only one contains a source term and this equation is o2 o2 - Eĩ H s -E ms c 2 Hsz s s c 2 mZ2 S 5-8 dx oy The other two are homogeneous and do not contain the field component Hsz ms . In addition the other SH components cannot emerge voluntarily without source terms so it is evident that the SH wave is a TM wave. Because the SH magnetization and pump field in the film both have been given to find the solution of equation 5-8 is easy. Let Hsz s As exp iksyy Bs exp -iksyy aexp 2ikyy 5-9 bexp -2ikyy c exp 2ikxx - iaist with ksy s ữs c 2 - 4k2 l 2 . Substituting SH solution 5-9 expression 5-1 and solution 5-6a into equation 5-8 we find the nonlinear amplitudes a A g 7-f. s f2 k2 1 S 2 k2 1 - A 2 5-10a 0 p v - 1 aụv c 2 L yV 1 b e2 g 7-Jf. s f-2 k2 1 -S 2 k22 1 S 2 5-10b 0 -1 c 2L yV J c -E02 . c 2 x s f f I k 1 - S2 k2 S 2 -1 5-10c 0 A0 4kx2 -s s c 2 4 c 2 y Solution 5-9 shows that the SH wave in the film also propagates in the incident plane and it will radiate out from the film. We use H z Rs exp i ksxX - ksy - si 5-11a to indicate the magnetic field of SH wave generated above the film and Hbz Ts exp i ksxx kSy - ast 5-11b to represent the SH field below with ks and k s determined by k2 k2x e1 as c 2 and k 2 k2x e2 as c 2 . The SH electric field in different spaces are found from to be Ea Rs exp i 2kxx - ksy - st k . - X Es ---------- -------- ksex ksxey 5-12a s 0 1 88 Electromagnetic Waves Propagation in Complex Matter exp i 2kxx- st l _ r . . _ . Es ----MEE ex ksy