tianmen |
2011-06-12 18:33 |
求解光孤子或超短脉冲耦合方程的Matlab程序
计算脉冲在非线性耦合器中演化的Matlab 程序 WCoF{* _^b@>C>O % This Matlab script file solves the coupled nonlinear Schrodinger equations of W'V@ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 7y;u} 1 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g#Mv&tU % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 5=m3J!? E\_W %fid=fopen('e21.dat','w'); *0-v!\{ N = 128; % Number of Fourier modes (Time domain sampling points) PC[cHgSYU M1 =3000; % Total number of space steps IyT?-R J =100; % Steps between output of space <g*.p@o T =10; % length of time windows:T*T0 _l<|1nH T0=0.1; % input pulse width 0w'|d@*wV MN1=0; % initial value for the space output location o|+E+l9\ dt = T/N; % time step ;*.(. n = [-N/2:1:N/2-1]'; % Index %P(;8sS t = n.*dt; -}< d(c u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10 '1]+8E
`Z u20=u10.*0.0; % input to waveguide 2
:4{Qh u1=u10; u2=u20; xHm/^C&px U1 = u1; 5pB^Y MP U2 = u2; % Compute initial condition; save it in U ]u;GNz}? ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. w/O<.8+ w=2*pi*n./T; m,=)qex g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @c0n2 Xcr L=4; % length of evoluation to compare with S. Trillo's paper a6k(9ZF dz=L/M1; % space step, make sure nonlinear<0.05 6GY32\Ac for m1 = 1:1:M1 % Start space evolution ,zG <7~m u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS D9,e3.?p u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; K q/~T7Ru ca1 = fftshift(fft(u1)); % Take Fourier transform 'xQna+ %h ca2 = fftshift(fft(u2)); R04.K! c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation 'N*!>mZ<
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift Is<x31R u2 = ifft(fftshift(c2)); % Return to physical space ;x,+*% u1 = ifft(fftshift(c1)); 0GS{F8f~, if rem(m1,J) == 0 % Save output every J steps. g)X7FxS,z U1 = [U1 u1]; % put solutions in U array {3.*7gnY\L U2=[U2 u2]; y#&$f MN1=[MN1 m1]; mMV2h|W z1=dz*MN1'; % output location 7Nd*,DV_ end ]NbX`' end E]\D>[0O hg=abs(U1').*abs(U1'); % for data write to excel 4}+xeGA$ ha=[z1 hg]; % for data write to excel `i=JjgG@ t1=[0 t']; Z+r%_|kZ hh=[t1' ha']; % for data write to excel file bd,Uz%o_ %dlmwrite('aa',hh,'\t'); % save data in the excel format ht2
f-EKf{ figure(1) C2CYIok$& waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn %)BwE figure(2) mXQl; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn A*rZQh
b[ S@9w'upd 非线性超快脉冲耦合的数值方法的Matlab程序 KbXbT @bc[
eas 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。 Sjw2 j#Q Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8mk}nex S&5Q~}{, AQB1gzE :0WkxEY9 % This Matlab script file solves the nonlinear Schrodinger equations P#w}3^ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of @YEw^J~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear /_$~rW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
o G(0i J"/JRn C=1; #DQX<:u M1=120, % integer for amplitude 17WNJ M3=5000; % integer for length of coupler E}]I%fi N = 512; % Number of Fourier modes (Time domain sampling points) I~d#p ]> dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05. Ko1AaX(I'+ T =40; % length of time:T*T0. 8FB\0LA!g dt = T/N; % time step kyy0&L n = [-N/2:1:N/2-1]'; % Index >Y,/dyT
Zm t = n.*dt; _L?v6MTj ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1. C<r(-qO{5 w=2*pi*n./T; `%FIgE^ g1=-i*ww./2; xIS\4]F?r g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; >W>##vK g3=-i*ww./2; /d{glOk P1=0; TrSN00 P2=0; 70'}f P3=1; q,<n,0)K P=0; zWF
5m )- for m1=1:M1 AeNyZ[40T p=0.032*m1; %input amplitude WpXODkQL s10=p.*sech(p.*t); %input soliton pulse in waveguide 1 2q`)GCES~ s1=s10; bHhC56[M s20=0.*s10; %input in waveguide 2 B0-4ZT s30=0.*s10; %input in waveguide 3 o,*folL s2=s20; 0t5Q9#RY s3=s30; RnMB Gxa p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); ~bQFk?ZN+ %energy in waveguide 1 <bEN8b p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); g0^~J2sDd %energy in waveguide 2 * \=2KIF' p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); u~'m7 %energy in waveguide 3 XX]5T`D for m3 = 1:1:M3 % Start space evolution M[:O( s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS YH/S2 D s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; AzHIp^ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; YWt"| sca1 = fftshift(fft(s1)); % Take Fourier transform el <<D sca2 = fftshift(fft(s2)); /2g)Z!&+L sca3 = fftshift(fft(s3)); [<#<:h&\ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift B6tcKh9d, sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); E[ )7tr sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); qT4I Y$h s3 = ifft(fftshift(sc3)); 8gVxiFjo s2 = ifft(fftshift(sc2)); % Return to physical space J{nyo1A s1 = ifft(fftshift(sc1)); pr0@sri@ end h]J&A p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); !A'`uf4u p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); GNhtnB p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); WmT}t P1=[P1 p1/p10]; 8w{#R{w P2=[P2 p2/p10]; n:5O9,umZ P3=[P3 p3/p10]; Z$OF|ZZQ P=[P p*p]; q|47;bK' end Gt\K Ln figure(1) :GwSs'$O plot(P,P1, P,P2, P,P3); *_4n2<W$ xJ[k#?T' 转自:http://blog.163.com/opto_wang/
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