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    [分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

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    离线tianmen
     
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    只看楼主 倒序阅读 楼主  发表于: 2011-06-12
    计算脉冲在非线性耦合器中演化的Matlab 程序 y)e8pPDG  
    %d#h<e|,.  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of @is!VzE  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of R9`37(c9+  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear h#7p&F  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 U^.kp#x#  
    {gwJ>]z"e  
    %fid=fopen('e21.dat','w'); ~y.t amNW  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) =7212('F  
    M1 =3000;              % Total number of space steps  &@h(6  
    J =100;                % Steps between output of space +=N#6 # 1  
    T =10;                  % length of time windows:T*T0 (!B1} 5"  
    T0=0.1;                 % input pulse width )UgLs|G~  
    MN1=0;                 % initial value for the space output location ?(d<n   
    dt = T/N;                      % time step AeN$AqQd/  
    n = [-N/2:1:N/2-1]';           % Index c Y(2}Ay  
    t = n.*dt;   KJ;;825?  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 L|H:&|F  
    u20=u10.*0.0;                  % input to waveguide 2 q71~Y:7f  
    u1=u10; u2=u20;                 2=/,9ka~  
    U1 = u1;   lOuO~`,J  
    U2 = u2;                       % Compute initial condition; save it in U T z?0E"yx  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. BL^\"Xh$|  
    w=2*pi*n./T; -) LiL  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T `!A<XiAOmM  
    L=4;                           % length of evoluation to compare with S. Trillo's paper VW/ICX~"d  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 @n Oj6b  
    for m1 = 1:1:M1                                    % Start space evolution ;bhD:$NB X  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS E6zSMl5b  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 7`_`V&3s  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform J70r`   
       ca2 = fftshift(fft(u2)); o3OtG#g2  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation f5ttQ&@FF  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   GI _.[  
       u2 = ifft(fftshift(c2));                        % Return to physical space #l?E2 U4WL  
       u1 = ifft(fftshift(c1)); #Li6RSeW  
    if rem(m1,J) == 0                                 % Save output every J steps. O-jpS?@  
        U1 = [U1 u1];                                  % put solutions in U array l1I\khS  
        U2=[U2 u2]; [;RO=  
        MN1=[MN1 m1]; O=E?m=FR"  
        z1=dz*MN1';                                    % output location Hru~Y}V  
      end 0Mu6R=s  
    end h1AZ+9  
    hg=abs(U1').*abs(U1');                             % for data write to excel ?hh#@61  
    ha=[z1 hg];                                        % for data write to excel x=%wP VJ  
    t1=[0 t']; mo()l8  
    hh=[t1' ha'];                                      % for data write to excel file bDADFitSo  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format T1[B*RwC  
    figure(1) k(23Zt]  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn .:/[%q{k  
    figure(2) [wv;CUmgc  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn &cHA xker  
    O@-|_N*;K  
    非线性超快脉冲耦合的数值方法的Matlab程序 k|D =Q  
    }u?DK,R  
    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。   RHv|ijYy  
    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 '}BYMEd/m%  
    rMEM$1vPU  
    T7qE 2  
    ;*[ oi  
    %  This Matlab script file solves the nonlinear Schrodinger equations K zWqHq  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of C=,O'U(ep  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 'D&[Y)f^  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ZXH{9hxd  
    *pj^d><  
    C=1;                           PDNbhUAV  
    M1=120,                       % integer for amplitude s)9d\{  
    M3=5000;                      % integer for length of coupler >\4"k4d}  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) w e}G%09L  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. u%b.#!  
    T =40;                        % length of time:T*T0. ag{cm'.  
    dt = T/N;                     % time step Cr>YpWm  
    n = [-N/2:1:N/2-1]';          % Index  SodYb  
    t = n.*dt;   S\<nCkE^  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. T7# }& >  
    w=2*pi*n./T; y^[?F>wB  
    g1=-i*ww./2; o_R_  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; "rU 2g  
    g3=-i*ww./2; n =qu?xu  
    P1=0; Aw"Y_S8.  
    P2=0; Hkzx(yTi  
    P3=1; >e M> Y@8=  
    P=0; Gph:'3 *X  
    for m1=1:M1                 `/RcE.5n\@  
    p=0.032*m1;                %input amplitude }!*CyO*  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 CX3yIe~u  
    s1=s10; d<_#Q7]I4  
    s20=0.*s10;                %input in waveguide 2 p,K!'\  
    s30=0.*s10;                %input in waveguide 3 W'"p:Uh q  
    s2=s20; UiQF4Uc"  
    s3=s30; m TgsvC  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   [5i }C K_=  
    %energy in waveguide 1 e]zd6{g[m  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Lpv,6#m`)  
    %energy in waveguide 2 fV o7wp  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ioJ|-@! #o  
    %energy in waveguide 3 aW*8t'm;m'  
    for m3 = 1:1:M3                                    % Start space evolution ;Z!x\{- L  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Zonr/sA~  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; nh*hw[Ord  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;  1 .Nfl@]  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ^u-;VoK  
       sca2 = fftshift(fft(s2)); -=4{X R3  
       sca3 = fftshift(fft(s3)); ~djHtd>  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   m5 l,Lxj  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); .1YiNmW=  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); %4^NX@1jV  
       s3 = ifft(fftshift(sc3)); <`")Zxf+  
       s2 = ifft(fftshift(sc2));                       % Return to physical space [m0G;%KR/  
       s1 = ifft(fftshift(sc1)); ;!pSYcT,  
    end S1U>Q~ZPA  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); H6Q!~o\"H  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); p(fL' J  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ycj\5+ g  
       P1=[P1 p1/p10]; Z3O_K  
       P2=[P2 p2/p10]; YckLz01jh  
       P3=[P3 p3/p10]; kK_9I (7c  
       P=[P p*p]; W0k7(v)  
    end a_(T9pr  
    figure(1) g). IF.  
    plot(P,P1, P,P2, P,P3); cceh`s=cU  
    Ctx{rf_~  
    转自:http://blog.163.com/opto_wang/
     
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~