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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 jUI'F4.5x-  
    vM1f-I-  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of [[Qu|?KEa  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of @FdtM<X  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear m+"?;;s  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 d*3k]Ie%5f  
    :JxShF:M  
    %fid=fopen('e21.dat','w'); *s S7^OZ*  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) *Jmy:C<>  
    M1 =3000;              % Total number of space steps ygWo9?  
    J =100;                % Steps between output of space 2^E.sf$f  
    T =10;                  % length of time windows:T*T0 LylB3BM  
    T0=0.1;                 % input pulse width #fRhG^QKp  
    MN1=0;                 % initial value for the space output location +0;6.PK  
    dt = T/N;                      % time step /F4rbL^:  
    n = [-N/2:1:N/2-1]';           % Index 3/@7$nV  
    t = n.*dt;   L#M9!  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ,L6d~>=41  
    u20=u10.*0.0;                  % input to waveguide 2 b{b2L.  
    u1=u10; u2=u20;                 M`9qo8zCi  
    U1 = u1;   JC_Y#kN@z  
    U2 = u2;                       % Compute initial condition; save it in U KArR.o }  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 4T{+R{_Y1  
    w=2*pi*n./T; tUDOL-Tv  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T i"r&CS)sT  
    L=4;                           % length of evoluation to compare with S. Trillo's paper _ohZTT%l  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 $ [by)  
    for m1 = 1:1:M1                                    % Start space evolution /![S 3Ol  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS k>FMy#N|@  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; kBS;SDl)  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform o6 'I%Gs  
       ca2 = fftshift(fft(u2)); #Ne<=ayS  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation gah3d*d7  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   <_dyUiT$J  
       u2 = ifft(fftshift(c2));                        % Return to physical space 4h@jJm  
       u1 = ifft(fftshift(c1)); q?nXhUD  
    if rem(m1,J) == 0                                 % Save output every J steps. Q&opnvN  
        U1 = [U1 u1];                                  % put solutions in U array <%8j#@OdZ  
        U2=[U2 u2]; _[<R<&jG  
        MN1=[MN1 m1]; j#f+0  
        z1=dz*MN1';                                    % output location /!=uM .  
      end j\B]>PP5  
    end rr>QG<i;G  
    hg=abs(U1').*abs(U1');                             % for data write to excel X};m\Bz  
    ha=[z1 hg];                                        % for data write to excel 8V`NQS$  
    t1=[0 t']; [2pp)wq  
    hh=[t1' ha'];                                      % for data write to excel file D^baXp8  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Kyt.[" p  
    figure(1) puF'w:I (  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn XZEawJ0  
    figure(2) W2D^%;mw  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 3l_Ko %qS  
    gPSUxE `O.  
    非线性超快脉冲耦合的数值方法的Matlab程序 0&mo1 k_U  
    y>Zvose  
    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。   s:'M[xI  
    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 vIF=kKl9,  
    4v_?i @,L  
    /;-KWu+5=  
    \V  /s  
    %  This Matlab script file solves the nonlinear Schrodinger equations %6+J]U  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 4EQ7OGU  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear W$B&asO  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 q#:,6HDd  
    8c(}*,O/  
    C=1;                           R7;SZo  
    M1=120,                       % integer for amplitude P~Q5d&1SO  
    M3=5000;                      % integer for length of coupler uSLO"\zysX  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) )xX(Et6+`  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 6&M $S$y  
    T =40;                        % length of time:T*T0. %jdV8D#Q  
    dt = T/N;                     % time step 9 yH95uaDF  
    n = [-N/2:1:N/2-1]';          % Index 7}OzTup  
    t = n.*dt;   J~eY,n.6]  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. o,[~7N  
    w=2*pi*n./T; w$n\`rQ  
    g1=-i*ww./2; Fh9%5-t:J  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; '@>FtF[Gu  
    g3=-i*ww./2; e4p:Zb:  
    P1=0; )8kcOBG^L  
    P2=0; ]:i :QiYD  
    P3=1; ,Xs%Cg_Ig  
    P=0; )X@Obg  
    for m1=1:M1                 *vc=>AEc  
    p=0.032*m1;                %input amplitude )A:2y +  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 W{O:j  
    s1=s10; b#bdz1@s  
    s20=0.*s10;                %input in waveguide 2 [_hHZMTH  
    s30=0.*s10;                %input in waveguide 3 A`v(hBM  
    s2=s20; %lNv?sWb  
    s3=s30; ("0@_05OH  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   xB_F?d40T5  
    %energy in waveguide 1 W.iL!x.B@  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   xoF]r$sC8  
    %energy in waveguide 2 k@JDG]R<{  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   qg#TE-Y`  
    %energy in waveguide 3 OSk:njyC[  
    for m3 = 1:1:M3                                    % Start space evolution vZj^&/F$=g  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ";E Mu(IXb  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; u.*@ l GVW  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; g9|B-1[  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform (mz5vzyw  
       sca2 = fftshift(fft(s2)); NsJt=~  
       sca3 = fftshift(fft(s3)); &o{I9MD  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Yr@_X  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ztf VXmi'  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); CXks~b3SD  
       s3 = ifft(fftshift(sc3)); lS]<~  
       s2 = ifft(fftshift(sc2));                       % Return to physical space WJ=DTON  
       s1 = ifft(fftshift(sc1)); 1{4d)z UB  
    end LuY`mi  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); vA@Kb3 ,  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); T0s7aw[zm  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ]vJZ v"ACn  
       P1=[P1 p1/p10]; rGuhYYvK  
       P2=[P2 p2/p10]; 8*kZ.-T B  
       P3=[P3 p3/p10]; vzJ69%E_  
       P=[P p*p]; e`k6YO  
    end Q W#]i  
    figure(1) Cbm  
    plot(P,P1, P,P2, P,P3); jT"P$0sJAd  
    ;ZX P*M9  
    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~!~