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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 :S'P lH  
    8gWifx #N  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of @T[}] e  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of xU+c?OLi  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 4%>iIPXi.(  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 v MTWtc!6  
    INqD(EG   
    %fid=fopen('e21.dat','w'); W m\HZ9PN  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 1uBnU2E  
    M1 =3000;              % Total number of space steps $\?BAkx  
    J =100;                % Steps between output of space }@%A@A{R  
    T =10;                  % length of time windows:T*T0 sc dU  
    T0=0.1;                 % input pulse width ?CIMez(h  
    MN1=0;                 % initial value for the space output location h}r64<Y2{  
    dt = T/N;                      % time step ovJwo r  
    n = [-N/2:1:N/2-1]';           % Index 0V6gNEAUg  
    t = n.*dt;   ]FV,}EZ  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10  Xr'Y[E [  
    u20=u10.*0.0;                  % input to waveguide 2 .vHSKd{  
    u1=u10; u2=u20;                 V("@z<b|  
    U1 = u1;   :MPWf4K2s  
    U2 = u2;                       % Compute initial condition; save it in U [)UL}vAO\q  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. A3D"b9<D  
    w=2*pi*n./T; X:Z4QqT  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %_Gc9SI  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 7`-fN|  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 d Bn/_  
    for m1 = 1:1:M1                                    % Start space evolution 'jh9n7mH  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS W&>ONo6ki  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;  JwEQR  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform vt)u`/u  
       ca2 = fftshift(fft(u2)); j_L1KB*  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 0\XG;KA  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   bV c"'RQ  
       u2 = ifft(fftshift(c2));                        % Return to physical space  _0^f  
       u1 = ifft(fftshift(c1)); eT 8(O36%  
    if rem(m1,J) == 0                                 % Save output every J steps. ~nO]R   
        U1 = [U1 u1];                                  % put solutions in U array j6x1JM  
        U2=[U2 u2]; #nG?}*#  
        MN1=[MN1 m1]; P X/{  
        z1=dz*MN1';                                    % output location K[} 5bjh>  
      end AA$+ayzx9{  
    end ~2 aR>R_nT  
    hg=abs(U1').*abs(U1');                             % for data write to excel e(nT2E  
    ha=[z1 hg];                                        % for data write to excel ^APPWQUl  
    t1=[0 t']; w0W9N%f#=  
    hh=[t1' ha'];                                      % for data write to excel file \/=w \Tj  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format D|m] ]B  
    figure(1) fsd,q?{a:  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 'Pk1 4`/  
    figure(2) 5X"y46i,H  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn G&ZpQ)  
    AcC'hr.N+  
    非线性超快脉冲耦合的数值方法的Matlab程序 }EFMJ,NQ  
    q6E8^7RtS@  
    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。   *\W *,D.I  
    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 Z*r;"WHB  
    tR`'( *wh  
    w]2tb  
    $'m&RzZ  
    %  This Matlab script file solves the nonlinear Schrodinger equations eYSVAj  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of d3% 1 P)  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear J*4byu|  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ::'DWD1  
    #$/SM_X14C  
    C=1;                           /m#!<t7  
    M1=120,                       % integer for amplitude @log=^  
    M3=5000;                      % integer for length of coupler #fT1\1[]  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 8&d s  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. BEU^,r3z  
    T =40;                        % length of time:T*T0. Y<1]{4Wt  
    dt = T/N;                     % time step rID_^g_tP8  
    n = [-N/2:1:N/2-1]';          % Index V* :Q~ ^  
    t = n.*dt;   WsHC%+\'  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ur*a!U  
    w=2*pi*n./T; wO\,?SI4  
    g1=-i*ww./2; G3 h&nH,>  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; e[5= ?p@|  
    g3=-i*ww./2; ;4E(n  
    P1=0; <<Zt.!hS  
    P2=0; $inpiO|s  
    P3=1; >LqW;/&S<  
    P=0; ">$.>sn{  
    for m1=1:M1                 M{sn{  
    p=0.032*m1;                %input amplitude L p(6K  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 s]=bg+v?j  
    s1=s10; RDFOUqS  
    s20=0.*s10;                %input in waveguide 2 3WH"NC-O<  
    s30=0.*s10;                %input in waveguide 3 Z{' .fq2A  
    s2=s20; 1w30Vj2<  
    s3=s30; <W$Ig@4[.d  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   KDt@Xi 6||  
    %energy in waveguide 1 t,CC~  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   D4';QCwo  
    %energy in waveguide 2 .W[[Z;D  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   nMz~.^Q-  
    %energy in waveguide 3 Kr;7~`$[  
    for m3 = 1:1:M3                                    % Start space evolution >9?BJv2  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS m\h. sg&  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; :Fv d?[  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 4tZnYGvqe  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform lQ t&K1m  
       sca2 = fftshift(fft(s2)); | .8lS3C  
       sca3 = fftshift(fft(s3)); fe,A\W&8  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Y(:.f-Du  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); O-5s}RT  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); -Odk'{nW  
       s3 = ifft(fftshift(sc3)); \I3={ii0  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 7mUpn:U  
       s1 = ifft(fftshift(sc1)); ;t^8lC?>V  
    end .1O  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); vocXk_  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); >icL,n"]  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); a.oZ}R7'Y  
       P1=[P1 p1/p10]; QH?}uX'x)G  
       P2=[P2 p2/p10]; $}9.4` F>  
       P3=[P3 p3/p10]; wK0= I\WN9  
       P=[P p*p]; KINKq`Sx  
    end 3n\eCdV-b<  
    figure(1) b[mAkm?9+1  
    plot(P,P1, P,P2, P,P3); g{]C@,W  
    %`o3YR  
    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~!~