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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 正序阅读 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 0.0!5D[  
    =lD]sk  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of +N@F,3yNa  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of &/?jMyD@  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 0Wm-` ZA  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tY=TY{RY  
    2f4c;YS  
    %fid=fopen('e21.dat','w');  RZ%X1$  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 0z#kV}wE  
    M1 =3000;              % Total number of space steps =7,U qMl_  
    J =100;                % Steps between output of space )&<ExJQ&  
    T =10;                  % length of time windows:T*T0 eR`<9KBH  
    T0=0.1;                 % input pulse width @E;pT3; )  
    MN1=0;                 % initial value for the space output location #B9[U} 8  
    dt = T/N;                      % time step 8m<<tv.  
    n = [-N/2:1:N/2-1]';           % Index 3Q)>gh*  
    t = n.*dt;   -P&e4sV{  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 IBh~(6  
    u20=u10.*0.0;                  % input to waveguide 2 Fo~v.+^?  
    u1=u10; u2=u20;                 18`%WUPnT  
    U1 = u1;   N2e<Y_T  
    U2 = u2;                       % Compute initial condition; save it in U V+z)B+  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. xvl  
    w=2*pi*n./T; X+8p2xSO|  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ,ua1xsZl&  
    L=4;                           % length of evoluation to compare with S. Trillo's paper f tDV3If  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 -~fI|A^  
    for m1 = 1:1:M1                                    % Start space evolution ,[ L$  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS q04Dj-2<  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; -+_&#twU  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 3PffQ,c[~  
       ca2 = fftshift(fft(u2)); @D=`iG%  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation &J:)*EjVl5  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   $uhDBmb  
       u2 = ifft(fftshift(c2));                        % Return to physical space Bx4GFCdifC  
       u1 = ifft(fftshift(c1)); A o$z )<d'  
    if rem(m1,J) == 0                                 % Save output every J steps. G - WJlu  
        U1 = [U1 u1];                                  % put solutions in U array /vu!5?S  
        U2=[U2 u2]; qV,j)b3M  
        MN1=[MN1 m1]; fM.|#eLi  
        z1=dz*MN1';                                    % output location Sw'?$j^3  
      end 9YhsJ~"Q  
    end zX`RN )C  
    hg=abs(U1').*abs(U1');                             % for data write to excel 0+LloB  
    ha=[z1 hg];                                        % for data write to excel Mk?I}  
    t1=[0 t']; 0B/a$NC  
    hh=[t1' ha'];                                      % for data write to excel file G9Tix\SpF  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format |'_<(z  
    figure(1) |"v{RC0  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ':4pH#E  
    figure(2) *'-^R9dN.S  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn &Sa~Wtm|*  
    7+4"+CA  
    非线性超快脉冲耦合的数值方法的Matlab程序 c\MDOD%9  
    D7/Bp4I#o  
    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。   |>GIPfVT  
    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 I xBO$ 2  
    8f5^@K\c  
    DjvgKy=Jr_  
    I=a$1%BzEX  
    %  This Matlab script file solves the nonlinear Schrodinger equations # HYkzjb  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of :j4 [_9\  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear HYmXPpse  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 );H[lKy  
    kZ%W?#  
    C=1;                           \;gt&*$-  
    M1=120,                       % integer for amplitude *PU,Rc()6  
    M3=5000;                      % integer for length of coupler Z]\^.x9S  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) NI:N W-!  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 4LJ}>e  
    T =40;                        % length of time:T*T0. U-<"i6mg ?  
    dt = T/N;                     % time step g>P9hIl  
    n = [-N/2:1:N/2-1]';          % Index ] Nipo'N;  
    t = n.*dt;   KBA%  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 'PYqp&gJ  
    w=2*pi*n./T; N\p]+[6  
    g1=-i*ww./2; v=-3 ,C  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ,s&~U<Z  
    g3=-i*ww./2; Uy|=A7Ad c  
    P1=0; -wMW@:M_  
    P2=0; [ {LnE:  
    P3=1;  j)6B^!  
    P=0; PGl-2Cr  
    for m1=1:M1                 N2s%p6RMPD  
    p=0.032*m1;                %input amplitude bKZ#>%|:o  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Q9tE^d+%  
    s1=s10; u@u.N2H.%  
    s20=0.*s10;                %input in waveguide 2 W+C_=7_  
    s30=0.*s10;                %input in waveguide 3 Vp"Ug,1  
    s2=s20; Go7hDmu  
    s3=s30; +J8/,d  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   $!C+i"q$  
    %energy in waveguide 1 _k.bGYldk  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   r ;8z"*  
    %energy in waveguide 2 h!CX`pBM  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   )Hm[j)YI  
    %energy in waveguide 3 : ";D.{||  
    for m3 = 1:1:M3                                    % Start space evolution b7sE  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS rGGepd  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; e4%*I8 ^e  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ey\{C`(__y  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 4@iJ|l  
       sca2 = fftshift(fft(s2)); G2{M#H  
       sca3 = fftshift(fft(s3)); AeCG2!8^0  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   H-KwkH`L4  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); (jMAa%  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); }Rxg E~ F  
       s3 = ifft(fftshift(sc3)); $_zkq@  
       s2 = ifft(fftshift(sc2));                       % Return to physical space (,c?}TP  
       s1 = ifft(fftshift(sc1)); ;s. 5\YZ"k  
    end "u8o?8+q~  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ww t()  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 1(7.V-(G  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 'Mx K}9  
       P1=[P1 p1/p10]; R:BBNzY}f  
       P2=[P2 p2/p10]; 3H}~eEg,  
       P3=[P3 p3/p10]; S*m`'  
       P=[P p*p]; JBEgiQ/  
    end AKC foJ  
    figure(1) Etc?;Z[F#  
    plot(P,P1, P,P2, P,P3); bZay/ Zkj  
    6`baQ!xc.  
    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~!~