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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 f`8mES'gc8  
    1IV R4:a  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 6O'6,%#  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 2V=bE-  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear R%^AW2   
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [;hCwj#  
    FK.Qj P:  
    %fid=fopen('e21.dat','w'); y7Sj^muBY  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ^_pJEX  
    M1 =3000;              % Total number of space steps S*?x|&a  
    J =100;                % Steps between output of space Q1?0 ]5  
    T =10;                  % length of time windows:T*T0 wv_<be[?*  
    T0=0.1;                 % input pulse width Shb"Jc_i  
    MN1=0;                 % initial value for the space output location ,N`D{H"F  
    dt = T/N;                      % time step 9>HCt*|_8  
    n = [-N/2:1:N/2-1]';           % Index $|r p5D6  
    t = n.*dt;   cp<jwcc!  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 9EKc{1 z  
    u20=u10.*0.0;                  % input to waveguide 2  L\("  
    u1=u10; u2=u20;                 xEvm>BZi  
    U1 = u1;   mY,t]#^m7  
    U2 = u2;                       % Compute initial condition; save it in U h5.AM?*TNd  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. lT~A~O  
    w=2*pi*n./T; ~Y'j8W  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T rLOdQN  
    L=4;                           % length of evoluation to compare with S. Trillo's paper R3Ka^l8R|  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ?br4 wl  
    for m1 = 1:1:M1                                    % Start space evolution R SqO$~  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS zV"oB9\9O  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; UV8K$n<  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 'ai!6[|SD  
       ca2 = fftshift(fft(u2)); om}jQJ]KH  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ~ 6-6aYhe  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   _4#&!b6  
       u2 = ifft(fftshift(c2));                        % Return to physical space Tx\g5rk  
       u1 = ifft(fftshift(c1)); , 1` -u$  
    if rem(m1,J) == 0                                 % Save output every J steps. >*cg K}!@  
        U1 = [U1 u1];                                  % put solutions in U array Jdp@3mP  
        U2=[U2 u2]; JypXQC}~  
        MN1=[MN1 m1]; m5rJY/  
        z1=dz*MN1';                                    % output location J}J7A5P  
      end dw]wQ\4B  
    end *QT|J6ng  
    hg=abs(U1').*abs(U1');                             % for data write to excel ,3E9H&@j  
    ha=[z1 hg];                                        % for data write to excel J=C63YB  
    t1=[0 t']; [.`%]Z(  
    hh=[t1' ha'];                                      % for data write to excel file s/J/kKj*s  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format e<[0H 8  
    figure(1) K{x FhdW  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn [Y=X^"PF  
    figure(2) F_&bE@k  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn -*r]9f6 x  
    ]J* y`jn  
    非线性超快脉冲耦合的数值方法的Matlab程序 &9F(uk=X  
    4%L-3Ij  
    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。   Om=*b#k  
    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 lYMNx|PF  
    ,dO$R.h  
    X ?lF,p  
    1_z6O!rx  
    %  This Matlab script file solves the nonlinear Schrodinger equations Qo;#}%}^^  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of oK3aW6  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear \<R.F  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 3Ta<7tEM  
    f8'$Mn,  
    C=1;                           HAr_z@#E  
    M1=120,                       % integer for amplitude oz- k_9%  
    M3=5000;                      % integer for length of coupler (ATCP#lF  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) :xP$iEA`G  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 11Hf)]M   
    T =40;                        % length of time:T*T0. "Nn+Zw43  
    dt = T/N;                     % time step e;/C}sK:  
    n = [-N/2:1:N/2-1]';          % Index p!~{<s]  
    t = n.*dt;   T|&2!Sh  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. +#d}3^_]  
    w=2*pi*n./T; (s\":5 C  
    g1=-i*ww./2; U~w g'  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 4Dd7 I  
    g3=-i*ww./2; VI (;8  
    P1=0; K{s% h0  
    P2=0; Iu -CXc  
    P3=1; ?$T39U^  
    P=0; khW9n*  
    for m1=1:M1                 9C{\=?e;  
    p=0.032*m1;                %input amplitude Fc"&lk4e  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 F}lgy;=h  
    s1=s10; ]U,K]y[Bj  
    s20=0.*s10;                %input in waveguide 2 l^IPN 'O@  
    s30=0.*s10;                %input in waveguide 3 XI*_ti  
    s2=s20; gAY%VFBP0  
    s3=s30; K~#wvUb  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   G{cTQH|  
    %energy in waveguide 1 weOzs]uc  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   z]YP  
    %energy in waveguide 2 Gkr^uXNg#  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Q l$t  
    %energy in waveguide 3 s\`Vr;R:|  
    for m3 = 1:1:M3                                    % Start space evolution 4P>tGO&*x  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS u%7a&1c  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 2 8j=q-9Z  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Bn"r;pqWiT  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform i~IQlyGr.  
       sca2 = fftshift(fft(s2)); lK? Z38  
       sca3 = fftshift(fft(s3)); /Jc?;@{  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   LxGE<xj|V%  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); D k'EKT-  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 0)8QOTeT  
       s3 = ifft(fftshift(sc3)); x Qh?  
       s2 = ifft(fftshift(sc2));                       % Return to physical space =oF6|\]{ ;  
       s1 = ifft(fftshift(sc1)); 4pF U`g=  
    end @HfWAFT  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); I~R<}volu  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); RTSR-<{z  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); -%=StWdb   
       P1=[P1 p1/p10]; fxDY:l  
       P2=[P2 p2/p10]; t#y   
       P3=[P3 p3/p10];  afEp4(X~  
       P=[P p*p]; xrT_ro8  
    end +fhyw{  
    figure(1) L-d8bA  
    plot(P,P1, P,P2, P,P3); wYf=(w \c  
    >5Zp x8W  
    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~!~