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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 O)R7t3t  
    GOYn\N;V2  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ( }]37  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of r@*=|0(OrK  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ).0V%}>  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tC2 )j7@  
    vQ-i xh  
    %fid=fopen('e21.dat','w'); %_B:EMPd  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) '2|1%NSW9  
    M1 =3000;              % Total number of space steps *[d~Nk%Y$  
    J =100;                % Steps between output of space n!0${QVnS  
    T =10;                  % length of time windows:T*T0 ~vW)1XnK  
    T0=0.1;                 % input pulse width \LIy:$`8  
    MN1=0;                 % initial value for the space output location @9OeC O  
    dt = T/N;                      % time step =cf{f]N  
    n = [-N/2:1:N/2-1]';           % Index M&uzOK+  
    t = n.*dt;   *.kj]BoO  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 P$p@5hl  
    u20=u10.*0.0;                  % input to waveguide 2 sg3h i"Im  
    u1=u10; u2=u20;                 KI E k/]<H  
    U1 = u1;   o"'iX UJ  
    U2 = u2;                       % Compute initial condition; save it in U PHQ{-b?4t  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. `t{D7I7  
    w=2*pi*n./T; 'R^iKNPs  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T wzD\8_;6N  
    L=4;                           % length of evoluation to compare with S. Trillo's paper O24Jj\"  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 -M"IVyy@  
    for m1 = 1:1:M1                                    % Start space evolution wl7 MfyU  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS qTyg~]e9(  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; N=>- Q)  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform eQ$N:]  
       ca2 = fftshift(fft(u2)); x  S   
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation >$2E1HW.  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   0Vf)Rw1%I  
       u2 = ifft(fftshift(c2));                        % Return to physical space 0-*Z<cu%l  
       u1 = ifft(fftshift(c1)); !+m@AQ:,  
    if rem(m1,J) == 0                                 % Save output every J steps. .D+RLO z  
        U1 = [U1 u1];                                  % put solutions in U array ]}BB/KQy^  
        U2=[U2 u2]; FQ+8J7  
        MN1=[MN1 m1]; Z*9L'd"D|  
        z1=dz*MN1';                                    % output location . =&Jo9  
      end e{5,'(1]  
    end KL "Y!PN:  
    hg=abs(U1').*abs(U1');                             % for data write to excel ])C>\@c6Gm  
    ha=[z1 hg];                                        % for data write to excel moCK- :  
    t1=[0 t']; Po> e kz_E  
    hh=[t1' ha'];                                      % for data write to excel file LaDY`u0G%  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format \ [cH/{nt  
    figure(1) RYt6=R+f  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn sD2 ^_w6j  
    figure(2) 9X3yp:>V  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn q'.;W@m  
    N*f^Z#B]  
    非线性超快脉冲耦合的数值方法的Matlab程序 TaOOq}8c#  
    WJAYM2 6\  
    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。   3g;T?E  
    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 ^+M><jE9  
    +I&J7ICV0  
    L%f;J/  
    b7!UZu]IEv  
    %  This Matlab script file solves the nonlinear Schrodinger equations m*gj|1k  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of C,.-Q"juH  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @m?{80;uQ  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 R3?:\d{  
    +lKrj\Xj  
    C=1;                           i *B:El1  
    M1=120,                       % integer for amplitude l]$40 j  
    M3=5000;                      % integer for length of coupler Ih()/(  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) QhCY}Q?X  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. v{.\iIg N  
    T =40;                        % length of time:T*T0. o_O+u%y  
    dt = T/N;                     % time step ) o xIzF  
    n = [-N/2:1:N/2-1]';          % Index E3f9<hm   
    t = n.*dt;   P% Q@9kO>  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. -?5$ PH  
    w=2*pi*n./T; l~['[Ub0)  
    g1=-i*ww./2; ?ql2wWsQO  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; n26>>N  
    g3=-i*ww./2; kxh 5}eB  
    P1=0; v J-LPTB  
    P2=0; SF^x=[ir  
    P3=1; *0~M  
    P=0;  g#qNHR  
    for m1=1:M1                 H*rx{F?  
    p=0.032*m1;                %input amplitude lBmm(<~Z  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 sQtf,e|p  
    s1=s10; LE K/mCL  
    s20=0.*s10;                %input in waveguide 2 Af9+HI O  
    s30=0.*s10;                %input in waveguide 3 H} 6CKP}  
    s2=s20; ]~8v^A7u  
    s3=s30; &n|*uLn  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   J\{ $ot  
    %energy in waveguide 1 ;E#\   
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Q&PB]D{  
    %energy in waveguide 2 &bLC(e ]  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   sB6dp D  
    %energy in waveguide 3 Gqt-_gga  
    for m3 = 1:1:M3                                    % Start space evolution FsY(02  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS D%U:!|G  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; &6/%k kv  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; x'qWM/  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Sdx Y>;  
       sca2 = fftshift(fft(s2)); hiwIWd:H  
       sca3 = fftshift(fft(s3)); @KA1"Wb_  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   > :Ze4}(  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); !| xZ6KV  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); wbi3lH:;  
       s3 = ifft(fftshift(sc3)); Qn.[{rw  
       s2 = ifft(fftshift(sc2));                       % Return to physical space QrC/ssf}  
       s1 = ifft(fftshift(sc1)); VNj@5s  
    end 8;#AO8+U7)  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); -72j:nk  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 9tk" :ld  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 9P.(^SD][z  
       P1=[P1 p1/p10]; J>%t<xYf4  
       P2=[P2 p2/p10]; LeHiT>aX!  
       P3=[P3 p3/p10]; FVgMmYU  
       P=[P p*p]; V7C1FV2  
    end #*2Rp8n  
    figure(1) FZXyfZw!|  
    plot(P,P1, P,P2, P,P3); qVBL>9O*.  
    p7C!G1+z  
    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~!~