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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 F5y&"Y_  
    cua( w  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of -ykD/  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of \&l@rMD3s  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear G +&pq  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Vg(M ^2L  
    Q_Wg4n5  
    %fid=fopen('e21.dat','w'); V%B~ q`4  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) h\2iArw8  
    M1 =3000;              % Total number of space steps [FZq'E"87  
    J =100;                % Steps between output of space 4hxa|f  
    T =10;                  % length of time windows:T*T0 ^H -a@QM  
    T0=0.1;                 % input pulse width }kF?9w  
    MN1=0;                 % initial value for the space output location +4Fw13ADE  
    dt = T/N;                      % time step EywBT  
    n = [-N/2:1:N/2-1]';           % Index J0imWluhQ  
    t = n.*dt;   >?#zPweA  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 K)  Ums-b  
    u20=u10.*0.0;                  % input to waveguide 2 B>4/[ YHr;  
    u1=u10; u2=u20;                 7X)4ec9H\  
    U1 = u1;   =ym<yI<  
    U2 = u2;                       % Compute initial condition; save it in U !zsrORF{  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. F B:nkUR`  
    w=2*pi*n./T; U^eos;:s8  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T =\ k:]  
    L=4;                           % length of evoluation to compare with S. Trillo's paper s7sTY   
    dz=L/M1;                       % space step, make sure nonlinear<0.05 {5fL!`6w  
    for m1 = 1:1:M1                                    % Start space evolution :>/6:c?atG  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS D&@Iuo  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; mlPvF%Ba  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform zkiwFEHA=  
       ca2 = fftshift(fft(u2)); Abi(1nXdQ  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation >_\[C?8  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   "LSzF_mK  
       u2 = ifft(fftshift(c2));                        % Return to physical space #WJ*)$A@&  
       u1 = ifft(fftshift(c1)); EqGpo_  
    if rem(m1,J) == 0                                 % Save output every J steps. 0yvp>{;p  
        U1 = [U1 u1];                                  % put solutions in U array \ @[Q3.VX  
        U2=[U2 u2]; .lq83; k  
        MN1=[MN1 m1]; S;y4Z:!  
        z1=dz*MN1';                                    % output location $4}G  
      end |fIyq}{7  
    end m;A[ 2 6X  
    hg=abs(U1').*abs(U1');                             % for data write to excel rLE+t(x(0  
    ha=[z1 hg];                                        % for data write to excel GwfCl{l  
    t1=[0 t']; ?z <-Ww  
    hh=[t1' ha'];                                      % for data write to excel file rL&Mq}7QK  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ktS^^!,l%  
    figure(1) 9UVT]acq  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn V#5$J Xp  
    figure(2) $:\`E 56\  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn @OGG]0 J  
    P -nhG  
    非线性超快脉冲耦合的数值方法的Matlab程序 Dx`-h#  
    Nd+1r|e'  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   &r~s3S{pQ  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 RKE"}|i +S  
    x(xi%?G  
    X:I2wJDs\  
    PEm2w#X%L  
    %  This Matlab script file solves the nonlinear Schrodinger equations 3!osQ1  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ~%C F3?e6  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Yb4ku7}  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 dgIH`<U$  
    y4LUC;[n  
    C=1;                           1_#;+S  
    M1=120,                       % integer for amplitude q5L^>"  
    M3=5000;                      % integer for length of coupler f$6N  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) cJv/)hRaz  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. P tLWFO  
    T =40;                        % length of time:T*T0. fISK3t/=C  
    dt = T/N;                     % time step G}^=(,jl  
    n = [-N/2:1:N/2-1]';          % Index HZZZ [km  
    t = n.*dt;   \/?J)k3H.  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 5 7t.Ud  
    w=2*pi*n./T; *U]&a^N  
    g1=-i*ww./2; Nh_\{ &r  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; fK+ 5   
    g3=-i*ww./2; oI[rxr  
    P1=0; ,ofE*Wt  
    P2=0; ZJQFn  
    P3=1; <+-n lK4  
    P=0; ,z>-_HOnw  
    for m1=1:M1                 )\ceanS  
    p=0.032*m1;                %input amplitude DKu$u ]Z  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 IsE3-X|  
    s1=s10; "C\yM{JZ  
    s20=0.*s10;                %input in waveguide 2 {_\cd.AuT  
    s30=0.*s10;                %input in waveguide 3 FZ ?eX`,  
    s2=s20; q(:L8nKT]  
    s3=s30; GT)7VFrL  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Z#-N$%^F  
    %energy in waveguide 1 cS7\,/4S  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   (lVMy\  
    %energy in waveguide 2 77yYdil^W+  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   bTmhz  
    %energy in waveguide 3 )!\6 "{  
    for m3 = 1:1:M3                                    % Start space evolution VOM@x%6#c  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ?z#*eoPr  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; "q+Z*   
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Vjv6d&Q  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform q%e'WMG~n  
       sca2 = fftshift(fft(s2)); _^#eO`4"  
       sca3 = fftshift(fft(s3)); 3&7? eO7*  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   oJr+RO  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); $%MgIy  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 1h?ve,$  
       s3 = ifft(fftshift(sc3)); o]Ne|PEpO  
       s2 = ifft(fftshift(sc2));                       % Return to physical space |cY,@X,X6  
       s1 = ifft(fftshift(sc1)); Se'SDJl=  
    end GI/NouaNfm  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); (k #xF"yI  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 5rB>)p05[  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); c{I]!y^!  
       P1=[P1 p1/p10]; #eOHe4Vt  
       P2=[P2 p2/p10]; {qi #  
       P3=[P3 p3/p10]; GZu12\0nZ  
       P=[P p*p]; O5-GrR^yt  
    end 5(J?C-Pk  
    figure(1) Ovk=s,a)K  
    plot(P,P1, P,P2, P,P3); I V# 8W  
    sV,Yz3E<u$  
    转自:http://blog.163.com/opto_wang/
     
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    离线ciomplj
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~