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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 !LN8=u.  
    K|7"YNohfG  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of v03cQw\"WE  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Ap dXsL  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear x4'@U<  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 q9/v\~m  
    ff#7}9_mh  
    %fid=fopen('e21.dat','w'); ]<f)Rf">:`  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 5CkG^9  
    M1 =3000;              % Total number of space steps ;}46Uc#WS  
    J =100;                % Steps between output of space d/7fJ8y8  
    T =10;                  % length of time windows:T*T0 p&<Ssc  
    T0=0.1;                 % input pulse width +vh|m5"7I7  
    MN1=0;                 % initial value for the space output location @k?vbq  
    dt = T/N;                      % time step Xsq@E#@S  
    n = [-N/2:1:N/2-1]';           % Index ob.<j  
    t = n.*dt;   7*5B  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 /Y7^!3uM  
    u20=u10.*0.0;                  % input to waveguide 2 Ma^jy.  
    u1=u10; u2=u20;                 $p0nq&4c  
    U1 = u1;   uAO!fE}CJ  
    U2 = u2;                       % Compute initial condition; save it in U 8MJJ w;  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Q]k< Y  
    w=2*pi*n./T; N"S`9B1eD(  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %~LY'cfPse  
    L=4;                           % length of evoluation to compare with S. Trillo's paper j_8 YFz5  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 f@OH~4FG  
    for m1 = 1:1:M1                                    % Start space evolution H5K Fm#  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 2@|`Ugjptl  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; uC'-: t#  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform oB:7R^a  
       ca2 = fftshift(fft(u2)); 11H`WOTQF  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation -+".ut:R  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   6j%%CWU{~  
       u2 = ifft(fftshift(c2));                        % Return to physical space P3zUaN \c  
       u1 = ifft(fftshift(c1)); O =Z}DGa+  
    if rem(m1,J) == 0                                 % Save output every J steps. }. &nEi`  
        U1 = [U1 u1];                                  % put solutions in U array mrTf[ "K  
        U2=[U2 u2]; p*g Fr hm  
        MN1=[MN1 m1]; ='7m$,{(Q[  
        z1=dz*MN1';                                    % output location 7H7 Xbi@  
      end )@g[aRFa  
    end b;i*}4h!  
    hg=abs(U1').*abs(U1');                             % for data write to excel iM]O  
    ha=[z1 hg];                                        % for data write to excel V%,,GmiU]  
    t1=[0 t']; x5lVb$!G  
    hh=[t1' ha'];                                      % for data write to excel file r&u1-%%9[  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ?WI v4  
    figure(1) q*hn5K*  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn .n 9.y8C  
    figure(2) P3oYk_oW  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn PQHztS"  
    yzS]FwW7  
    非线性超快脉冲耦合的数值方法的Matlab程序 jD S?p)&  
    o|xf2k  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ,1]UOQ>AP  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 uyj!$}4  
    d^v#x[1msZ  
    +25}X{r$_  
    x ytrd.  
    %  This Matlab script file solves the nonlinear Schrodinger equations Rk$7jZdTf  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of r_7%|T8  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 1[egCC\Mo_  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]cRvdUGv  
    CsR[@&n'  
    C=1;                           MK#   
    M1=120,                       % integer for amplitude -laH^<jm5  
    M3=5000;                      % integer for length of coupler HSruue8  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 1 iH@vd  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. :5kDc" =Z|  
    T =40;                        % length of time:T*T0. (hc!!:N~q  
    dt = T/N;                     % time step Jz8P':6[  
    n = [-N/2:1:N/2-1]';          % Index Kw fd S(  
    t = n.*dt;   (:iMs) iO{  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. i\xs!QU  
    w=2*pi*n./T; #$WnMJ@  
    g1=-i*ww./2; re/-Yu$'  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; &8VH m?h  
    g3=-i*ww./2; (B#FLoK  
    P1=0; lxn/97rA  
    P2=0; htB2?%S=T  
    P3=1; ]OpGD5jZ  
    P=0; HNZ$CaJh  
    for m1=1:M1                 E~y8X9HZ)  
    p=0.032*m1;                %input amplitude { 4+/0\  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [if(B\&  
    s1=s10; D0J{pAJ  
    s20=0.*s10;                %input in waveguide 2 B)q}]Qn  
    s30=0.*s10;                %input in waveguide 3 9SC1A-nF  
    s2=s20; ruaZ(R[  
    s3=s30; C|y^{4 |R  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   -x ?Z2EA!  
    %energy in waveguide 1 bdrE2m  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   c&;" Y{  
    %energy in waveguide 2 )CXlPbhY?  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ".jO2GO^  
    %energy in waveguide 3 u6C_*i{2  
    for m3 = 1:1:M3                                    % Start space evolution Uz;^R@  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS v&:[?<6-  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; @3n!5XM{EE  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; l>*X+TpA,  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform DY`0 `T  
       sca2 = fftshift(fft(s2)); U&"L9o`2  
       sca3 = fftshift(fft(s3)); +v/y{8Fu  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   6jpzyf=~  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); \Fjasz5E'  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); PTHxvml  
       s3 = ifft(fftshift(sc3)); g9C-!X-<T  
       s2 = ifft(fftshift(sc2));                       % Return to physical space %)V=)l.j  
       s1 = ifft(fftshift(sc1)); C b'|  
    end wPU5L*/*i  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Rd8mn'A  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));  W2` 3 p  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); WvU[9ME^)  
       P1=[P1 p1/p10]; GUL~k@:_k  
       P2=[P2 p2/p10]; aPJTH0u  
       P3=[P3 p3/p10]; X au %v5r  
       P=[P p*p]; YusmMsN?  
    end 1 F:bExQ  
    figure(1) :U\* 4l  
    plot(P,P1, P,P2, P,P3); .i\ FK@2  
    c Lyf[z)W  
    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~!~