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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 o^gqpQv  
    L{osh0  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of *"4 OXyV  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of nz+DPk["  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear }9{6{TD  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 O+c@B}[!  
    spgY &OI;  
    %fid=fopen('e21.dat','w'); NNSn]LP  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) |VTm5.23  
    M1 =3000;              % Total number of space steps C$Ldz=d  
    J =100;                % Steps between output of space fXO"Mr1  
    T =10;                  % length of time windows:T*T0 X8F _Mb*  
    T0=0.1;                 % input pulse width Fj -mo>"  
    MN1=0;                 % initial value for the space output location QD q2<  
    dt = T/N;                      % time step rAk*~OK  
    n = [-N/2:1:N/2-1]';           % Index ^D"}OQoh  
    t = n.*dt;   &QLCij5:  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 [\eUCt F  
    u20=u10.*0.0;                  % input to waveguide 2 Spt[b.4mF  
    u1=u10; u2=u20;                 wbVM'E/&  
    U1 = u1;   J7_'@zU  
    U2 = u2;                       % Compute initial condition; save it in U if r!ha+8!  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. CQQX7Y\  
    w=2*pi*n./T; 8K7zh.E  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T qFt%{~a S  
    L=4;                           % length of evoluation to compare with S. Trillo's paper hP,SvN#!2  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 % ;09J  
    for m1 = 1:1:M1                                    % Start space evolution H+\rCefba  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS @\b*a]CV  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; \snbU'lfP  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 8&f}GdZh  
       ca2 = fftshift(fft(u2)); yUqvF6+26  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation pu,/GBG_  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   '9]%#^[Q  
       u2 = ifft(fftshift(c2));                        % Return to physical space No!P?  
       u1 = ifft(fftshift(c1)); *!Vic#D%  
    if rem(m1,J) == 0                                 % Save output every J steps. A: 0  
        U1 = [U1 u1];                                  % put solutions in U array iMYvCw/t6  
        U2=[U2 u2]; e*:[#LJ]C  
        MN1=[MN1 m1]; e#)}.   
        z1=dz*MN1';                                    % output location ]Y}faW(&Y  
      end &(IL`%  
    end O=G2bdY{,  
    hg=abs(U1').*abs(U1');                             % for data write to excel t-3wjS1v  
    ha=[z1 hg];                                        % for data write to excel 7f~DD8R  
    t1=[0 t']; -|:7<$2#I  
    hh=[t1' ha'];                                      % for data write to excel file (+q?xwl!N  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format w'#VN|;;!  
    figure(1) &7XB $  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn *.~hn5Y|?  
    figure(2) JIjqGxR  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn lD _  u  
    `9kjYSd#E  
    非线性超快脉冲耦合的数值方法的Matlab程序 &B/cy<;y,  
    DbH{; Fb  
    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。   f @Hp,-  
    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 gjk=`lU  
    > rB7ms/@E  
    EAqTXB@XU  
     QSmE:Y  
    %  This Matlab script file solves the nonlinear Schrodinger equations vx5;}[Bhm  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of kS8srT /H  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear GL.& g{$#+  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 %]nLCoQh  
    Cx} Yp-  
    C=1;                           U]@t\T3W  
    M1=120,                       % integer for amplitude )jn|+M  
    M3=5000;                      % integer for length of coupler l)Q,*i  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 8n,i5>!d  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. cs8bRXjHa  
    T =40;                        % length of time:T*T0. t9zPJQlT}  
    dt = T/N;                     % time step VQ$=F8ivG  
    n = [-N/2:1:N/2-1]';          % Index eN,s#/ip]  
    t = n.*dt;   acRPKTs H  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ?k<wI)JR  
    w=2*pi*n./T;  N_=7  
    g1=-i*ww./2; );@@>~  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; !3-mPG< ]  
    g3=-i*ww./2; 9 %,_G.  
    P1=0; #z6RzZu  
    P2=0; N?p9h{DG  
    P3=1; o`DBzC  
    P=0; BT2[@qH|qF  
    for m1=1:M1                  i('z~  
    p=0.032*m1;                %input amplitude ~bWqoJ;Q  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 nsaf6y&E  
    s1=s10; w-HgC  
    s20=0.*s10;                %input in waveguide 2  4O[5,  
    s30=0.*s10;                %input in waveguide 3 uY5f mM9  
    s2=s20; *J 7>6N:-  
    s3=s30; "k"q)5c  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   i6h:%n]Io  
    %energy in waveguide 1 !Z<GUbl t  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   #:"\6s  
    %energy in waveguide 2 Rl=NVo  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   t8U)za  
    %energy in waveguide 3 eOZA2  
    for m3 = 1:1:M3                                    % Start space evolution |/]bpG'z  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS RIC'JLWQ  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; %_@8f|# ,M  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 1;?b-FEq:  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform MztT/31S  
       sca2 = fftshift(fft(s2)); z,P:i$  
       sca3 = fftshift(fft(s3)); &julw;E  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   X`.4byqdK  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); L_<&oq  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); "@$o'rfT  
       s3 = ifft(fftshift(sc3)); c42p>}P[  
       s2 = ifft(fftshift(sc2));                       % Return to physical space W a2V Z  
       s1 = ifft(fftshift(sc1)); ceH7Rq:4W  
    end %UV_ 3  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); oMkB!s  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 1mFc]1W  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); z=?ainnKx  
       P1=[P1 p1/p10]; qV/"30,K  
       P2=[P2 p2/p10]; AZI%KM[  
       P3=[P3 p3/p10]; ~.VWrHC  
       P=[P p*p]; 6:330"9  
    end f|m.v +7k  
    figure(1) ZT"?W $  
    plot(P,P1, P,P2, P,P3); [\@!~F{  
    RgRyo  
    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~!~