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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 bf/z T0  
    `t2Y IwOK  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of )| F O>  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of HJ!P]X_J1  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear D:XjJMW3r  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |fPR7-  
    KA elq*  
    %fid=fopen('e21.dat','w'); H'jo 3d~+  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) in2m/q?  
    M1 =3000;              % Total number of space steps s$xm  
    J =100;                % Steps between output of space 5$c*r$t_RK  
    T =10;                  % length of time windows:T*T0 43Ua@KNi  
    T0=0.1;                 % input pulse width >Dq&[9,8  
    MN1=0;                 % initial value for the space output location IhXP~C6  
    dt = T/N;                      % time step ^@;P-0Sy  
    n = [-N/2:1:N/2-1]';           % Index N2&h yM  
    t = n.*dt;   M! uE#|  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 B dxV [SF  
    u20=u10.*0.0;                  % input to waveguide 2 Z;cA_}5  
    u1=u10; u2=u20;                 -qpe;=g&f  
    U1 = u1;   \8]("l}ms8  
    U2 = u2;                       % Compute initial condition; save it in U T<U_Iq  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 9%DLdc\z;  
    w=2*pi*n./T; b\C1qM4  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T xvW# ~T]  
    L=4;                           % length of evoluation to compare with S. Trillo's paper ~Z5Wwp]a  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 }M &hcw<  
    for m1 = 1:1:M1                                    % Start space evolution RIq\IQ_|  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS |qtZb}"|  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 2 P9{?Y  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform A3Y}|7QA  
       ca2 = fftshift(fft(u2)); @Wd1+Yky  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation kjj?X|Un  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   tTPjCl  
       u2 = ifft(fftshift(c2));                        % Return to physical space g]U! ]  
       u1 = ifft(fftshift(c1)); goc"+ K  
    if rem(m1,J) == 0                                 % Save output every J steps. _Q}vPSJviC  
        U1 = [U1 u1];                                  % put solutions in U array 'Xg9MS&  
        U2=[U2 u2]; yi,Xs|%.  
        MN1=[MN1 m1]; JjQ9AJ?-V  
        z1=dz*MN1';                                    % output location  S=X_7V  
      end  8s>OO&  
    end [[KIuW~ot  
    hg=abs(U1').*abs(U1');                             % for data write to excel LR y&/d  
    ha=[z1 hg];                                        % for data write to excel J pKCux  
    t1=[0 t']; zJG=9C?  
    hh=[t1' ha'];                                      % for data write to excel file xi=Qxgx0I  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format >RXDuCVi  
    figure(1) 8:jakOeT  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Zmy:Etqi  
    figure(2) ,pa=OF  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn _OJ19Ry  
    .%_=(C< E  
    非线性超快脉冲耦合的数值方法的Matlab程序 q[%SF=~<k{  
    |4F'Zu}g>  
    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。   %^bN^Sq -  
    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 >{#QS"J#  
    2UEjn>2  
     o*xft6U  
    6<9gVh<=w  
    %  This Matlab script file solves the nonlinear Schrodinger equations G/&Wc2k  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of YBQ{/"v%|  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear z_L><}H  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 z=K hbh  
    z&Lcl{<MA  
    C=1;                           Vn6]h|vm  
    M1=120,                       % integer for amplitude =B"^#n ;  
    M3=5000;                      % integer for length of coupler sF p% T4j  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) vS G vv43G  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. #80M+m  
    T =40;                        % length of time:T*T0. z:JJ>mxV  
    dt = T/N;                     % time step }RZN3U=  
    n = [-N/2:1:N/2-1]';          % Index DQ= /Jr~  
    t = n.*dt;   I5w> *F   
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. L*1yK*  
    w=2*pi*n./T; U$j?2|v-x  
    g1=-i*ww./2; n<Z1i)  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; m]'P3^<{P  
    g3=-i*ww./2; X!f` !tZ:{  
    P1=0; >npFg@A  
    P2=0; h3P^W(=&  
    P3=1; i>z {QE  
    P=0; p$l'y""i  
    for m1=1:M1                 ^-26K|{3  
    p=0.032*m1;                %input amplitude tQcn%CK  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 X>ck.}F  
    s1=s10; ]McDN[h:  
    s20=0.*s10;                %input in waveguide 2 u51Lp  
    s30=0.*s10;                %input in waveguide 3 YUQKy2  
    s2=s20; N6%M+R/Q  
    s3=s30; td(4Fw||1y  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ~3qt<"  
    %energy in waveguide 1 }Z8DVTpX}  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   v42Z&PO   
    %energy in waveguide 2 "$PX [:  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   nBGcf(BE.$  
    %energy in waveguide 3 S/xCX!  
    for m3 = 1:1:M3                                    % Start space evolution JG=z~STz  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS NnqAr ,  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; wZKEUJpQ  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; T#-U\C~o  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 5ii:93Hlj  
       sca2 = fftshift(fft(s2)); ?a'P;&@7  
       sca3 = fftshift(fft(s3)); OQh4 MN#$  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   T:!Re*=JJ  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ljJR7<  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ?7R&=B1g  
       s3 = ifft(fftshift(sc3)); 4'`y5E  
       s2 = ifft(fftshift(sc2));                       % Return to physical space z*G(AcS)  
       s1 = ifft(fftshift(sc1)); e\' =#Hw  
    end ZoroK.N4A%  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ~?uch8H  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); peGh-  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); tqicyNL  
       P1=[P1 p1/p10];  R]"3^k*  
       P2=[P2 p2/p10]; 's 'H&sa  
       P3=[P3 p3/p10]; 3Tz~DdB  
       P=[P p*p]; n_@cjO  
    end s:Io5C(  
    figure(1) n$y@a? al  
    plot(P,P1, P,P2, P,P3); ::2(pgH  
    > PONu]^  
    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~!~