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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 MAYb.>X#>  
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    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of d'96$e o~  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of [QxP9EC  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear w8X5kk   
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 'etA1]<N  
    @.7/lRr@bp  
    %fid=fopen('e21.dat','w'); )>1}I_1j)  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) )IcSdS0@M  
    M1 =3000;              % Total number of space steps QwX81*nx  
    J =100;                % Steps between output of space D`@a*YIq  
    T =10;                  % length of time windows:T*T0 d'W2I*Zc<  
    T0=0.1;                 % input pulse width _5rKuL  
    MN1=0;                 % initial value for the space output location !-`L1D_hy  
    dt = T/N;                      % time step &j:e<{@  
    n = [-N/2:1:N/2-1]';           % Index MZ}0.KmaZ  
    t = n.*dt;   //c6vG  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ntH`\ )xi  
    u20=u10.*0.0;                  % input to waveguide 2  lPZ>#  
    u1=u10; u2=u20;                 ;\w3IAa|V  
    U1 = u1;   CaZc{  
    U2 = u2;                       % Compute initial condition; save it in U dI\_I]  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. kqKT>xo4EZ  
    w=2*pi*n./T; 2vpQ"e- A  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T /V*SI!C<f  
    L=4;                           % length of evoluation to compare with S. Trillo's paper >fYcr#i0[  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 m+XHFU  
    for m1 = 1:1:M1                                    % Start space evolution ?w(hPUd!2  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS \C$e+qb~{  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; M ]047W  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform lPR^~&/  
       ca2 = fftshift(fft(u2)); Xb:* KeZq  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation [RKk-8I  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   pG"wQ  
       u2 = ifft(fftshift(c2));                        % Return to physical space .hH_1Mo8  
       u1 = ifft(fftshift(c1)); MDytA0M  
    if rem(m1,J) == 0                                 % Save output every J steps. XB!qPh .  
        U1 = [U1 u1];                                  % put solutions in U array c/+6M  
        U2=[U2 u2]; DU6j0lz  
        MN1=[MN1 m1]; bJn&Y  
        z1=dz*MN1';                                    % output location 9@CRL=  
      end G%HG6  
    end f~W+Rt7o  
    hg=abs(U1').*abs(U1');                             % for data write to excel SWw!s&lP&  
    ha=[z1 hg];                                        % for data write to excel 5 <k)tF%  
    t1=[0 t']; =-Hhm($n  
    hh=[t1' ha'];                                      % for data write to excel file C5^WJx[  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format L|WrdT D;  
    figure(1) 2z{B  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn ?u#s?$Y?  
    figure(2) \bT0\ (Js\  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 2&*#k  
    -6J <{1V  
    非线性超快脉冲耦合的数值方法的Matlab程序 jywS<9c@  
    w#)u+^-  
    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。   l| uiC%T  
    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 E+i(p+=4  
    3ux7^au  
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    &iWTf K7  
    %  This Matlab script file solves the nonlinear Schrodinger equations `^/8dIya  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of .'o=J`|  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear !4Zy$69R  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 - c>Vw&1  
    +pgHCzwJE  
    C=1;                           h._eP.W`  
    M1=120,                       % integer for amplitude 2p9^ =  
    M3=5000;                      % integer for length of coupler 'AK '(cZ  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Gjeb)Y6N  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 9IXy96]]6  
    T =40;                        % length of time:T*T0. ~zfF*A  
    dt = T/N;                     % time step A-L1vu;  
    n = [-N/2:1:N/2-1]';          % Index 0p[k7W u  
    t = n.*dt;   {HY3E}YJL  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ]h1.1@>xc  
    w=2*pi*n./T; t0fgG/f'  
    g1=-i*ww./2; Q\s+w){f%  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; c`x4."m  
    g3=-i*ww./2; ? ch?q~e)  
    P1=0; dH5*%  
    P2=0; vTFG*\Cq  
    P3=1; ?@PSD\  
    P=0; cvy 5|;-u  
    for m1=1:M1                 Y[)mHs2  
    p=0.032*m1;                %input amplitude rAtCG1Vr  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 yCR8c,'8  
    s1=s10; {,uSDI Oj$  
    s20=0.*s10;                %input in waveguide 2 Y$XzZ>VW  
    s30=0.*s10;                %input in waveguide 3 9=$ pV==  
    s2=s20; 5cf?u3r!qJ  
    s3=s30; [xY-=-T*4  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   |WS@q'  
    %energy in waveguide 1 Q?T+^J   
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   [Y!HQ9^LEp  
    %energy in waveguide 2 l"JM%LV  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   e.L&A|  
    %energy in waveguide 3 b]?5r)GK  
    for m3 = 1:1:M3                                    % Start space evolution {hN\=_6*EW  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS /"="y'Wx  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; N`7OJ)l  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; zQ:nL*X'Z"  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform +}at#%1@  
       sca2 = fftshift(fft(s2)); lIEZ=CEmY  
       sca3 = fftshift(fft(s3)); jFg19C{=X  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   z[ ;n2o|s  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }~&0<8m  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); o=94H7@  
       s3 = ifft(fftshift(sc3)); Has}oe[  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ~]no7O4  
       s1 = ifft(fftshift(sc1)); 837:;<T  
    end N:Q.6_%^  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 2{WZ?H93a  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); !XjZt  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); NG3:=  
       P1=[P1 p1/p10]; m Qx1co  
       P2=[P2 p2/p10]; yqK_|7I+  
       P3=[P3 p3/p10]; &S*{a  
       P=[P p*p]; cM9> V2:P  
    end U) xeta+  
    figure(1) < ~CY?  
    plot(P,P1, P,P2, P,P3); Yur}<>`(  
     ^F?B_'  
    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~!~