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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 iII=;:p  
    &dM. d!  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of <0b)YJb4M  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Y$Z x,  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear  .E`\MtA  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ~Sj9GxTe  
    ,}3 'I [  
    %fid=fopen('e21.dat','w'); hIy~B['  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) n^Hm;BiE#  
    M1 =3000;              % Total number of space steps hQYL`Dni  
    J =100;                % Steps between output of space w65K[l;2  
    T =10;                  % length of time windows:T*T0 d,+Hd2o^X  
    T0=0.1;                 % input pulse width }>>1<P<8-  
    MN1=0;                 % initial value for the space output location T|nDTezr  
    dt = T/N;                      % time step U' H$`$Ov  
    n = [-N/2:1:N/2-1]';           % Index RRmz"j>  
    t = n.*dt;   O_ `VV*  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 BXtCSfY $  
    u20=u10.*0.0;                  % input to waveguide 2 b*a#<K$T_  
    u1=u10; u2=u20;                 IwQ"eUnK  
    U1 = u1;   i3tg6o4C  
    U2 = u2;                       % Compute initial condition; save it in U EK {Eo9l  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ]<ldWL  
    w=2*pi*n./T; 24 [+pu  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 2BQ j  
    L=4;                           % length of evoluation to compare with S. Trillo's paper zQcL|  (N  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 Hx"ob_^'7  
    for m1 = 1:1:M1                                    % Start space evolution  7''??X  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS &XIt5<$~R  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; u(@$a4z  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform k.uH~S_  
       ca2 = fftshift(fft(u2)); uGwm r  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation n&$j0k  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Ro\8ZXUQa  
       u2 = ifft(fftshift(c2));                        % Return to physical space o} J&E{Tk  
       u1 = ifft(fftshift(c1)); Jl( &!?j  
    if rem(m1,J) == 0                                 % Save output every J steps. '~5LY!H(pT  
        U1 = [U1 u1];                                  % put solutions in U array T1ut"Zu  
        U2=[U2 u2]; 6eLR2  
        MN1=[MN1 m1]; fz|cnU  
        z1=dz*MN1';                                    % output location '*K:  lx  
      end YmL06<Mh  
    end s2h@~y  
    hg=abs(U1').*abs(U1');                             % for data write to excel ^yWL,$  
    ha=[z1 hg];                                        % for data write to excel `g(Y*uCp  
    t1=[0 t']; EAT"pxP  
    hh=[t1' ha'];                                      % for data write to excel file /a{la8Ni  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ]^yFaTfS  
    figure(1) l{5IUuUi  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn s3z$e+A8  
    figure(2) Kz~ps 5  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6Y^23W F  
    p*< 0"0  
    非线性超快脉冲耦合的数值方法的Matlab程序 H=<S 9M  
    8m-U){r!U^  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   PY{ G [  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 m4**~xfC  
    tI`Q/a5@  
    {+ ][5<q  
    .!Oo|m`V@  
    %  This Matlab script file solves the nonlinear Schrodinger equations 51#_Vg  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of "i nd$Z`c  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 5&QJ7B,!  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 B-xGX$<z  
    . k#U]M  
    C=1;                           $|L Sx  
    M1=120,                       % integer for amplitude *{YlN}vA  
    M3=5000;                      % integer for length of coupler m}C>ti`VD  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) .8@$\ZRP  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. IoxgjUa  
    T =40;                        % length of time:T*T0. tRs [ YK  
    dt = T/N;                     % time step Bn^0^J-  
    n = [-N/2:1:N/2-1]';          % Index ! +a. Ei  
    t = n.*dt;   rNrxaRQ  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. CnU*Jb  
    w=2*pi*n./T; .I7pA5V{#  
    g1=-i*ww./2; 2a-w% (K  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; EMh7z7}Rr  
    g3=-i*ww./2; C;;Sih5  
    P1=0; ' KP@W9j  
    P2=0; 6@Y_*4$|  
    P3=1; (]Z_UTT  
    P=0; ~FZ&.<s  
    for m1=1:M1                 tWJZoD6}h  
    p=0.032*m1;                %input amplitude n4s+>|\M  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ?ME6+Z\  
    s1=s10; +O"!qAiK  
    s20=0.*s10;                %input in waveguide 2 Z 8S\@I  
    s30=0.*s10;                %input in waveguide 3 ,-$LmECg  
    s2=s20; zvvhFN2s  
    s3=s30;  q['Euy  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ot,jp|N>f~  
    %energy in waveguide 1 mi=Q{>rb  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   /'Ass(=6  
    %energy in waveguide 2 ?5+.`L9H  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   "fQ~uzg="  
    %energy in waveguide 3 _64A( U  
    for m3 = 1:1:M3                                    % Start space evolution xmNB29#  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS }QN1|mP2  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; %oF}HF.  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; spGb!Y`mR  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 9`T)@Uj2n  
       sca2 = fftshift(fft(s2)); XR8,Vt)=  
       sca3 = fftshift(fft(s3)); ]jtK I4  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Y4OPEo5o  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); qt"G[9;  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); NiNM{[3oS  
       s3 = ifft(fftshift(sc3)); =qoWCmg"&  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 7G:s2432  
       s1 = ifft(fftshift(sc1)); zE336  
    end :I"2V  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); h(<,fg1  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); cCSs  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); >] qc-{>&  
       P1=[P1 p1/p10]; !lREaSM  
       P2=[P2 p2/p10]; GX)u|g  
       P3=[P3 p3/p10]; jk"`Z<j~  
       P=[P p*p]; ~t@cO.c  
    end !xzeMVI  
    figure(1) <vnHz?71c  
    plot(P,P1, P,P2, P,P3); V8 e>l[tH  
    Bp*K]3_  
    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~!~