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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 <KX#;v!I  
    /8T{bJ5  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of =j-{Mxb3  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 3&f{lsLAC  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear KW\`&ki  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 \&0NH=*^  
    k$c!J'qL&  
    %fid=fopen('e21.dat','w'); Dlp::U*N'  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) p P&~S<[  
    M1 =3000;              % Total number of space steps mMH0 o  
    J =100;                % Steps between output of space ~7g6o^A>  
    T =10;                  % length of time windows:T*T0 Y!zlte|P  
    T0=0.1;                 % input pulse width |EunDb[Y  
    MN1=0;                 % initial value for the space output location &/p 9+gd  
    dt = T/N;                      % time step l]gf T&  
    n = [-N/2:1:N/2-1]';           % Index ]h6<o*  
    t = n.*dt;   GU`2I/R  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 D@e:Fu1\R  
    u20=u10.*0.0;                  % input to waveguide 2 i fUgj8i_  
    u1=u10; u2=u20;                 cqDnZ`|6  
    U1 = u1;   7JbrIdDl|  
    U2 = u2;                       % Compute initial condition; save it in U 4[D@[k As  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. +FI]0r  
    w=2*pi*n./T; nM#\4Q[}Jh  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %"D-1&%zY  
    L=4;                           % length of evoluation to compare with S. Trillo's paper qW*)]s)z  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 Jh1fM`kB5K  
    for m1 = 1:1:M1                                    % Start space evolution \oyr[so(i  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS y$rp1||lH  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; c{[WOrA~#  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform f`cO5lP/:)  
       ca2 = fftshift(fft(u2)); *"wsMO  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation "Z <1Msz  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   /OEj]DNY  
       u2 = ifft(fftshift(c2));                        % Return to physical space S:wmm}XQ  
       u1 = ifft(fftshift(c1)); t+t&eg  
    if rem(m1,J) == 0                                 % Save output every J steps. A#}IbcZ|b  
        U1 = [U1 u1];                                  % put solutions in U array :|bPr_&U$  
        U2=[U2 u2]; gU:jx  
        MN1=[MN1 m1]; Onao'sjY  
        z1=dz*MN1';                                    % output location yd $y\pN=<  
      end pnWDsC~)  
    end pV_2JXM~@  
    hg=abs(U1').*abs(U1');                             % for data write to excel ==& =3  
    ha=[z1 hg];                                        % for data write to excel ;-59#S&?tB  
    t1=[0 t']; ~~&M&Fe  
    hh=[t1' ha'];                                      % for data write to excel file +u7mw<A 8  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format R"jX9~3Ln  
    figure(1) d4/ZOj+%  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 0oD?4gn  
    figure(2) BO^e.iB/  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ].eGsh2  
    s<:J(gD  
    非线性超快脉冲耦合的数值方法的Matlab程序 Q/':<QY  
    tq{ aa  
    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。   |X>:"?4t  
    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 /J^yOR9  
    ~e|~c<!z8@  
    uXXwMc<p  
    N7XRk= J  
    %  This Matlab script file solves the nonlinear Schrodinger equations 4q2aVm  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of BQsy)H`4E  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear YkTEAI|i  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 h-V5&em"_  
    >Py=H+d!j  
    C=1;                           mAz':R[  
    M1=120,                       % integer for amplitude > >p3#~/  
    M3=5000;                      % integer for length of coupler X=lOwPvP  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Zx@{nVoYe~  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. R ~#\gMs  
    T =40;                        % length of time:T*T0. R4{2+q=0  
    dt = T/N;                     % time step ) b?HK SqI  
    n = [-N/2:1:N/2-1]';          % Index L0}"H .  
    t = n.*dt;   WL<Cj_N_{H  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. wT;D<rqe`  
    w=2*pi*n./T; ?_IRO|  
    g1=-i*ww./2; }{s<!b  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 7^=O^!sa  
    g3=-i*ww./2; 6#v"+V  
    P1=0; t68h$u  
    P2=0; $Ad 5hkz  
    P3=1; 7cH[}v`pn  
    P=0; xI$B",?(  
    for m1=1:M1                 .Gw;]s3  
    p=0.032*m1;                %input amplitude $5l8V  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 lCDXFy(E  
    s1=s10; M(xd:Fa?  
    s20=0.*s10;                %input in waveguide 2 5F $W^N  
    s30=0.*s10;                %input in waveguide 3 :Fm)<VN"  
    s2=s20; lj(}{O  
    s3=s30; :`25@<*u  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   \)pk/  
    %energy in waveguide 1 52=?! JM  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   lIz"mk  
    %energy in waveguide 2 1-4W4"#  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   *22}b.)  
    %energy in waveguide 3 J"# o #~  
    for m3 = 1:1:M3                                    % Start space evolution |\J8:b> }  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS UT%^!@u  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; h5>JBLawQP  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; m z) O  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform &^9 2z:?  
       sca2 = fftshift(fft(s2)); 4gzrxV  
       sca3 = fftshift(fft(s3)); Y;G+jC8   
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Vv#|% ^0  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ND77(I$3s  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); })%WL;~  
       s3 = ifft(fftshift(sc3)); t[|^[%i  
       s2 = ifft(fftshift(sc2));                       % Return to physical space blEs!/A`  
       s1 = ifft(fftshift(sc1)); L> > %  
    end F<VoPqHq  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); =y.?=`"  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); sz9C':`W  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));  ,SNN[a  
       P1=[P1 p1/p10]; # **vIwX-Q  
       P2=[P2 p2/p10]; 8K=sx @l  
       P3=[P3 p3/p10]; '#L.w6<B  
       P=[P p*p]; -AWL :<  
    end LR|LP)I  
    figure(1) : A9G>qg  
    plot(P,P1, P,P2, P,P3); hi^@969  
    d ]R&mp|'  
    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~!~