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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 Y=i_2R2e2  
    B~E>=85z  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of .] 0:`Y,;  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of -UWyBM3c@  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear cJ>^@pd{  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 yjOZed;M  
    i!G<sfL  
    %fid=fopen('e21.dat','w'); ~<}?pDA}~  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) vl!o^_70(  
    M1 =3000;              % Total number of space steps tR .>d  
    J =100;                % Steps between output of space aI;fNy /K  
    T =10;                  % length of time windows:T*T0 +f}w+  
    T0=0.1;                 % input pulse width 1]W8A.ZS  
    MN1=0;                 % initial value for the space output location J[UTn'M8]  
    dt = T/N;                      % time step S#0C^  
    n = [-N/2:1:N/2-1]';           % Index 3*F|`js"  
    t = n.*dt;   &?I3xzvK  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 |}: D_TX  
    u20=u10.*0.0;                  % input to waveguide 2 {qm5H7sL  
    u1=u10; u2=u20;                 djn<Oc`  
    U1 = u1;   7H)tF&  
    U2 = u2;                       % Compute initial condition; save it in U ivSpi?   
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Snq0OxS[v  
    w=2*pi*n./T; o9v.]tb  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 2h) *  
    L=4;                           % length of evoluation to compare with S. Trillo's paper {M23a _t\  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 A&d_! u>  
    for m1 = 1:1:M1                                    % Start space evolution 1`1Jn*|TI  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS H:t2;Z'  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; BOl*. t  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform Q@s G6 iz  
       ca2 = fftshift(fft(u2)); m[w~h\FS  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 'h> l_A  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   [C3wjYi  
       u2 = ifft(fftshift(c2));                        % Return to physical space }]pOR&o  
       u1 = ifft(fftshift(c1)); cr!sq.)s  
    if rem(m1,J) == 0                                 % Save output every J steps. $wcV~'fM  
        U1 = [U1 u1];                                  % put solutions in U array r3YfY \  
        U2=[U2 u2]; 2bf#L?5g/  
        MN1=[MN1 m1]; "9RW<+  
        z1=dz*MN1';                                    % output location 5(DnE?}vo  
      end `J}FSUn\  
    end bR=TGL&  
    hg=abs(U1').*abs(U1');                             % for data write to excel K&&YxX~ 3  
    ha=[z1 hg];                                        % for data write to excel  P!/:yWd  
    t1=[0 t']; PkK#HD  
    hh=[t1' ha'];                                      % for data write to excel file 602=qb  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format AVp"<Uv  
    figure(1) E;r~8^9)  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn &RlYw#*1.  
    figure(2) \qbEC.-K  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6}_J;g\|  
    (k %0|%eR  
    非线性超快脉冲耦合的数值方法的Matlab程序 0[s<!k9=  
    !_:|mu'  
    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。   ^p~3H  
    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 sv*xO7D.  
    rzKn5Z  
    Wp=:|J   
    1gH>B5`  
    %  This Matlab script file solves the nonlinear Schrodinger equations -vS7%Fbr  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 68!=`49r>  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear IUy5=Sl   
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 vFGVz  
    i^/D_L.  
    C=1;                           .7H* F9  
    M1=120,                       % integer for amplitude G]I^zd&P  
    M3=5000;                      % integer for length of coupler c6HH%|  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) ;4(FS  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ,,(BW7(  
    T =40;                        % length of time:T*T0. "\kr;X'  
    dt = T/N;                     % time step E2|c;{ c  
    n = [-N/2:1:N/2-1]';          % Index YwF\  
    t = n.*dt;   _lG\_6oJ,  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. jF%l\$)/  
    w=2*pi*n./T; +|Qe/8Q  
    g1=-i*ww./2; -MeO|HWm  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; tP/R9Ezp  
    g3=-i*ww./2; FuO'%3;c  
    P1=0; (2%z9W  
    P2=0; xwrleB  
    P3=1; 2ZFp(e^%  
    P=0; 96CC5  
    for m1=1:M1                 t/:]\|]WB  
    p=0.032*m1;                %input amplitude _qhYG1t  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ht^xc c  
    s1=s10; V: ivnx*  
    s20=0.*s10;                %input in waveguide 2 lmr:PX  
    s30=0.*s10;                %input in waveguide 3 btU:=6  
    s2=s20; `@i! 'h  
    s3=s30; 8Vqh1<  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   r1X\$&  
    %energy in waveguide 1 :S{+|4pH  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   XDq*nA8#5B  
    %energy in waveguide 2 /bv4/P  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ]+i~Cbj  
    %energy in waveguide 3 hlTM<E  
    for m3 = 1:1:M3                                    % Start space evolution C9FQo7   
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS eI*o9k$Qs  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; g"L$}#iTsl  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; +tPqU6  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform [P746b_\e  
       sca2 = fftshift(fft(s2)); E 14Dq#L  
       sca3 = fftshift(fft(s3)); bT{iei]?  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   69u"/7X  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); m%km@G$  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); GFBku^pi  
       s3 = ifft(fftshift(sc3)); + %07J6  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 2N:|BO>  
       s1 = ifft(fftshift(sc1)); <Xr {1M D  
    end P ||:?3IH  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); JA~v:ec  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ')>&:~  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |\MgE.N  
       P1=[P1 p1/p10]; P>3 ;M'KsO  
       P2=[P2 p2/p10]; G\ht)7SGgf  
       P3=[P3 p3/p10]; ?ydqmj2[F  
       P=[P p*p]; O o+pi$W  
    end s!j[Ovtx  
    figure(1) UL.x*@o  
    plot(P,P1, P,P2, P,P3); f?A1=lm~  
    7U\GX  
    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~!~