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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 8ZW?|-i  
    JCNk\@0i*  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of Qww^P/vm  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of l0:5q?g  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear x^X$M$o,l  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Hsgy'X%om  
    EavX8r  
    %fid=fopen('e21.dat','w'); dHq#  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) bs BZ E  
    M1 =3000;              % Total number of space steps bQ"N ;d)e  
    J =100;                % Steps between output of space HS7_MGU  
    T =10;                  % length of time windows:T*T0 @0D![oA  
    T0=0.1;                 % input pulse width `zY!`G  
    MN1=0;                 % initial value for the space output location [g`,AmR\!  
    dt = T/N;                      % time step %E  aE,  
    n = [-N/2:1:N/2-1]';           % Index d@Q][7  
    t = n.*dt;   S+iP^*L,c  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 M7vj^mt?  
    u20=u10.*0.0;                  % input to waveguide 2 Hit Ac8  
    u1=u10; u2=u20;                 /K@$#x_{  
    U1 = u1;   ZtR&wk  
    U2 = u2;                       % Compute initial condition; save it in U ||XIWKF<n2  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. D'n L  
    w=2*pi*n./T; ~{P:sjsU  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 6"+8M 3M l  
    L=4;                           % length of evoluation to compare with S. Trillo's paper M/} aq  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 pqH4w(;  
    for m1 = 1:1:M1                                    % Start space evolution EX+,:l\^  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS :/i~y$t  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Mi?}S6bp  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform eC;!YG Z  
       ca2 = fftshift(fft(u2)); Y&g&n o_  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation [%?y( q  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   \lW_f{X)  
       u2 = ifft(fftshift(c2));                        % Return to physical space 'W(xgOP1  
       u1 = ifft(fftshift(c1)); !UcOl0"6  
    if rem(m1,J) == 0                                 % Save output every J steps. 4w;~4#ZPp  
        U1 = [U1 u1];                                  % put solutions in U array T .hb#oO  
        U2=[U2 u2]; $kl$D"*0  
        MN1=[MN1 m1]; %Hwbw],kl8  
        z1=dz*MN1';                                    % output location -X8eabb  
      end LipxAE?O  
    end k}U JVH21k  
    hg=abs(U1').*abs(U1');                             % for data write to excel )88nMH-  
    ha=[z1 hg];                                        % for data write to excel Um\0i;7 ~4  
    t1=[0 t']; ;s}3e#$L  
    hh=[t1' ha'];                                      % for data write to excel file Wcn[gn<  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 3S;N(A4  
    figure(1) lQL:3U0DjU  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn R8 jovr  
    figure(2) ($S Lb6  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1eD.:_t4  
    /PW&$P1.]"  
    非线性超快脉冲耦合的数值方法的Matlab程序 S=PJhAF  
    6c &Y  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ^yJ:+m;6K  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 -TS? fne)  
    R04J3D|  
    /WYh[XKe  
    Q;wB{vr$  
    %  This Matlab script file solves the nonlinear Schrodinger equations !+KhFC&Py  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of f'_M0x  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear anC+r(jjg9  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Dft%ip2  
    ;RHNRVP  
    C=1;                           hDvpOIUL1  
    M1=120,                       % integer for amplitude  CC#C  
    M3=5000;                      % integer for length of coupler ,ux+Qz5(  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) }dKLMNqPA  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 7xT[<?,  
    T =40;                        % length of time:T*T0. ?(D}5`Nfu  
    dt = T/N;                     % time step "-0;#&!  
    n = [-N/2:1:N/2-1]';          % Index { i;6vRr  
    t = n.*dt;   *<q4S(l  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. J3IRP/*z  
    w=2*pi*n./T; 'HB~Dbq`V  
    g1=-i*ww./2; ^Plc}W7h  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; EY$?^iS  
    g3=-i*ww./2; 61|B]ei/  
    P1=0; C0(sAF@  
    P2=0; >3P9 i ;W  
    P3=1; tT-=hDw  
    P=0; enumK\  
    for m1=1:M1                 VYigxhP7  
    p=0.032*m1;                %input amplitude iC*U$+JG  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 41}/w3Z4  
    s1=s10; /buWAX 1  
    s20=0.*s10;                %input in waveguide 2 -)RJ\V^{9  
    s30=0.*s10;                %input in waveguide 3 n_P(k-^U*  
    s2=s20; ?!7 SzLll  
    s3=s30; #HG&[Ywi  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   f[}|rf  
    %energy in waveguide 1 } # Xi`<{  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   [+Un ^gD  
    %energy in waveguide 2 RJPcn)@l  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   &^+3er rO  
    %energy in waveguide 3 WHk/$7_"i  
    for m3 = 1:1:M3                                    % Start space evolution VDa|U9N  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Nf5WQTa4  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; MA6P"?  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; KZ  )Ys  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform \ 3G*j`  
       sca2 = fftshift(fft(s2)); MS{{R +&  
       sca3 = fftshift(fft(s3)); :o$@F-$k  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   g@u;Y5  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); H"D 5 e  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 0!_*S )  
       s3 = ifft(fftshift(sc3)); (3O1?n[n  
       s2 = ifft(fftshift(sc2));                       % Return to physical space  (YrR8  
       s1 = ifft(fftshift(sc1)); f3t. T=S  
    end ~S;!T  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); b0YNac.l  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); /RqhykgZ  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); =GTD"*vwr  
       P1=[P1 p1/p10]; u-39r^`5  
       P2=[P2 p2/p10]; LzE/g)>  
       P3=[P3 p3/p10]; `p1DaV  
       P=[P p*p]; $3 vhddO  
    end 9GPb$ gtx  
    figure(1) $',3Pv  
    plot(P,P1, P,P2, P,P3); !sG"n&uZq  
    {+\'bIV[  
    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~!~