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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 >e5q2U   
    $cp16  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of z&6]vN'  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Cw9@2E'b  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear uyS^W'fF  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 %B*<BgJ;4F  
    EU&6 Tg  
    %fid=fopen('e21.dat','w'); ~_/<PIm  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) zz+M1n-;o  
    M1 =3000;              % Total number of space steps cQUH%7m  
    J =100;                % Steps between output of space E.WNykF-  
    T =10;                  % length of time windows:T*T0 wz|Q%.%?[  
    T0=0.1;                 % input pulse width ?[NTw./'7A  
    MN1=0;                 % initial value for the space output location )U"D4j*p  
    dt = T/N;                      % time step !=k*hl0h  
    n = [-N/2:1:N/2-1]';           % Index &+|jJ{93z  
    t = n.*dt;   ImT+8p a  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 \]~kyy  
    u20=u10.*0.0;                  % input to waveguide 2 3.GdKP.%  
    u1=u10; u2=u20;                 ` maN5)  
    U1 = u1;   c)n0D=  
    U2 = u2;                       % Compute initial condition; save it in U p: Q%Lg_I  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 8as$h*W h  
    w=2*pi*n./T; 5KA FUR0  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T P_^ |KEz  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 2:6Y83  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 *1 J#Mdd  
    for m1 = 1:1:M1                                    % Start space evolution 6@ (k8<3  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS h~^qG2TYWq  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Pv/%s) &y&  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform )U/@J+{{  
       ca2 = fftshift(fft(u2)); b@Mng6R  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation C4X{Ps \  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   GFy0R"&d[  
       u2 = ifft(fftshift(c2));                        % Return to physical space 56j/w[&8  
       u1 = ifft(fftshift(c1)); fs)q7 7g  
    if rem(m1,J) == 0                                 % Save output every J steps. Fc{6*wtO  
        U1 = [U1 u1];                                  % put solutions in U array WMdz+^\(  
        U2=[U2 u2]; ,sRrV $,"  
        MN1=[MN1 m1]; $ uIwRG <  
        z1=dz*MN1';                                    % output location I,`D&   
      end C6;](rN)N  
    end (Db*.kd8,  
    hg=abs(U1').*abs(U1');                             % for data write to excel tp,mw24  
    ha=[z1 hg];                                        % for data write to excel STF}~`b:3  
    t1=[0 t']; A=YEY n  
    hh=[t1' ha'];                                      % for data write to excel file VgC9'"|  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format [> aoDJ  
    figure(1) Q e2 /4j4  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn -+S~1`0  
    figure(2) \qK}(xq[  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn LBiv]3  
    Nf?, _Rl  
    非线性超快脉冲耦合的数值方法的Matlab程序 *M\i4FO8  
    WriJco<v  
    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& Fy55  
    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 `QyALcO   
    =QxE-)v  
    >i#_)th"U!  
    tV}ajs  
    %  This Matlab script file solves the nonlinear Schrodinger equations V n!az}  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of jP7+s.j>  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear "'p+qbT8  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 eMP Q| W  
    7<C~D,x6  
    C=1;                           Lq8Z!AIw>  
    M1=120,                       % integer for amplitude ; hRpAN  
    M3=5000;                      % integer for length of coupler />j+7ts  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) \kJt@ [w%  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ,+5VeRyrV  
    T =40;                        % length of time:T*T0. x2IU PM  
    dt = T/N;                     % time step Ok{:QA~#  
    n = [-N/2:1:N/2-1]';          % Index N\?Az668?  
    t = n.*dt;   r :MaAT<  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. kjKpzdbD  
    w=2*pi*n./T; lO[jf6gB  
    g1=-i*ww./2; iJj?~\zp  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; +>9^])K|  
    g3=-i*ww./2; \oZUG  
    P1=0; =K< I)2   
    P2=0; y2hFUq  
    P3=1; %JH_Nw.P  
    P=0; UFY~D"% /  
    for m1=1:M1                 X]^E:'E!  
    p=0.032*m1;                %input amplitude GWE0 UO}  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ]GPz>k  
    s1=s10; zxmI/]3+/  
    s20=0.*s10;                %input in waveguide 2 PC(iqL8r  
    s30=0.*s10;                %input in waveguide 3 `]I5WTt*X  
    s2=s20; `h{mj|~  
    s3=s30; $Aoqtz d\  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   1^"aR#  
    %energy in waveguide 1 ydFhw}1>  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   dcTM02kEh  
    %energy in waveguide 2 v+_Y72h*a  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   GBOmVQ $Hb  
    %energy in waveguide 3 .p*D[o2 9  
    for m3 = 1:1:M3                                    % Start space evolution $=QO_t)?  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS &Or=_5Y`  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ,( kXF:  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 7a_n\]t465  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform fy-Z{  
       sca2 = fftshift(fft(s2)); v.&*z48  
       sca3 = fftshift(fft(s3)); zc~xWy+  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   8q[WfD  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); F?AfB[PM  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 6f9<&dCK  
       s3 = ifft(fftshift(sc3)); 1?$!y  
       s2 = ifft(fftshift(sc2));                       % Return to physical space `Ta(P30  
       s1 = ifft(fftshift(sc1)); >{) #|pWU  
    end W%ZU& YBc  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ;Sl0kSu  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ]~ eWr2uG?  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); }Fe{s;  
       P1=[P1 p1/p10]; GoA>sK  
       P2=[P2 p2/p10]; w*kFtNBfU  
       P3=[P3 p3/p10]; ={vtfgxl  
       P=[P p*p]; 72.IhBNtT  
    end )KQv4\0y<  
    figure(1) >w#3fTJ  
    plot(P,P1, P,P2, P,P3); dnc!=Z89  
    _ll aH  
    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~!~