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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 5 CnNp?.t^  
    @ws&W=NQ  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of W,8Uu1X =  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of N-N]BS6  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear KyIUz9$  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 mBIksts5h  
    USART}Us4  
    %fid=fopen('e21.dat','w'); ~xzr8 P  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) &SIf|IX.  
    M1 =3000;              % Total number of space steps 7 @\i5  
    J =100;                % Steps between output of space / 8O=3  
    T =10;                  % length of time windows:T*T0 8XVRRk  
    T0=0.1;                 % input pulse width NvzPZ9=@-  
    MN1=0;                 % initial value for the space output location )E9c6'd  
    dt = T/N;                      % time step 'xd8rN %T  
    n = [-N/2:1:N/2-1]';           % Index h_-4Q"fb(  
    t = n.*dt;   )fo0YpE^|  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 h5P ]`r  
    u20=u10.*0.0;                  % input to waveguide 2 "E<+idoz  
    u1=u10; u2=u20;                 ;/NC[:'$D  
    U1 = u1;   nK< v  
    U2 = u2;                       % Compute initial condition; save it in U ]@y%j'e  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 0fj C>AS  
    w=2*pi*n./T; y?cN  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ftmP dha%+  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 1N65 M=)  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ,g'>Ib%  
    for m1 = 1:1:M1                                    % Start space evolution ,J2qLH1  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS [PXq<ST  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; xA^E+f:W_  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 8@ f!,!Wn  
       ca2 = fftshift(fft(u2)); 7"Nda3  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation C-ORI}o  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   d@^%fVhG  
       u2 = ifft(fftshift(c2));                        % Return to physical space ElTB{C>u  
       u1 = ifft(fftshift(c1)); 3AENY@*  
    if rem(m1,J) == 0                                 % Save output every J steps. ;HYEJ3  
        U1 = [U1 u1];                                  % put solutions in U array [$K8y&\L  
        U2=[U2 u2]; (z;lNl(*C  
        MN1=[MN1 m1]; 1mHS -oI9J  
        z1=dz*MN1';                                    % output location iN[6}V6Sm  
      end Zs|Ga,T  
    end Rkg)yme!N  
    hg=abs(U1').*abs(U1');                             % for data write to excel @}PXBU   
    ha=[z1 hg];                                        % for data write to excel Fa`%MR1  
    t1=[0 t']; \{Q_\s&)  
    hh=[t1' ha'];                                      % for data write to excel file Y8%l)g  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format `uLr^G=;  
    figure(1) c ?<)!9:  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn iM7 ^  
    figure(2) t+d7{&B  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn Q%~BD@Io  
    L9^ M?.a  
    非线性超快脉冲耦合的数值方法的Matlab程序 #c' B2Jn  
    A *:| d~  
    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*xgf  
    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 L1+s0g>  
    tz?3R#rM  
    n>,GmCo  
    oR8'^G0<  
    %  This Matlab script file solves the nonlinear Schrodinger equations THy?Y  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ]7TOA$Q  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear z.(DDj  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 `e;r$Vpd_  
    t%e<]2-8  
    C=1;                           *MlEfmB(  
    M1=120,                       % integer for amplitude LRWM}'.s  
    M3=5000;                      % integer for length of coupler .* `]x  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 'Qg!ww7O  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. -B/'ArOo]  
    T =40;                        % length of time:T*T0. IDf\! QGx  
    dt = T/N;                     % time step )RTWt`  
    n = [-N/2:1:N/2-1]';          % Index _U LzA  
    t = n.*dt;   `<~=6H  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 9fs-|E[5  
    w=2*pi*n./T; 2[=3-1c  
    g1=-i*ww./2; !#%>,X#+  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 7. $wK.  
    g3=-i*ww./2; Wj!+ E{y<r  
    P1=0; B#IUSHC  
    P2=0; ckV\f({  
    P3=1; )l! /7WKY  
    P=0; {U>N*&_`  
    for m1=1:M1                 nC[aEZ7  
    p=0.032*m1;                %input amplitude mrsmul{  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 I0H]s/*C%9  
    s1=s10; b{aB^a:f=L  
    s20=0.*s10;                %input in waveguide 2 y]PuY \+  
    s30=0.*s10;                %input in waveguide 3 ?Bq^#i |m  
    s2=s20; < @GO]vY  
    s3=s30; L58#ri=  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   /;}%E  
    %energy in waveguide 1 |.m)UFV  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   \6MM7x(U3  
    %energy in waveguide 2 tw.GBR  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   SWhzcqp  
    %energy in waveguide 3 M:oM(K+  
    for m3 = 1:1:M3                                    % Start space evolution ~Gh7i>n*  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS e T;@pc  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; uh.;Jj;  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; =#pYd~  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform f@Jrbg  
       sca2 = fftshift(fft(s2)); sG_/E-%5'  
       sca3 = fftshift(fft(s3)); G!B:>P|\l  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ^$% Sg//  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ^ Lc\{,m  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); KiI+ V;o  
       s3 = ifft(fftshift(sc3)); ]&P\|b1*g  
       s2 = ifft(fftshift(sc2));                       % Return to physical space P%Vq#5  
       s1 = ifft(fftshift(sc1)); z k}AGw  
    end uY>M3h#qx  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); w1-P6cf  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); N>*+Wg$Ne  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); XKws_  
       P1=[P1 p1/p10]; Pf,@U'f|  
       P2=[P2 p2/p10]; b+:J?MR;}  
       P3=[P3 p3/p10]; /RqWrpzx@  
       P=[P p*p]; H I_uR$m  
    end ZQfPDH=  
    figure(1) -L]-u6kC[  
    plot(P,P1, P,P2, P,P3); Mh~}RA"H  
    &V~l(1  
    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~!~