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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 4d G-  
    --`LP[ll  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of &o@5%Rz2/  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9`xFZMd31A  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >;v0zE  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 NRSse"  
    03WRj+w  
    %fid=fopen('e21.dat','w'); ~4MjJKzA  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) "n }fEVJ,  
    M1 =3000;              % Total number of space steps ]a#]3(o]}  
    J =100;                % Steps between output of space tcEf ~|3  
    T =10;                  % length of time windows:T*T0 hX%v`8  
    T0=0.1;                 % input pulse width ddDJXk)!0  
    MN1=0;                 % initial value for the space output location Az9J{)  
    dt = T/N;                      % time step ;}~Bv<#  
    n = [-N/2:1:N/2-1]';           % Index K)UOx#xe1  
    t = n.*dt;   &W+G{W{3  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Ko|xEz=  
    u20=u10.*0.0;                  % input to waveguide 2 P=[x!}.I  
    u1=u10; u2=u20;                  jnzz~:  
    U1 = u1;   w9<FX>@  
    U2 = u2;                       % Compute initial condition; save it in U OCO,-(  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. t0H=NUP8  
    w=2*pi*n./T; +1jqCW  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T h$ iyclX  
    L=4;                           % length of evoluation to compare with S. Trillo's paper _8pkejg  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 TL{pc=eBo  
    for m1 = 1:1:M1                                    % Start space evolution lkWeQ)V  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 7TPLVa=hO  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; *2 $m>N  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform "rDzrz  
       ca2 = fftshift(fft(u2)); [I<'E LX  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation q\ y#  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   T>Rf?%o  
       u2 = ifft(fftshift(c2));                        % Return to physical space 1qKxg  
       u1 = ifft(fftshift(c1)); sFM>gG  
    if rem(m1,J) == 0                                 % Save output every J steps. S%s|P=u  
        U1 = [U1 u1];                                  % put solutions in U array 'A(-MTd%  
        U2=[U2 u2]; m\Fb ,  
        MN1=[MN1 m1]; Ldj^O9p(  
        z1=dz*MN1';                                    % output location &R FM d=  
      end us,,W(q  
    end C\ 2 >7  
    hg=abs(U1').*abs(U1');                             % for data write to excel xiOrk  
    ha=[z1 hg];                                        % for data write to excel 2td|8vDA  
    t1=[0 t']; ="w8U'  
    hh=[t1' ha'];                                      % for data write to excel file VmH_0IM^6  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format aco}pXz  
    figure(1) lyH X#]  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn }Oh'YX#[  
    figure(2) 9c5G6n0  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn =']};  
    8j+:s\  
    非线性超快脉冲耦合的数值方法的Matlab程序 19w,'}CGk  
    sEJ;t0.LX  
    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。   J(&M<<%  
    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 ny_ kr`$42  
    OG?j6q hpl  
    zmfRZ!Eh  
    I%Po/+|+  
    %  This Matlab script file solves the nonlinear Schrodinger equations ':2*+  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of . I&)MZ>n  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g9weJ6@}M  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ]^6y NtLK  
    si!9Gz;  
    C=1;                           JU=\]E@8c  
    M1=120,                       % integer for amplitude zTBi{KrZ  
    M3=5000;                      % integer for length of coupler {Fp`l\,  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Vh.;p.!e  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ;$tv8%_L[  
    T =40;                        % length of time:T*T0. !%RJC,X  
    dt = T/N;                     % time step u388Wj   
    n = [-N/2:1:N/2-1]';          % Index L3=YlX`UL  
    t = n.*dt;   LY88;*:S  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. zr;Y1Xt4  
    w=2*pi*n./T; 71<PEawL  
    g1=-i*ww./2; lfpt:5a9&  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Eagmafu  
    g3=-i*ww./2; tp0!,ne*  
    P1=0; < ;,S"e  
    P2=0; N}x/&e  
    P3=1; &b@!DAwAJ  
    P=0; qvfAG 0p  
    for m1=1:M1                 3e!Yu.q:  
    p=0.032*m1;                %input amplitude Puth8$  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [>M*_1F  
    s1=s10; dj y:  
    s20=0.*s10;                %input in waveguide 2 WP% {{zR$  
    s30=0.*s10;                %input in waveguide 3 ahi57r[  
    s2=s20; [;IDTo!<>  
    s3=s30; X\3 ,NR,  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   kTi PZZI  
    %energy in waveguide 1 =4M.QA@lI!  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   rMXOwkE  
    %energy in waveguide 2 ej"o?1l@  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   }KaCf,O  
    %energy in waveguide 3 ]g8i>,G  
    for m3 = 1:1:M3                                    % Start space evolution B )1<`nJA  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS z7t'6Fy9'  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; @^:7UI_  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 5;K-,"UQ  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform BudWbZ5>Ep  
       sca2 = fftshift(fft(s2)); JW%/^'  
       sca3 = fftshift(fft(s3)); u .pKK  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   5}d/8tS  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); HV$9b~(  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); lEyG9Xvi  
       s3 = ifft(fftshift(sc3)); q(jkit~`A  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 9#EHXgz  
       s1 = ifft(fftshift(sc1)); az \<sWb#  
    end P"V{y|2  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); I4o =6ts  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); B.Zm$JZ:  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); [ n0##/  
       P1=[P1 p1/p10]; fOK+DT~  
       P2=[P2 p2/p10]; e$ XY\{  
       P3=[P3 p3/p10]; !0!U01SWa  
       P=[P p*p]; ,{uW8L  
    end "J8;4p  
    figure(1) ySixYt  
    plot(P,P1, P,P2, P,P3); #4P3xa  
    KTLbqSS\  
    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~!~