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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 }f'1x%RS^  
    sYP@>tHC  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of OIT;fKl9  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of sYI':UQe  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear W+S; Do  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 -{%''(G  
    .4(f0RG  
    %fid=fopen('e21.dat','w'); )eMh,r  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) \ \}/2#1=c  
    M1 =3000;              % Total number of space steps <BA&S _=4  
    J =100;                % Steps between output of space ,LO-!\L  
    T =10;                  % length of time windows:T*T0 D.!7jA#  
    T0=0.1;                 % input pulse width y ]%,Y=%X  
    MN1=0;                 % initial value for the space output location r,KK%B  
    dt = T/N;                      % time step {3Wc<&D C1  
    n = [-N/2:1:N/2-1]';           % Index _=x_"rz x  
    t = n.*dt;   9D w&b  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 0.0!5D[  
    u20=u10.*0.0;                  % input to waveguide 2 Q0_W<+`  
    u1=u10; u2=u20;                 -Lb^O/  
    U1 = u1;   +N@F,3yNa  
    U2 = u2;                       % Compute initial condition; save it in U VrxH6Y  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 0Wm-` ZA  
    w=2*pi*n./T; mIo7 K5z{  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T lHqx}n@e  
    L=4;                           % length of evoluation to compare with S. Trillo's paper A$6b=2hc>  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 LTct0Gh  
    for m1 = 1:1:M1                                    % Start space evolution W10fjMC}^  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 1z:N$O _v  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; N|S xAg  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform - S-1<xR  
       ca2 = fftshift(fft(u2)); Th^#H  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation dhkpkt<G8  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   nWu4HFi  
       u2 = ifft(fftshift(c2));                        % Return to physical space L{pg?#\yC  
       u1 = ifft(fftshift(c1)); R!G7;m'N1  
    if rem(m1,J) == 0                                 % Save output every J steps. EPRs%(w`  
        U1 = [U1 u1];                                  % put solutions in U array 18`%WUPnT  
        U2=[U2 u2]; N2e<Y_T  
        MN1=[MN1 m1]; V+z)B+  
        z1=dz*MN1';                                    % output location w'XgW0j{  
      end i@L2W>{P  
    end 3fTI&2:  
    hg=abs(U1').*abs(U1');                             % for data write to excel s\!vko'M  
    ha=[z1 hg];                                        % for data write to excel Bdepvc}[#  
    t1=[0 t']; #+k[[; 0  
    hh=[t1' ha'];                                      % for data write to excel file ![^h<Om  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format {Z.@-Tl_  
    figure(1) tvRy8u;  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1bkUT_  
    figure(2) hh&y2#Io  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn pa-4|)qY  
    1+($"$ZC&B  
    非线性超快脉冲耦合的数值方法的Matlab程序 edx'p`%d5  
    [^~9wFNtd  
    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。   y@_?3m7B=  
    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 RiG!TTa b  
    w-Fk&dC69  
    A!yLwkc:5  
    lJ#>Y5Qg  
    %  This Matlab script file solves the nonlinear Schrodinger equations 8$Yf#;m[  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 'O9=*L) X  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear d 4R+gIA  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 G|_aU8b|t  
    3~rc=e  
    C=1;                           1A-EP@# J  
    M1=120,                       % integer for amplitude &y\2:IyA  
    M3=5000;                      % integer for length of coupler DU8LU*q'  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) %WR"85  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. +to9].O7y  
    T =40;                        % length of time:T*T0. !3# }ZC2  
    dt = T/N;                     % time step ]M;! ])b$  
    n = [-N/2:1:N/2-1]';          % Index \-ws[  
    t = n.*dt;   <t{AY^:r  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. H%aLkV!J  
    w=2*pi*n./T; vW3ZuB  
    g1=-i*ww./2; %$| k3[4V  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 0EXNq*=EE  
    g3=-i*ww./2; Qpf]3  
    P1=0; zAJUL  
    P2=0; @8yFM%  
    P3=1; y:[]+  
    P=0; 7g+]  
    for m1=1:M1                 Ct+%  
    p=0.032*m1;                %input amplitude Qe.kN dT+_  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 IQ~7vk()  
    s1=s10; l}c2l'  
    s20=0.*s10;                %input in waveguide 2 a@ }r[0O  
    s30=0.*s10;                %input in waveguide 3 ;NeEgqW "  
    s2=s20; /j@ `aG(a  
    s3=s30; rxeXz<  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ZY$@_DOB}  
    %energy in waveguide 1 ; @~*z4U  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   rd4'y~#S  
    %energy in waveguide 2 )m;qv'=!  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   l?_!eA  
    %energy in waveguide 3 q.km>XRk~  
    for m3 = 1:1:M3                                    % Start space evolution q|l|mO  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS -GVG1#5  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; IkNt! 2s_  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; $IZZ`Z]B  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform % ul{nL:  
       sca2 = fftshift(fft(s2)); R9G)X]  
       sca3 = fftshift(fft(s3)); vaJXX  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   )0MshgM  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); chzR4"WZFt  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Vp"Ug,1  
       s3 = ifft(fftshift(sc3)); Go7hDmu  
       s2 = ifft(fftshift(sc2));                       % Return to physical space +J8/,d  
       s1 = ifft(fftshift(sc1)); $!C+i"q$  
    end _k.bGYldk  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); r ;8z"*  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); h!CX`pBM  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); i9k]Q(o  
       P1=[P1 p1/p10]; y$V)^-U>fw  
       P2=[P2 p2/p10]; ~<OjXuYu  
       P3=[P3 p3/p10]; |hQ|'VCN  
       P=[P p*p]; C-^%g [#  
    end (H%d]  
    figure(1) 3N0X?* (x|  
    plot(P,P1, P,P2, P,P3); ruA+1-<f  
    rtmt 3  
    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~!~