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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 0g=`DSC<(  
    iL]'y\?lv  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of l7}g^\I  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of cYNV\b4-  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +wO#'D  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Q2|p \rO  
    T:iP="?{  
    %fid=fopen('e21.dat','w'); p(JlvJjo  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) oPQtGl p  
    M1 =3000;              % Total number of space steps b-^p1{A0zW  
    J =100;                % Steps between output of space LT@OWH  
    T =10;                  % length of time windows:T*T0 r[txlQI9  
    T0=0.1;                 % input pulse width !mJo'K  
    MN1=0;                 % initial value for the space output location uJU*")\V  
    dt = T/N;                      % time step sLL7]m}  
    n = [-N/2:1:N/2-1]';           % Index 'UU\4M  
    t = n.*dt;   :t("L-GPW  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ~I=Y{iM  
    u20=u10.*0.0;                  % input to waveguide 2 0?DC00O  
    u1=u10; u2=u20;                 K^l:MxO-X  
    U1 = u1;   /t%u"dP"T~  
    U2 = u2;                       % Compute initial condition; save it in U iw9Q18:I}  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. b=;nm#cAI  
    w=2*pi*n./T; ;#/@+4@a&  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T vH[47CvG5  
    L=4;                           % length of evoluation to compare with S. Trillo's paper pB:$lS  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 RFaSwf,5n  
    for m1 = 1:1:M1                                    % Start space evolution p#P~Q/;  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS eU@Cr7@,|  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 23\RJpKb  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform Z.PBu|Kx  
       ca2 = fftshift(fft(u2)); K2)!h.W  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation hqvE!Of  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   cre;P5^E  
       u2 = ifft(fftshift(c2));                        % Return to physical space d3Mva,bw<  
       u1 = ifft(fftshift(c1)); W_|0y4QOo  
    if rem(m1,J) == 0                                 % Save output every J steps. 4u;9J*r4  
        U1 = [U1 u1];                                  % put solutions in U array J:*-gwv9*m  
        U2=[U2 u2]; r=uN9ro  
        MN1=[MN1 m1]; =uHnRY  
        z1=dz*MN1';                                    % output location K5>p89mZ  
      end "/Pjjb:2  
    end 56lCwXCgA  
    hg=abs(U1').*abs(U1');                             % for data write to excel /1UOT\8U  
    ha=[z1 hg];                                        % for data write to excel 7cDU2l  
    t1=[0 t']; LW6ZAETyL  
    hh=[t1' ha'];                                      % for data write to excel file `r"+644  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format WsU)Y&  
    figure(1) 9m2, qr|  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn !|hoYU>@2L  
    figure(2) )-15 N  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1$/MrPT(b  
    3g'S\ G@  
    非线性超快脉冲耦合的数值方法的Matlab程序 (& "su3z  
    t_z>Cl^u  
    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。   ))kF<A_MK  
    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 3rW|kkn  
    S^@S%Eg  
    }_/Hdmmx  
     .~A*=  
    %  This Matlab script file solves the nonlinear Schrodinger equations AN:sQX`  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of z}QwP~Z  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear lf{e[!ML'  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 <P[T!gST  
    9_s6l  
    C=1;                           z<sg0K8z63  
    M1=120,                       % integer for amplitude G'2#9<c*  
    M3=5000;                      % integer for length of coupler :NHH Dl  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 9O` m,t  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. {^mNJ  
    T =40;                        % length of time:T*T0. 5,qj7HZF  
    dt = T/N;                     % time step d<!3`qe  
    n = [-N/2:1:N/2-1]';          % Index /tV/85r  
    t = n.*dt;   ? &G`{Ey  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 6vuq1  
    w=2*pi*n./T; S:4crI  
    g1=-i*ww./2; q5h*`7f  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Ds #/  
    g3=-i*ww./2; 4a0:2 kIKa  
    P1=0; fx=Awba  
    P2=0; 'w>_+jLT  
    P3=1; d2oh/j6`TA  
    P=0; O ,rwP  
    for m1=1:M1                 >EL)X #e  
    p=0.032*m1;                %input amplitude 8`4<R6]LKB  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 9CA^B2u  
    s1=s10; IEKU-k7}Z  
    s20=0.*s10;                %input in waveguide 2 >_rha~   
    s30=0.*s10;                %input in waveguide 3 i|w8.}0  
    s2=s20; xq-17HKs  
    s3=s30; [Vd[-  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   NaVQ9ku7VW  
    %energy in waveguide 1 /27JevE  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Vd".u'r  
    %energy in waveguide 2 lzw3=H  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ul%h@=n  
    %energy in waveguide 3 w%WF-:u7|  
    for m3 = 1:1:M3                                    % Start space evolution V fv@7@q  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS <VD8bTk  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 7g R@$(1Z  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; h\plQ[T  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform JnHo9K2.  
       sca2 = fftshift(fft(s2)); >fH=DOz$&  
       sca3 = fftshift(fft(s3)); a+hd(JX0~  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   -.g|l\  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); |mdi]TL  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); g{W;I_P^9  
       s3 = ifft(fftshift(sc3)); d(g^M1 m  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ~m|Mg9-  
       s1 = ifft(fftshift(sc1)); u0P)7~%  
    end u6`=x$&  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); * ),8PoT  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); (`SRJ$~f  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); *~m+Nc`D,N  
       P1=[P1 p1/p10]; &1+X\c+t b  
       P2=[P2 p2/p10]; &/Ro lIHF  
       P3=[P3 p3/p10]; Bo<>e~6P  
       P=[P p*p]; 8$(Dz]v|[&  
    end !LkW zn3  
    figure(1) YF+n b.0.  
    plot(P,P1, P,P2, P,P3); aM7uBx\8 5  
    S1D@vnZ3O\  
    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~!~