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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 I(|{/{P,  
    #4?3OU#  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of S7]cF5N  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of |H49 FL  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear n"vI>_|G  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 EO^0sF<  
    bcg)K`'N  
    %fid=fopen('e21.dat','w'); JM0)x}] +  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) i[swOY z]X  
    M1 =3000;              % Total number of space steps ,;;~dfHm  
    J =100;                % Steps between output of space pK%'S  
    T =10;                  % length of time windows:T*T0 NaIVKo  
    T0=0.1;                 % input pulse width .7q#{`K^=  
    MN1=0;                 % initial value for the space output location W%x#ps5%  
    dt = T/N;                      % time step `Jo}/c 5R  
    n = [-N/2:1:N/2-1]';           % Index -!" 8j"pA:  
    t = n.*dt;   9i@*\Ada  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ~ i,my31  
    u20=u10.*0.0;                  % input to waveguide 2 :.^{!  
    u1=u10; u2=u20;                 a+d|9y/k  
    U1 = u1;   '=5N?)  
    U2 = u2;                       % Compute initial condition; save it in U uM$=v]e^ 4  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. C" {j0X`  
    w=2*pi*n./T; 0nX5 $Kn  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T OpfFF;"A'  
    L=4;                           % length of evoluation to compare with S. Trillo's paper #i? TCO  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 v%r!}s  
    for m1 = 1:1:M1                                    % Start space evolution 0Pe.G0 #  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Al?XJ C B@  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; BC^WPr  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 1Pbp=R/7ar  
       ca2 = fftshift(fft(u2)); ?hO*~w;UU|  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 6_7d1.wv9  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   G{<wXxq%  
       u2 = ifft(fftshift(c2));                        % Return to physical space =0A{z#6  
       u1 = ifft(fftshift(c1)); }[|"db  
    if rem(m1,J) == 0                                 % Save output every J steps. x!J L9  
        U1 = [U1 u1];                                  % put solutions in U array '5IJ;4k  
        U2=[U2 u2]; F+X3CB,f  
        MN1=[MN1 m1]; Mg].#  
        z1=dz*MN1';                                    % output location B{Rig5Sc  
      end QP'* )gjO7  
    end %(i(ZW "  
    hg=abs(U1').*abs(U1');                             % for data write to excel =1D*K%  
    ha=[z1 hg];                                        % for data write to excel y]k`}&-~  
    t1=[0 t']; #RcmO **  
    hh=[t1' ha'];                                      % for data write to excel file jhHb[je~{4  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 6*%lnd+_  
    figure(1) w ^A0l.{  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 0xsvxH"*  
    figure(2) h<uQ~CQg  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ?r/7:  
    CZ @M~Si_  
    非线性超快脉冲耦合的数值方法的Matlab程序 1i{B47|  
    7+0hIKrFC  
    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。   ]HRE-g  
    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 0]T ;{  
    L\"$R":3{d  
    (7"qT^s3  
    YO=;)RA  
    %  This Matlab script file solves the nonlinear Schrodinger equations v<O\ l~S  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &" b0`&l  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 9F3`hJZRy>  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 tZ(Wh  
    A!NT 2YdHZ  
    C=1;                           +ISB"a  
    M1=120,                       % integer for amplitude X;-,3dy  
    M3=5000;                      % integer for length of coupler &c A?|(7-  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) ^s%Qt  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. c$p1Sovw  
    T =40;                        % length of time:T*T0. Ros5]5=dP  
    dt = T/N;                     % time step :QN,T3i'/3  
    n = [-N/2:1:N/2-1]';          % Index /wmJMX  
    t = n.*dt;   W2REwUps  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. [QeKT8  
    w=2*pi*n./T; H~ (I  
    g1=-i*ww./2; bju0l[;=  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; UF}fmDi  
    g3=-i*ww./2; F M`pPx  
    P1=0; $UKDXQF"  
    P2=0; qWo|LpxWt  
    P3=1; `OduBUI]]  
    P=0; MEg|AhP  
    for m1=1:M1                 X]`\NNx  
    p=0.032*m1;                %input amplitude rBpr1XKl,  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ? [ =P  
    s1=s10; ofS9h*wrJ  
    s20=0.*s10;                %input in waveguide 2 [<cP~  
    s30=0.*s10;                %input in waveguide 3 7 0KZXgBy_  
    s2=s20; >5 Ce/P'R  
    s3=s30; GlVq<RG*  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   zS.7O'I<'  
    %energy in waveguide 1 #E>f.:)  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   75<E0O  
    %energy in waveguide 2 LM0 TSB?  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   .2OP>:9F  
    %energy in waveguide 3 l46O=?usDX  
    for m3 = 1:1:M3                                    % Start space evolution T_pE'U%[  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS G$ipWi  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ci ,o'`Q  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; |Y:T3hra61  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform )00#Rrt9  
       sca2 = fftshift(fft(s2)); n_iq85  
       sca3 = fftshift(fft(s3)); P^+Og_$  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   [4 "%NY  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }**^ g:  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); H,] D}r  
       s3 = ifft(fftshift(sc3)); cpf8f i  
       s2 = ifft(fftshift(sc2));                       % Return to physical space @"Do8p!*(6  
       s1 = ifft(fftshift(sc1)); g~N)~]0{  
    end T< P4+#JK  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); r)ga{Nn,.  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); +BmA4/P$  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); #~nI^ ggW  
       P1=[P1 p1/p10]; k5W5 9tz  
       P2=[P2 p2/p10]; m_oBV|v{  
       P3=[P3 p3/p10]; |qfnbi-\  
       P=[P p*p]; f'*HP%+Y  
    end >pz/wTOi  
    figure(1) ;sb0,2YyP  
    plot(P,P1, P,P2, P,P3); lkBab$S)  
    I C7n;n9  
    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~!~