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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 if@,vc  
    oKiD8':  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of Wp4K6x  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of .e$%[ )D  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear mJ$Htyr  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @dV9Dpu  
    V6+Zh>'S  
    %fid=fopen('e21.dat','w'); \HG$V>2  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) :c<*%*e  
    M1 =3000;              % Total number of space steps !a[$)c  
    J =100;                % Steps between output of space 6Ahr_{  
    T =10;                  % length of time windows:T*T0 ,s? dAy5  
    T0=0.1;                 % input pulse width +2y&B,L_Wh  
    MN1=0;                 % initial value for the space output location p`p?li  
    dt = T/N;                      % time step NL-_#N$  
    n = [-N/2:1:N/2-1]';           % Index 8^T2^gs  
    t = n.*dt;   gvo?([j-m  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 -fPT}v  
    u20=u10.*0.0;                  % input to waveguide 2 ai^t= s  
    u1=u10; u2=u20;                 H:Lt$  
    U1 = u1;   $_bZA;EMQ  
    U2 = u2;                       % Compute initial condition; save it in U :<UtHf<=k  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. $WClpvVj  
    w=2*pi*n./T; >[P%Ty);  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T `EVg'?pl  
    L=4;                           % length of evoluation to compare with S. Trillo's paper *;X-\6  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 LYNZP4(R  
    for m1 = 1:1:M1                                    % Start space evolution s7M}NA 0  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS \!4|tBKVY  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; j%5a+(H,z;  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform mQ=sNZ-d]  
       ca2 = fftshift(fft(u2)); m9Il\PoTq  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ol#yjrv  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ]|y}\7Aa  
       u2 = ifft(fftshift(c2));                        % Return to physical space -%=RFgU4  
       u1 = ifft(fftshift(c1)); e?1KbJ?.  
    if rem(m1,J) == 0                                 % Save output every J steps. OA5f}+  
        U1 = [U1 u1];                                  % put solutions in U array ~4+8p9f  
        U2=[U2 u2]; D&f!( n  
        MN1=[MN1 m1]; S ;h&5.p  
        z1=dz*MN1';                                    % output location p2^)2v  
      end g@(4ujOT  
    end `fMpV8vv  
    hg=abs(U1').*abs(U1');                             % for data write to excel 94YA2_f;  
    ha=[z1 hg];                                        % for data write to excel & L'6KEahR  
    t1=[0 t']; !"%S#nrL$  
    hh=[t1' ha'];                                      % for data write to excel file )r pD2H  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ?cJA^W  
    figure(1) kw#X]`c3  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn qzHU)Ns(_  
    figure(2) ,@479ZvvR3  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn u ]SZ{[ e  
    n5\}KZh  
    非线性超快脉冲耦合的数值方法的Matlab程序 u`+ 'lBE,  
    d^y86pq.  
    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。   JeL~]F  
    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 =t HD 4I  
    3wo'jOb  
    jVs(x  
    wE8]'o  
    %  This Matlab script file solves the nonlinear Schrodinger equations B/rzh? b  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of G4O3h Y.`  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g kn)V~ij  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 n@_)fFD%  
    xlk5Gob*  
    C=1;                           ]An_5J  
    M1=120,                       % integer for amplitude }q]jjs  
    M3=5000;                      % integer for length of coupler 9LHa&""  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) ZLuPz#  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. gz#+  
    T =40;                        % length of time:T*T0. ) u-ns5  
    dt = T/N;                     % time step # 'wL\3  
    n = [-N/2:1:N/2-1]';          % Index *iYMX[$  
    t = n.*dt;   !L/tLHk+  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 4NJVW+:2  
    w=2*pi*n./T; 88#N~j~P  
    g1=-i*ww./2; OFp#<o,p  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; i"< ZVw  
    g3=-i*ww./2; -G FwFkWm  
    P1=0; q{[1fE"[K4  
    P2=0; g(1"GKg3K  
    P3=1; y%JF8R;n  
    P=0; _E&U?>g+  
    for m1=1:M1                 YT][\x  
    p=0.032*m1;                %input amplitude r<v_CFJ  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 b13nE .  
    s1=s10; !#C)99L"F  
    s20=0.*s10;                %input in waveguide 2 k~& o  
    s30=0.*s10;                %input in waveguide 3 oH=4m~'V  
    s2=s20; 5R)[Ou.  
    s3=s30; G%Y*q(VrEu  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   raSF3b/0  
    %energy in waveguide 1 p?}&)Un  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   )G mb? !/^  
    %energy in waveguide 2 X"wF Qa  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   a!&bc8J7  
    %energy in waveguide 3 80dSQ"y  
    for m3 = 1:1:M3                                    % Start space evolution z"9aAytd  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS =%xIjxYl  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; nM=2"`@$  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; V, E9Uds  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform haN"/C^  
       sca2 = fftshift(fft(s2)); ]!q }|bP  
       sca3 = fftshift(fft(s3)); Q:kwQg:~  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   0= 2H9v  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); g~eJ YS,  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); pz.Y=V\t  
       s3 = ifft(fftshift(sc3)); w' .'Yu6  
       s2 = ifft(fftshift(sc2));                       % Return to physical space hjw4Xzju  
       s1 = ifft(fftshift(sc1)); gfV]^v  
    end \A` gK\/h  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); $ V3n~.=  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); w 7Cne%J8  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); dvC0 <*V  
       P1=[P1 p1/p10]; H^ESA s6  
       P2=[P2 p2/p10]; 7? +5%7-  
       P3=[P3 p3/p10]; 5aa}FdUq  
       P=[P p*p];  b$PT_!d  
    end /5&3WG&<u  
    figure(1) O 0Vn";Q 4  
    plot(P,P1, P,P2, P,P3); 7ZL,p:f  
    4 `j,&=  
    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~!~