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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 RzSN,bL R  
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    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of `+@%l*TQ  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of `V0]t_*D  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear %}&9[#  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 }@A~a`9g  
    Ix5yQgnB}j  
    %fid=fopen('e21.dat','w'); 8c$IsvJg  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) d{GXFT;0  
    M1 =3000;              % Total number of space steps c Ky%0oTla  
    J =100;                % Steps between output of space J.`.lQ$z  
    T =10;                  % length of time windows:T*T0 CUw 9aH  
    T0=0.1;                 % input pulse width I`KN8ll  
    MN1=0;                 % initial value for the space output location !*#=7^#  
    dt = T/N;                      % time step IWpUbD|kC  
    n = [-N/2:1:N/2-1]';           % Index WCWBvw4&"{  
    t = n.*dt;   XJOo.Y  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ]X _&  
    u20=u10.*0.0;                  % input to waveguide 2 p|bpE F=U  
    u1=u10; u2=u20;                 CGg6nCB  
    U1 = u1;   )5V1H WjU  
    U2 = u2;                       % Compute initial condition; save it in U Cw^)}23R  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. d ly 08 74  
    w=2*pi*n./T; C"mb-n 7s  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T #QDV_ziE5  
    L=4;                           % length of evoluation to compare with S. Trillo's paper %r,2ZLZ  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 (}qLxZ/U  
    for m1 = 1:1:M1                                    % Start space evolution 1Q;` <=  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS @',;/j80  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; "Ii!)n,  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform (c*Dvpo1  
       ca2 = fftshift(fft(u2)); bKaV]Uy  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation >) :d38M  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   O@Kr}8^,  
       u2 = ifft(fftshift(c2));                        % Return to physical space -jw=Iyv  
       u1 = ifft(fftshift(c1)); 6qA{l_V  
    if rem(m1,J) == 0                                 % Save output every J steps. t[ MRyi)LF  
        U1 = [U1 u1];                                  % put solutions in U array aY+>85?g  
        U2=[U2 u2]; =UP)b9*h  
        MN1=[MN1 m1]; hP#&]W3:  
        z1=dz*MN1';                                    % output location  JuI,wA  
      end f3h9CV  
    end J/*[wj  
    hg=abs(U1').*abs(U1');                             % for data write to excel nBj7Q!lW  
    ha=[z1 hg];                                        % for data write to excel QBo^{],  
    t1=[0 t']; <z4!m/f [(  
    hh=[t1' ha'];                                      % for data write to excel file #sHP\|rA  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format MdfkC6P  
    figure(1) \5l}5<|  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn %?$"oWmenS  
    figure(2) ,J#5Y.  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 1|89-Ii]  
    Z n!SHj  
    非线性超快脉冲耦合的数值方法的Matlab程序 ljCgIfZ_4  
    n(+:l'#HJ  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ZtT`_G&  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 rYqvG  
    Y#5S;?bR  
    Q&LkST-i  
    +Snjb0  
    %  This Matlab script file solves the nonlinear Schrodinger equations (^4%Fk&I-  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of eyWwE%  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear fe$WR~  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 /L 4WWQ5  
    Glr.)PA  
    C=1;                           1$W!<:uh  
    M1=120,                       % integer for amplitude / u{r5`4  
    M3=5000;                      % integer for length of coupler _ Owz%  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) J5"*OH:f  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. xVP GlU  
    T =40;                        % length of time:T*T0. &Hqu`A/^  
    dt = T/N;                     % time step V+q RDQ  
    n = [-N/2:1:N/2-1]';          % Index re*/JkDq3K  
    t = n.*dt;   1XKk~G"D  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ^b#E%Rd  
    w=2*pi*n./T; @wPmx*SF  
    g1=-i*ww./2; 5W48z%MN  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 9.B7Owgr89  
    g3=-i*ww./2; .wSAysiQ|P  
    P1=0; pf_ /jR  
    P2=0; S7vE[VF5  
    P3=1; Y4O L 82Y  
    P=0; ;a`X|N9  
    for m1=1:M1                 >A/=eW/q  
    p=0.032*m1;                %input amplitude \v_C7R;&  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ik*_,51Zj  
    s1=s10; JNz0!wi  
    s20=0.*s10;                %input in waveguide 2 `dZ|}4[1  
    s30=0.*s10;                %input in waveguide 3 $%-?S]6)  
    s2=s20; :Mk}Suf&H  
    s3=s30; v(O.GhJ@  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   =)8Ct  
    %energy in waveguide 1 #`$7$Y~]  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   v2'J L(=  
    %energy in waveguide 2 gib]#n1!p  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   'Ap 5Aq  
    %energy in waveguide 3 %U 7B0-  
    for m3 = 1:1:M3                                    % Start space evolution @gc"-V*-/  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Vvj]2V3  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Tjqn::~D  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; %K7}yy&9C  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform h~p}08  
       sca2 = fftshift(fft(s2)); ?s]`G'=>V`  
       sca3 = fftshift(fft(s3)); F{ ,O+\  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift    P+0xi  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); `9l\ ~t(M  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); KF)i66  
       s3 = ifft(fftshift(sc3)); ,GIqRT4K  
       s2 = ifft(fftshift(sc2));                       % Return to physical space &?6w 2[}  
       s1 = ifft(fftshift(sc1)); t,,^^ll  
    end mtHz6+  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ~~,<+X:  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); )[*O^bPowI  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); k Dt)S$N4n  
       P1=[P1 p1/p10]; ex458^N_  
       P2=[P2 p2/p10]; }i:'f 2/  
       P3=[P3 p3/p10]; *lAdS]I  
       P=[P p*p]; uw!|G>  
    end (xed(uFEK  
    figure(1) H)Ge#=;ckQ  
    plot(P,P1, P,P2, P,P3); :\_MA^<  
    6,1|y%(f  
    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~!~