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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 O)&V}hU*  
    &Y\`FY\   
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of IF<jq\M  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of H=*;3gM,'  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear O5E\#*<K  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ,}J(&  
    \h:$q E7  
    %fid=fopen('e21.dat','w'); o_{-X 1w  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) JVN0];IL}  
    M1 =3000;              % Total number of space steps l@':mX3xd  
    J =100;                % Steps between output of space "zv?qS  
    T =10;                  % length of time windows:T*T0 T$SGf.-  
    T0=0.1;                 % input pulse width &)1+WrU  
    MN1=0;                 % initial value for the space output location W<\KRF$S;  
    dt = T/N;                      % time step F6yMk%  
    n = [-N/2:1:N/2-1]';           % Index tX)^$3A  
    t = n.*dt;   *!vwW T  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 6m?}oMz  
    u20=u10.*0.0;                  % input to waveguide 2 o H$4K8j  
    u1=u10; u2=u20;                 @2V#bK  
    U1 = u1;   {"-uaH>,  
    U2 = u2;                       % Compute initial condition; save it in U u1rT:\G1  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. L)kwMk  
    w=2*pi*n./T; H|5\c=  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T d7A vx  
    L=4;                           % length of evoluation to compare with S. Trillo's paper  2>p>AvcK  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ZPRkk?M}.  
    for m1 = 1:1:M1                                    % Start space evolution %R."  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS sZ_+6+ :  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; [8[g_  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ;~F&b:CyG  
       ca2 = fftshift(fft(u2)); !2=< MO  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation bDK72cQ  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   eqV;4dhm  
       u2 = ifft(fftshift(c2));                        % Return to physical space lx(kbSxF  
       u1 = ifft(fftshift(c1)); T:dV[3  
    if rem(m1,J) == 0                                 % Save output every J steps. @w?hX K=  
        U1 = [U1 u1];                                  % put solutions in U array ^Yul|0*J  
        U2=[U2 u2]; @!`x^Tzz  
        MN1=[MN1 m1]; | bDUekjR  
        z1=dz*MN1';                                    % output location T@Mrbravc  
      end )CKPzNf  
    end e-Mei7{%  
    hg=abs(U1').*abs(U1');                             % for data write to excel .]24V!J(1w  
    ha=[z1 hg];                                        % for data write to excel ;Lr]w8d  
    t1=[0 t']; zb.dVK`7N-  
    hh=[t1' ha'];                                      % for data write to excel file vL}e1V:  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ' >4 H#tu  
    figure(1) o!bV;]  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn d0YDNP%,_  
    figure(2) sN"<baZ  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn U4M}E h8  
    HHzAmHt  
    非线性超快脉冲耦合的数值方法的Matlab程序 `)?N7g[\u  
    it77x3Mm F  
    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。   W"$sN8K>)  
    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 \SKobO?qI  
    /-s-W<S[  
    ZMEU4?F  
    n<3qr}ZG^  
    %  This Matlab script file solves the nonlinear Schrodinger equations d;@"Naw  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of fRh}n ^X  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear B63puX{u#  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 xl>8B/Zmf#  
    j]P'xrWl]8  
    C=1;                           eCFMWFhC  
    M1=120,                       % integer for amplitude , Ox$W  
    M3=5000;                      % integer for length of coupler }JI@f14  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) H< 51dJn~  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 2fN2!OT  
    T =40;                        % length of time:T*T0. \:y oS>G  
    dt = T/N;                     % time step %>Q[j`9y  
    n = [-N/2:1:N/2-1]';          % Index \w#)uYK{i_  
    t = n.*dt;   XCvL`  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. v9*31Jx  
    w=2*pi*n./T; ?*LVn~y  
    g1=-i*ww./2; [8jIu&tJf  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 4Dy|YH$>S  
    g3=-i*ww./2; x/NjdK  
    P1=0; i/|}#yw8A  
    P2=0; sD#*W<  
    P3=1; /Ixv{H)H  
    P=0; hU'h78bt(  
    for m1=1:M1                 {f"oqry_g  
    p=0.032*m1;                %input amplitude YC[c QX  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Q%r KKOX8  
    s1=s10; Lo,uH`qU  
    s20=0.*s10;                %input in waveguide 2 \Vb|bw'e(  
    s30=0.*s10;                %input in waveguide 3 QZ& 4W  
    s2=s20;  gx9=L&=d  
    s3=s30; &ea6YQ  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Y[!s:3\f  
    %energy in waveguide 1 { k>T*/  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   []:&WA 9N  
    %energy in waveguide 2 7?ICXhu9  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   "*< )pnJ  
    %energy in waveguide 3 7y4jk  
    for m3 = 1:1:M3                                    % Start space evolution hh!4DHv   
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS "O~7s}  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; nD.K*#u  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; i"#pk"@`  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ^ 6b27_=  
       sca2 = fftshift(fft(s2)); y**YFQ*sc  
       sca3 = fftshift(fft(s3)); $+|. @ss  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   :Z%-&) F  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); @.)WS\Cv#E  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ]w0_!Z&  
       s3 = ifft(fftshift(sc3)); ?U+nR/H:6  
       s2 = ifft(fftshift(sc2));                       % Return to physical space (<2!^v0.M  
       s1 = ifft(fftshift(sc1)); &6e A.  
    end yXQ 28A  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); `*WzHDv5p  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ]TVc 'G;  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); #+&"m7 s  
       P1=[P1 p1/p10];  oP~%7Jt  
       P2=[P2 p2/p10]; ~6=aoF5"3?  
       P3=[P3 p3/p10]; ;Wgkf_3  
       P=[P p*p]; =%SH2kb  
    end +#L'g c  
    figure(1) U1Y0G[i)  
    plot(P,P1, P,P2, P,P3); _Un*x5u2O  
    GXi)3I%  
    转自:http://blog.163.com/opto_wang/
     
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    离线ciomplj
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~