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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 ][Ne;F6  
    R*m=V{iu`  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of zT;F4_p3G-  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of `/WX!4eR,  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear NWK+.{s>m  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 '`.bmiM  
    6 w"-&  
    %fid=fopen('e21.dat','w'); )_$F/ug  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) lLq9)+HGN  
    M1 =3000;              % Total number of space steps :nk$?5ib  
    J =100;                % Steps between output of space lJe=z  
    T =10;                  % length of time windows:T*T0 ==$>M d  
    T0=0.1;                 % input pulse width 0taopDi ;d  
    MN1=0;                 % initial value for the space output location pq<302uBQ  
    dt = T/N;                      % time step ~Q  q0  
    n = [-N/2:1:N/2-1]';           % Index +mc0:e{WF  
    t = n.*dt;   (`z`ni  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 lIs<&-0  
    u20=u10.*0.0;                  % input to waveguide 2 $:v!*0/  
    u1=u10; u2=u20;                 7 (}gs?&w  
    U1 = u1;   4d\1W?i-  
    U2 = u2;                       % Compute initial condition; save it in U 9d4Agj M  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Xbm\"g \  
    w=2*pi*n./T; %XIPPEHU  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T +YS0yTWeX  
    L=4;                           % length of evoluation to compare with S. Trillo's paper <,r(^Ntz  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ~,199K#'  
    for m1 = 1:1:M1                                    % Start space evolution <{ Z$!]i1  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS r-Nv<oH;  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; uif1)y`Q$C  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform =#tQhg,_  
       ca2 = fftshift(fft(u2)); s>i`=[qFc  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Uc j eB  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   D_n(T ')  
       u2 = ifft(fftshift(c2));                        % Return to physical space ]`p*ZTr)\  
       u1 = ifft(fftshift(c1)); Us5P?}  
    if rem(m1,J) == 0                                 % Save output every J steps. AD_aI %7  
        U1 = [U1 u1];                                  % put solutions in U array :cx}I  
        U2=[U2 u2]; fu}ZOPu  
        MN1=[MN1 m1]; d&z^u.SY  
        z1=dz*MN1';                                    % output location g\Ck!KJ/y  
      end 3%"r%:fQB/  
    end ^xB=d S~  
    hg=abs(U1').*abs(U1');                             % for data write to excel ^#^\@jLm  
    ha=[z1 hg];                                        % for data write to excel F;I %9-R  
    t1=[0 t']; 'a}<|Et.  
    hh=[t1' ha'];                                      % for data write to excel file r`t|}m  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format vMDX  
    figure(1) jB"?iC.  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 6*!R'  
    figure(2) m^6& !`CD  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn !|SVRaS  
    Bu:h_sV D  
    非线性超快脉冲耦合的数值方法的Matlab程序 s]D&):  
    ncF|wz  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   9_~[  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 O@[jNs)].  
    -d|Q|zF^x  
    X4- _l$j  
    d[cqs9=\  
    %  This Matlab script file solves the nonlinear Schrodinger equations %fv;C  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of O.ce"5Y^  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear C(RZ09,.S  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @raw8w\Zj+  
    st|;] q9?  
    C=1;                           >EMsBX  
    M1=120,                       % integer for amplitude -AJ$-y  
    M3=5000;                      % integer for length of coupler @|N'V"*MT  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) R:Pw@  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Y? 1 3_~ K  
    T =40;                        % length of time:T*T0. 2HxT+|~d6  
    dt = T/N;                     % time step |zJxR_)  
    n = [-N/2:1:N/2-1]';          % Index 1;e"3x"  
    t = n.*dt;   fV 6$YCf  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. s8/sH];  
    w=2*pi*n./T; f{} zqCK  
    g1=-i*ww./2; {iz,iv/U  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; u]D>O$_ s  
    g3=-i*ww./2; \R m2c8Z2  
    P1=0; v#HaZT]u  
    P2=0; J ejDF*Q  
    P3=1; ]bPj%sb*@  
    P=0; 3)? v  
    for m1=1:M1                 5BztOYn,  
    p=0.032*m1;                %input amplitude mnZS](>  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 \[nvdvJv  
    s1=s10; }I1A4=d  
    s20=0.*s10;                %input in waveguide 2 Lq-Di|6q  
    s30=0.*s10;                %input in waveguide 3 c h_1 -  
    s2=s20; QG|KZ8uO  
    s3=s30; 13:yaRo  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ,b&-o?.{  
    %energy in waveguide 1 +IRr&J*P  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   =LFrV9  
    %energy in waveguide 2 e:h(,  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   I6k S1  
    %energy in waveguide 3 '1$#onx  
    for m3 = 1:1:M3                                    % Start space evolution -<R"  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS jK!Y-  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; c`hj^t  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; r35'U#VMk?  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform zW,Nv>Ac5  
       sca2 = fftshift(fft(s2)); (Wj2%*NT  
       sca3 = fftshift(fft(s3)); N@oNg}D&:  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   8Wa&&YTB  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 3?}W0dZ$d  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); {3jV ,S  
       s3 = ifft(fftshift(sc3)); #Cwzk{p(  
       s2 = ifft(fftshift(sc2));                       % Return to physical space RR%[]M#_T  
       s1 = ifft(fftshift(sc1)); &TpzJcd"  
    end h-^7cHI}  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); B\/"$"  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); d%"?^e  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); \:ELO[(#|{  
       P1=[P1 p1/p10]; FY^#%0~  
       P2=[P2 p2/p10]; +cDz`)N,,  
       P3=[P3 p3/p10]; S.!0~KR: U  
       P=[P p*p]; C*S%aR  
    end Ws+Zmpk%  
    figure(1) K*ZH<@o4  
    plot(P,P1, P,P2, P,P3); BUuU#e5  
    w&M)ws;$  
    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~!~