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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 =)YYx8gR  
    ;8T=uCi  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of I0vn d7  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of X@&uu0JJ  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear )JQQ4D  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 FBAC9}V"  
    ebe@.ZVSi  
    %fid=fopen('e21.dat','w'); *F*fH>?C#  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) $tHwJ!<$&  
    M1 =3000;              % Total number of space steps .K1E1Z_  
    J =100;                % Steps between output of space {\/nUbo[  
    T =10;                  % length of time windows:T*T0 1!wEXH(  
    T0=0.1;                 % input pulse width Y^Q|l%Qrb  
    MN1=0;                 % initial value for the space output location cu^*x/0,  
    dt = T/N;                      % time step Sc$wR{W<:  
    n = [-N/2:1:N/2-1]';           % Index YiuOu(X  
    t = n.*dt;   _0q~s@-  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 w%dIe!sV  
    u20=u10.*0.0;                  % input to waveguide 2 |Du13i4].&  
    u1=u10; u2=u20;                 Ju7C?)x  
    U1 = u1;   X&?lDL7?  
    U2 = u2;                       % Compute initial condition; save it in U J<#`IaV  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. %OW9cqL>l  
    w=2*pi*n./T; %Dls36F  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T z~e~K`S  
    L=4;                           % length of evoluation to compare with S. Trillo's paper @n X2*j*u  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 w LN2`ucC  
    for m1 = 1:1:M1                                    % Start space evolution niEEm`"  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS tW:/R@@  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; wv.Ul rpx.  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform K}<!{/fi)  
       ca2 = fftshift(fft(u2)); #K1BJ#KUt  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Y0yO `W4  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   x<j"DS}S)D  
       u2 = ifft(fftshift(c2));                        % Return to physical space AV 5\W}  
       u1 = ifft(fftshift(c1)); W}2 &Pax  
    if rem(m1,J) == 0                                 % Save output every J steps. Owpg]p yVD  
        U1 = [U1 u1];                                  % put solutions in U array LL[#b2CKa  
        U2=[U2 u2]; .hlQ?\  
        MN1=[MN1 m1]; n~ >h4=h  
        z1=dz*MN1';                                    % output location #G  +  
      end Ipz 1+ #s'  
    end \*%i#]wO@  
    hg=abs(U1').*abs(U1');                             % for data write to excel BZ;}ROmqk  
    ha=[z1 hg];                                        % for data write to excel EcU'*  
    t1=[0 t']; /1W7<']>xV  
    hh=[t1' ha'];                                      % for data write to excel file ,J (5@8(>a  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format mOgOHb2  
    figure(1) A]iv)C;]  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn r d6F"W  
    figure(2) g{W6a2  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn $JhZ'Z  
    TjUZv1(L  
    非线性超快脉冲耦合的数值方法的Matlab程序 B>|U-[A  
    !P~ PF:W~|  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   45)ogg2  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 RCh$j&Tn  
    v*H &F   
    s"=F^#  
    hX8gV~E=y  
    %  This Matlab script file solves the nonlinear Schrodinger equations sUbz)BS#.  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Z6R: rq  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear {yHB2=nI  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 P~\a)Szy  
    V%BJNJ  
    C=1;                           Sj0 ucnuHi  
    M1=120,                       % integer for amplitude !2Xr~u7a  
    M3=5000;                      % integer for length of coupler (~G5t(+  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) 2E3?0DL",  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. [W9e>Nsp0  
    T =40;                        % length of time:T*T0. K$<`4#i  
    dt = T/N;                     % time step Ld\LKwo  
    n = [-N/2:1:N/2-1]';          % Index qIDWl{b<  
    t = n.*dt;   s!@=rq  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 1 ;\]D9i  
    w=2*pi*n./T; E/~"j  
    g1=-i*ww./2; (:?5 i`  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; +~w?Xw,  
    g3=-i*ww./2; H~?*KcZ 0\  
    P1=0; ;]gsJ9FK<  
    P2=0; "%oH@ =  
    P3=1; YN%=Oq  
    P=0; "ep`  
    for m1=1:M1                 abROFI5.L  
    p=0.032*m1;                %input amplitude !F+|Y"c  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 M<{5pH(K  
    s1=s10; h v$uH7Fz  
    s20=0.*s10;                %input in waveguide 2 ;|>q zx  
    s30=0.*s10;                %input in waveguide 3 ?w]"~   
    s2=s20; {PODisl>\D  
    s3=s30; [$( sUc(%  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   &/ >;LgN  
    %energy in waveguide 1 r,2Xu  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   Wl& >6./{  
    %energy in waveguide 2 (s}Rj)V[^  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   yhcNE8mkQ/  
    %energy in waveguide 3 {{V ;:+62  
    for m3 = 1:1:M3                                    % Start space evolution cBz!U 8(  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS g08*}0-k  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; pqyWv;  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; z5XYpi_;[  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Ku<b0<`  
       sca2 = fftshift(fft(s2)); MV"E?}0  
       sca3 = fftshift(fft(s3)); 5^/,aI  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   `zdH1p^w  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 42rj6m\  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); %`xV'2H  
       s3 = ifft(fftshift(sc3)); Qg'c?[~W@  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ZYE' C  
       s1 = ifft(fftshift(sc1)); oLgg  
    end b#D9eJhS  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); J[ e}  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ![*:.CW  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); iYk':iv}S  
       P1=[P1 p1/p10]; Uc_jQ4e_  
       P2=[P2 p2/p10]; [J a)<!]<  
       P3=[P3 p3/p10]; /xl4ohL$a  
       P=[P p*p]; \hs/D+MCk  
    end r_b8,I6{]  
    figure(1) nd.57@*M  
    plot(P,P1, P,P2, P,P3); w Y8@1>ah  
    <+V-k|  
    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~!~