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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 /?P!.!W&  
    3ev -Iqz  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of u{Ak:0G7  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 7 >bMzdH  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear iD714+N(  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 V&iS~V0.  
    |IN[uQ  
    %fid=fopen('e21.dat','w'); j^nu|  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ~b6GrY"vB  
    M1 =3000;              % Total number of space steps %K l(>{N  
    J =100;                % Steps between output of space e2wvc/gG6  
    T =10;                  % length of time windows:T*T0 0>FE%  
    T0=0.1;                 % input pulse width 'Wp @b678  
    MN1=0;                 % initial value for the space output location ;MPKJS68@  
    dt = T/N;                      % time step RG1\=J$:E  
    n = [-N/2:1:N/2-1]';           % Index \=fh-c(J,  
    t = n.*dt;   F>-}*o  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 $8g42LR'  
    u20=u10.*0.0;                  % input to waveguide 2 [0!{_E)<  
    u1=u10; u2=u20;                 P)hi||[  
    U1 = u1;   w & P&7  
    U2 = u2;                       % Compute initial condition; save it in U "V}qf3 qU  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. n[CoS  
    w=2*pi*n./T; ]r959+\$  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T x.UaQ |F  
    L=4;                           % length of evoluation to compare with S. Trillo's paper h.}u?{  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 ) EXJ   
    for m1 = 1:1:M1                                    % Start space evolution H=<LutnZ  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS +`}o,z/^  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; b#='^W3  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform T 1zi0fa'  
       ca2 = fftshift(fft(u2)); MI*Sq\-i  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation taDQ65  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   .iT4-  
       u2 = ifft(fftshift(c2));                        % Return to physical space [K:29N9~4  
       u1 = ifft(fftshift(c1)); C:j]43`  
    if rem(m1,J) == 0                                 % Save output every J steps. &*gbK6JB  
        U1 = [U1 u1];                                  % put solutions in U array &,MFB  
        U2=[U2 u2]; Ct!S Tk[2  
        MN1=[MN1 m1]; FYl3c   
        z1=dz*MN1';                                    % output location !\x?R6K  
      end {[^#h|U  
    end <5IQc[3]aP  
    hg=abs(U1').*abs(U1');                             % for data write to excel Uk'U?9O  
    ha=[z1 hg];                                        % for data write to excel a+ GJVJ  
    t1=[0 t']; ir&.Z5=  
    hh=[t1' ha'];                                      % for data write to excel file Pm?B 9S  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format |^Kjz{  
    figure(1) C}Qt "-%  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 9g]M4*?C9P  
    figure(2) "8/dD]=f^a  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn mi^hvks<  
    39D }  
    非线性超快脉冲耦合的数值方法的Matlab程序 1;&T^Gdj  
    PGX+p+wB  
    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。   CDCC1BG"  
    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  hY=I5[*  
    '5rU e\k  
    Gru ALx7  
    X| <yq  
    %  This Matlab script file solves the nonlinear Schrodinger equations ; k}H(QI  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of c0[k T  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear a.,_4;'UE1  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 i@,]Z~]  
    }N,>A-P  
    C=1;                           xZ+]QDKC  
    M1=120,                       % integer for amplitude >S.91!x  
    M3=5000;                      % integer for length of coupler =DMbz`t  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) C*rd;+1A  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. *s\sa+2al  
    T =40;                        % length of time:T*T0. XeU<^ [  
    dt = T/N;                     % time step Kz[BB@[  
    n = [-N/2:1:N/2-1]';          % Index P4 6,o  
    t = n.*dt;   jdlG#j-\  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. rBfg*r`)  
    w=2*pi*n./T; j-32S!  
    g1=-i*ww./2; _9kIRmT{  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; *h:kmT  
    g3=-i*ww./2; RGp'b  
    P1=0; p;`N\.ld  
    P2=0; _6rKC*Pe1  
    P3=1; )eR$:uO  
    P=0; `%y5\!X  
    for m1=1:M1                 QJSr:dP4dG  
    p=0.032*m1;                %input amplitude .Dx2 ;lj  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 !<r8~A3!(  
    s1=s10; ^'W%X  
    s20=0.*s10;                %input in waveguide 2 ^:z7E1 ~  
    s30=0.*s10;                %input in waveguide 3 V(..8}LlD  
    s2=s20; %6i=lyH-  
    s3=s30; sN]Z #7  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   `qu] Pxk  
    %energy in waveguide 1 )4ncutb  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   7I3:u+  
    %energy in waveguide 2 B.K4!/cF  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   w-FHhf  
    %energy in waveguide 3 / O)6iJ  
    for m3 = 1:1:M3                                    % Start space evolution SqqDV)Uih1  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS SRWg[H  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; |yv]Y/ =  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; _FsB6 G]mc  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform rzT{-DZB[4  
       sca2 = fftshift(fft(s2)); bNs[O22  
       sca3 = fftshift(fft(s3)); ? s4oDi|:  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   cL7C 2wB`  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ;)|nkI  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); r|-J8s#  
       s3 = ifft(fftshift(sc3)); 3EOyq^I%  
       s2 = ifft(fftshift(sc2));                       % Return to physical space o?\Gm  
       s1 = ifft(fftshift(sc1)); 2sun=3qb  
    end !. eAOuq  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); o9+Q{|r  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); v, 0<9!'v  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); j@t{@Ke  
       P1=[P1 p1/p10]; mz-N{>k  
       P2=[P2 p2/p10]; **HrWM%?8o  
       P3=[P3 p3/p10]; ,qu:<  
       P=[P p*p]; w4A#>;Qu*  
    end BS.=  
    figure(1) \(bj(any  
    plot(P,P1, P,P2, P,P3); yHOqzq56  
    !Bj^i cR  
    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~!~