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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 7x ?2((   
    (RtjD`e}  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 7\e96+j|f  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of sKU?"|G81G  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear v?S~ =$.  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 LG6k KG  
    ;p U=>  
    %fid=fopen('e21.dat','w'); 'CkN  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 60`4 _Uy]_  
    M1 =3000;              % Total number of space steps ;?`l1:C5)  
    J =100;                % Steps between output of space <Z6tRf;B  
    T =10;                  % length of time windows:T*T0 jh|4Y(  
    T0=0.1;                 % input pulse width nL[ zXl  
    MN1=0;                 % initial value for the space output location v7kR]HU[y  
    dt = T/N;                      % time step tq^d1b(j4  
    n = [-N/2:1:N/2-1]';           % Index o"5[~$O  
    t = n.*dt;   =Lyo]8>,X  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 PiTe/  
    u20=u10.*0.0;                  % input to waveguide 2 /Wqx@#  
    u1=u10; u2=u20;                 qp6*v&  
    U1 = u1;   Bt\z0*t=s  
    U2 = u2;                       % Compute initial condition; save it in U eJm7}\/6`  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. FYtf<C+  
    w=2*pi*n./T; _a e&@s1  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T y_Tc$g~  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 7KzMa%=  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 \h&ui]V  
    for m1 = 1:1:M1                                    % Start space evolution %j*i=  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ,*w  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; V&>\U?q:  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform h)746T )  
       ca2 = fftshift(fft(u2)); ZX Sl+k .  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation #ErIot  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   OSsxO(;g  
       u2 = ifft(fftshift(c2));                        % Return to physical space nfV32D|3  
       u1 = ifft(fftshift(c1)); d'yA"b]  
    if rem(m1,J) == 0                                 % Save output every J steps. az=(6PX  
        U1 = [U1 u1];                                  % put solutions in U array I )LO@  
        U2=[U2 u2]; ?(!<m'jEy  
        MN1=[MN1 m1]; 0B;cQSH!q  
        z1=dz*MN1';                                    % output location H"g$qSx  
      end q:9#Vcw  
    end {ta0dS;1  
    hg=abs(U1').*abs(U1');                             % for data write to excel ?<#2raH-  
    ha=[z1 hg];                                        % for data write to excel i(k]}Di:  
    t1=[0 t']; c T!L+z g  
    hh=[t1' ha'];                                      % for data write to excel file RRBokj)]  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format v FL\O  
    figure(1) i{$h]D_fD  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Po: )b  
    figure(2) +C(v4@=nd  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn t#0/_tD  
    $m:4'r  
    非线性超快脉冲耦合的数值方法的Matlab程序 %!>~2=Q2*  
    #''q :^EQ  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   K^_Mt!%  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1{.=T&eG#  
    Viu+#J;l  
    +gQn,HX  
    c<8RRYs  
    %  This Matlab script file solves the nonlinear Schrodinger equations ( _{\tgSm  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of onuhNn_=>  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear  MR/8  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {Y%X  
    E!eBQ[@  
    C=1;                           73C  
    M1=120,                       % integer for amplitude U1>VKP;5Nn  
    M3=5000;                      % integer for length of coupler ~$zodrS9  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) :V%XEN)  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. F_Q?0 Do0'  
    T =40;                        % length of time:T*T0. c==` r C  
    dt = T/N;                     % time step ^r7-|  
    n = [-N/2:1:N/2-1]';          % Index W|PKcZ ]Uc  
    t = n.*dt;   4}~zVT0'~  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. l1|z; $_z  
    w=2*pi*n./T; r] +V:l3  
    g1=-i*ww./2; )7e[o8O_6  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; DJtKLG0  
    g3=-i*ww./2; ml|[x M8  
    P1=0; 95,{40;X7  
    P2=0; -1Luyuy/`  
    P3=1; 0ang^v;q  
    P=0; u= |hRTD=  
    for m1=1:M1                 .Jt&6N  
    p=0.032*m1;                %input amplitude SOyE$GoOsx  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 3zO'=gwJ  
    s1=s10; *CA7 {2CX  
    s20=0.*s10;                %input in waveguide 2 );^] is~  
    s30=0.*s10;                %input in waveguide 3 dnby&-+T  
    s2=s20; FuZ7xM,  
    s3=s30; M~/%V NX  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   HqW|  
    %energy in waveguide 1 {-sy,EYcw  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   w%no6 ;  
    %energy in waveguide 2 N{]|!#  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   w,\#)<boyb  
    %energy in waveguide 3 Kf XE=v{t  
    for m3 = 1:1:M3                                    % Start space evolution <uugT9By  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS |]5g+sd  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ,3k"J4|d  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;  *q8L$D  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform x,\PV>   
       sca2 = fftshift(fft(s2)); hCX}*  
       sca3 = fftshift(fft(s3)); y[*Bw)F\N  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   -ISI!EU$  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); %bnDxCj"  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); nj*B-M\p  
       s3 = ifft(fftshift(sc3)); eCY gi7?  
       s2 = ifft(fftshift(sc2));                       % Return to physical space #'Q_eBX  
       s1 = ifft(fftshift(sc1)); +"!,rZ7,A  
    end t@Qs&DZ7k  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); _MZqH8  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); PrIS L[@  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); N#')Qz:P  
       P1=[P1 p1/p10]; Hnwir!=7  
       P2=[P2 p2/p10]; ;r[@;2p*(  
       P3=[P3 p3/p10]; */Oq$3QGsV  
       P=[P p*p]; :^DuB_  
    end S6 F28 d[j  
    figure(1) R{~Yh.)~  
    plot(P,P1, P,P2, P,P3); xf8C$|,  
    Aw )='&;^z  
    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~!~