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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 ?'+ kZ|  
    N Obw/9JO  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of #Zt(g(T  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ,7mB`0j>  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7dtkylW  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 s\3OqJo%)  
    qpXsQim$~  
    %fid=fopen('e21.dat','w'); m9 D' yXZ  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) vvmG46IgZ  
    M1 =3000;              % Total number of space steps  mB<*we  
    J =100;                % Steps between output of space (hFyp}jkk  
    T =10;                  % length of time windows:T*T0 P1IL ]  
    T0=0.1;                 % input pulse width ~3,k8C"pRq  
    MN1=0;                 % initial value for the space output location .}ePm(  
    dt = T/N;                      % time step XAw0Nn   
    n = [-N/2:1:N/2-1]';           % Index O 6Mxp -  
    t = n.*dt;   kYnp$8  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 WI}cXXUKm0  
    u20=u10.*0.0;                  % input to waveguide 2 F0]xc  
    u1=u10; u2=u20;                 A#KfG1K>  
    U1 = u1;   $fFh4O4  
    U2 = u2;                       % Compute initial condition; save it in U |cIv&\ x  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. W2T6JFv  
    w=2*pi*n./T; ?3Y~q;I]O  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 5}NTqN0@  
    L=4;                           % length of evoluation to compare with S. Trillo's paper ['jr+gIfQ  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 1yV+~)by3  
    for m1 = 1:1:M1                                    % Start space evolution g=L80$1  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ^SC2k LI  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; TAp8x  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform AtYqD<hl:  
       ca2 = fftshift(fft(u2)); L. DD  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation jN T+?2  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   fe8}2#<o  
       u2 = ifft(fftshift(c2));                        % Return to physical space i.Z iLDs\7  
       u1 = ifft(fftshift(c1)); y ]D[JX[  
    if rem(m1,J) == 0                                 % Save output every J steps. 7-A/2/G<  
        U1 = [U1 u1];                                  % put solutions in U array Wf:LYL  
        U2=[U2 u2]; iph}!3f  
        MN1=[MN1 m1]; (Qf. S{;  
        z1=dz*MN1';                                    % output location I#PhzGC@  
      end ,Vfjt=6]}  
    end CWa~~h<r-  
    hg=abs(U1').*abs(U1');                             % for data write to excel _bn "c@s  
    ha=[z1 hg];                                        % for data write to excel 4=qZ Z>[t  
    t1=[0 t']; ?4cj"i  
    hh=[t1' ha'];                                      % for data write to excel file E4, J"T|@  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format rt'pc\|O&  
    figure(1) Fxv5kho  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 2Og<e|  
    figure(2) i !;9A6D  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn $Ts;o  
    Q)Q1a;o  
    非线性超快脉冲耦合的数值方法的Matlab程序 sf"vii,1A  
    / }Pj^^6A<  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   .,F`*JVFq  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 BlfadM;  
    7j8lhrM}^  
    .t7ME{  
    K.Tob,5`  
    %  This Matlab script file solves the nonlinear Schrodinger equations kgh0  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of M;9s  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >Og|*g  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ,ygUy]  
    x;{Hd;<YF  
    C=1;                           X& mD/1  
    M1=120,                       % integer for amplitude '<{Jlz(u9  
    M3=5000;                      % integer for length of coupler !<>*|a  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) {5]c \_.  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. "x3x$JQZy  
    T =40;                        % length of time:T*T0. jN-!1O._G  
    dt = T/N;                     % time step 4W#DLip9  
    n = [-N/2:1:N/2-1]';          % Index XAZPbvG|$  
    t = n.*dt;   #I1q,fm  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. %,(X R`  
    w=2*pi*n./T; n8tw8o%&[  
    g1=-i*ww./2; +ZOKfX  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ,b4oV  
    g3=-i*ww./2; WK0:3q(P  
    P1=0; E0AbVa.  
    P2=0; QP/ZD|/ t1  
    P3=1; \q\"=  
    P=0; b]  
    for m1=1:M1                 Fw:_O2  
    p=0.032*m1;                %input amplitude C1>zwU_zo  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 -lrcb/)Gz  
    s1=s10; n?U^vK_  
    s20=0.*s10;                %input in waveguide 2 zf>*\pZE  
    s30=0.*s10;                %input in waveguide 3 ) "Z6Q5k^  
    s2=s20; /_qHF-  
    s3=s30; JIIc4fyy8s  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   rp+]f\] h  
    %energy in waveguide 1 T%Bz>K  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   =3ovaP  
    %energy in waveguide 2 W1521:  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   1nw\?r2  
    %energy in waveguide 3 'E&tEbY  
    for m3 = 1:1:M3                                    % Start space evolution S+"Bq:u"  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS E]v?:!!ds  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; w{t]^w:  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; E*h!{)z@F  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform \t 5_V)P  
       sca2 = fftshift(fft(s2)); w3z'ZCcr;"  
       sca3 = fftshift(fft(s3)); I{h KN V  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   Q :.i[  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); bYoBJ #UX  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); P aeq  
       s3 = ifft(fftshift(sc3)); ?4oP=.  
       s2 = ifft(fftshift(sc2));                       % Return to physical space I,<?Kv  
       s1 = ifft(fftshift(sc1)); S}a]Bt  
    end plp-[eKcD  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 2W2T  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); I&m' a  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); )ki Gk}2  
       P1=[P1 p1/p10]; c& I  
       P2=[P2 p2/p10]; ?O3d Sxi  
       P3=[P3 p3/p10]; Q6wa-Y,  
       P=[P p*p]; @%G?Nht]o  
    end 6ypLE@Mk  
    figure(1) DVVyWn[  
    plot(P,P1, P,P2, P,P3); [uK{``"  
    iPkCuLQ}  
    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~!~