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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 uQH]  
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    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 0 cKsGDm  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of  m-4#s  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear &iw,||#  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Wjq9f;  
    J \|~k2~  
    %fid=fopen('e21.dat','w'); Epp>L.?r  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ;6R9k]5P%  
    M1 =3000;              % Total number of space steps r=3`Eb"t  
    J =100;                % Steps between output of space %[KnpJ{\  
    T =10;                  % length of time windows:T*T0 d+)LK~  
    T0=0.1;                 % input pulse width N KgEs   
    MN1=0;                 % initial value for the space output location \y?*} L  
    dt = T/N;                      % time step 9^g8VlQdT  
    n = [-N/2:1:N/2-1]';           % Index BMO,eQcB  
    t = n.*dt;   &Qda|  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 5'f_~>1Wt  
    u20=u10.*0.0;                  % input to waveguide 2 _+P*XY5  
    u1=u10; u2=u20;                 %8I^&~E1  
    U1 = u1;   3HXeBW  
    U2 = u2;                       % Compute initial condition; save it in U ^_v94!a 9  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. {J1rjrPo  
    w=2*pi*n./T; 9\?&u_ U"  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T R5QW4i9  
    L=4;                           % length of evoluation to compare with S. Trillo's paper xib}E[-l#  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 !]s=9(O  
    for m1 = 1:1:M1                                    % Start space evolution V^FM-bg%9  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 7Fpa%N/WL  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; YIW9z{rrs  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform <H] PP6_g:  
       ca2 = fftshift(fft(u2)); /Z*$k{qIR&  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation =>PX~/o  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ynra%"sd  
       u2 = ifft(fftshift(c2));                        % Return to physical space *IbDA  
       u1 = ifft(fftshift(c1)); z5({A2q  
    if rem(m1,J) == 0                                 % Save output every J steps. }P%gwgPK  
        U1 = [U1 u1];                                  % put solutions in U array wT+60X'  
        U2=[U2 u2]; )?&mCI*  
        MN1=[MN1 m1]; w7~]c,$y.  
        z1=dz*MN1';                                    % output location PT,*KYF_O"  
      end } %0 w25  
    end yg}L,JJU<  
    hg=abs(U1').*abs(U1');                             % for data write to excel m8L %!6o  
    ha=[z1 hg];                                        % for data write to excel exSwx-zxI  
    t1=[0 t']; o"RE4s\G~r  
    hh=[t1' ha'];                                      % for data write to excel file oIOeX1$V  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ! weYOOu  
    figure(1) 7Y~5gn  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn JYjc^m  
    figure(2) !^L}LtqHI  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn (*eX'^Q)d  
    .Sw4{m[g  
    非线性超快脉冲耦合的数值方法的Matlab程序 ;QuxTmWp^  
    GPAC0K^p  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   fU.hb%m)Q\  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >/.jB/q  
    myXGMN$i  
    0j;|IU\  
    2\$<&]q  
    %  This Matlab script file solves the nonlinear Schrodinger equations .-s!} P"  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of PTpCiiA@  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ~:!& }e5  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 gDfM}2]/  
    6"?#s/fk  
    C=1;                           -{eiV0<^  
    M1=120,                       % integer for amplitude +A,cdi9z  
    M3=5000;                      % integer for length of coupler ZKI` ;  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) vA*NJ%&`  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. jvd3_L-@E<  
    T =40;                        % length of time:T*T0. hhjsg?4uL  
    dt = T/N;                     % time step 2s 9U&  
    n = [-N/2:1:N/2-1]';          % Index cP/(h  
    t = n.*dt;   ,V4pFQzL  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. *qMjoP,  
    w=2*pi*n./T; 6*ZZ)W<  
    g1=-i*ww./2; Rx%kAt2X  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; N9)ERW2`*  
    g3=-i*ww./2; QIN# \  
    P1=0; jAt6 5a  
    P2=0; K1<l/ s  
    P3=1; $[=`*m  
    P=0; DML0paOm5  
    for m1=1:M1                 wL0"1Ya  
    p=0.032*m1;                %input amplitude gJOswN;([  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 jT QN(a9Y  
    s1=s10; jaux:fU  
    s20=0.*s10;                %input in waveguide 2 n |,}   
    s30=0.*s10;                %input in waveguide 3 S;vZXgyN?  
    s2=s20; >273V+dy  
    s3=s30; 9*|An  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   )>=|oY3  
    %energy in waveguide 1 x~yd/ R  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   HZ2zL17  
    %energy in waveguide 2 kS7T'[d  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   .fW`/BXE  
    %energy in waveguide 3 |4Q><6"G  
    for m3 = 1:1:M3                                    % Start space evolution >y q L  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS uqy~hY  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; P|)SXR  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ~u-`L+G"6  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform |om3*]7  
       sca2 = fftshift(fft(s2)); KQqQ@D&n  
       sca3 = fftshift(fft(s3)); @1[LD[<  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   b}q,cm  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }KkH7XksF  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); wY}+d0Ch  
       s3 = ifft(fftshift(sc3)); {la ^useg[  
       s2 = ifft(fftshift(sc2));                       % Return to physical space &9g#Vq%   
       s1 = ifft(fftshift(sc1)); t,P +~ A  
    end gzdgnF2  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); C{S6Ri  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Z=sAR(n}~  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); eZJOI1wNp  
       P1=[P1 p1/p10]; >"nk}@  
       P2=[P2 p2/p10]; y.oJzU[p%  
       P3=[P3 p3/p10]; ,>jm|BTD {  
       P=[P p*p]; C,z]q$4  
    end @',;/j80  
    figure(1) ZmHl~MR@  
    plot(P,P1, P,P2, P,P3); :3Jh f$  
    3 \WdA$Wx  
    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~!~