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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 1I*b7t  
    <lj;}@qQ<  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ?n 9<PMo  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of -Q6njt&  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +O 2H":$  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 F|t3%dpj  
    2`XG"[@  
    %fid=fopen('e21.dat','w'); gn>qd6P  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) J_]B,' 6  
    M1 =3000;              % Total number of space steps 2cy: l03  
    J =100;                % Steps between output of space e^?0uVxS1  
    T =10;                  % length of time windows:T*T0 FvpI\%#~  
    T0=0.1;                 % input pulse width ^a6c/2K  
    MN1=0;                 % initial value for the space output location p<w2e  
    dt = T/N;                      % time step xWv@PqXD  
    n = [-N/2:1:N/2-1]';           % Index dvWQ?1l_  
    t = n.*dt;   @pcmVsIp  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 'gDhi!h%  
    u20=u10.*0.0;                  % input to waveguide 2 gZI88Q  
    u1=u10; u2=u20;                 &&/2oP+z  
    U1 = u1;   L 1FT h  
    U2 = u2;                       % Compute initial condition; save it in U dX4"o?KD>  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. fO+$`r>9  
    w=2*pi*n./T; Fc{X$hh<  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T n2NxO0  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 8ug\GlZc  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 g]sc)4  
    for m1 = 1:1:M1                                    % Start space evolution \OV><|Lkh  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 8<gYB$* S  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; u|v2J/_5Y  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform $IZ02ZM$  
       ca2 = fftshift(fft(u2)); K"%_q$[YQ  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation g%P6f  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   z+RA  
       u2 = ifft(fftshift(c2));                        % Return to physical space n-/ {H4\  
       u1 = ifft(fftshift(c1)); +K6j p  
    if rem(m1,J) == 0                                 % Save output every J steps. vkFq/+'U  
        U1 = [U1 u1];                                  % put solutions in U array k E^%w?C  
        U2=[U2 u2]; gLyXe,Jp  
        MN1=[MN1 m1]; D%CKkQ<u2  
        z1=dz*MN1';                                    % output location oCw>b]S  
      end O#j&8hQ>  
    end k,p:!S(bl  
    hg=abs(U1').*abs(U1');                             % for data write to excel =0Z^q0.  
    ha=[z1 hg];                                        % for data write to excel |\PI"rW  
    t1=[0 t']; {h< V^r  
    hh=[t1' ha'];                                      % for data write to excel file l :e&w(1H  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ID/=YG@  
    figure(1) g j(|#n5C  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn <OQn |zU\  
    figure(2) sqtMhUQ?>w  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 2pKkg>/S  
    cPFs K*w  
    非线性超快脉冲耦合的数值方法的Matlab程序 7Nu.2qE  
    5G >{*K/  
    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。   g4Y1*`}2f  
    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 ] LcCom:]  
    b0QC91   
    %\i OX|F_  
    Q L0  
    %  This Matlab script file solves the nonlinear Schrodinger equations {5%u G2g  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of FTVV+9.l:  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear s7"NK"  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Pv- i.  
    /2%646  
    C=1;                           w"A.*8Iu  
    M1=120,                       % integer for amplitude ~AqFLv/%  
    M3=5000;                      % integer for length of coupler AQx:}PO  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) oGtz*AP%  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. e}xx4mYo  
    T =40;                        % length of time:T*T0. J@ CKgE  
    dt = T/N;                     % time step RgB5'$x}  
    n = [-N/2:1:N/2-1]';          % Index ]0Y5 Z)3:z  
    t = n.*dt;   GkOZ =ej  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. F gi&CJ8Q  
    w=2*pi*n./T; v(|Arm?  
    g1=-i*ww./2; No|T#=BZ[  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; I34|<3t$  
    g3=-i*ww./2; !HV<2q()  
    P1=0; ^x BQ#p  
    P2=0; i[IOR0  
    P3=1; |\# ~  
    P=0; kYW>o}J|  
    for m1=1:M1                 ~AvB5  
    p=0.032*m1;                %input amplitude W@b Z~Q9  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 [w1 4hHnq  
    s1=s10; })V^t3  
    s20=0.*s10;                %input in waveguide 2 IqA'Vz,lL  
    s30=0.*s10;                %input in waveguide 3 ?:sk [f6  
    s2=s20; S S)9+0$  
    s3=s30; eYpK!9  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   rpB0?h!$  
    %energy in waveguide 1 o)V@|i0Js  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   k1.h|&JJN  
    %energy in waveguide 2 n|p(Cb#G  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   V_x8 Q+~?  
    %energy in waveguide 3 ;4%Co)Rw  
    for m3 = 1:1:M3                                    % Start space evolution H;1_"  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS `X8wnD  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; _ SuW86  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Bn4wr  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ?@>PKUv{  
       sca2 = fftshift(fft(s2)); j;7:aM"BQW  
       sca3 = fftshift(fft(s3)); +u[^@>_I0  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ]jB`"to*}  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ]B2%\}c  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); vWs#4JoG  
       s3 = ifft(fftshift(sc3)); |7$Q'3V  
       s2 = ifft(fftshift(sc2));                       % Return to physical space qexnsL  
       s1 = ifft(fftshift(sc1)); : Yb_  
    end +{r~-Rn3  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 2+oS'nL  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); >d9b"T  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 5qL;@Y  
       P1=[P1 p1/p10]; )8JfBzR  
       P2=[P2 p2/p10]; 75"&"*R/*G  
       P3=[P3 p3/p10]; "XB6k 0.#  
       P=[P p*p]; M(|6YF7u  
    end -U BH,U  
    figure(1) 2{6%+>jB  
    plot(P,P1, P,P2, P,P3); M669G;w(K  
    u[<ij  
    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~!~