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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 jC> l<d_  
    X9C)FS  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of @=q,,t$r  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of lob{{AB,!  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear DG}YQr.L  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 cy8+@77  
    #<|5<U  
    %fid=fopen('e21.dat','w'); [vb>5EhL!  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) j>X;a39|  
    M1 =3000;              % Total number of space steps PI~LbDE  
    J =100;                % Steps between output of space 7q?u`3l  
    T =10;                  % length of time windows:T*T0 zlzr;7m  
    T0=0.1;                 % input pulse width J&%vBg^  
    MN1=0;                 % initial value for the space output location C-4NiXa  
    dt = T/N;                      % time step {^gb S  
    n = [-N/2:1:N/2-1]';           % Index itb0dF1G  
    t = n.*dt;   Z)Y--`*  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ]^MOFzSz~  
    u20=u10.*0.0;                  % input to waveguide 2 {?m;DY v  
    u1=u10; u2=u20;                 Dv?'(.z  
    U1 = u1;   Z#YkAQHv5  
    U2 = u2;                       % Compute initial condition; save it in U ?F'gh4  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. #=/eu=  
    w=2*pi*n./T; (v(!l=3  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T &P{  
    L=4;                           % length of evoluation to compare with S. Trillo's paper /'?Fz*b  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 IQ[ ?ej3W  
    for m1 = 1:1:M1                                    % Start space evolution j(/Bf m  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS > ^fY`x,  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ?T-6|vZA  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 6dQa|ACX_  
       ca2 = fftshift(fft(u2)); .E:[ \H"  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 2/S~l;x  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   uV.3g 1 m  
       u2 = ifft(fftshift(c2));                        % Return to physical space \7z&iGe!  
       u1 = ifft(fftshift(c1)); \ &1)k/  
    if rem(m1,J) == 0                                 % Save output every J steps. P lJl#-BO  
        U1 = [U1 u1];                                  % put solutions in U array 2h0I1a,7  
        U2=[U2 u2]; oZ95)'L,  
        MN1=[MN1 m1]; A3ad9?LR[R  
        z1=dz*MN1';                                    % output location K1#Y{k5D}  
      end Ao)hb4ex  
    end /=Bz[ O  
    hg=abs(U1').*abs(U1');                             % for data write to excel k^AI7H  
    ha=[z1 hg];                                        % for data write to excel S W(h%`U  
    t1=[0 t']; (;YO]U4  
    hh=[t1' ha'];                                      % for data write to excel file 8>a/x,  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Knsb`1"E^6  
    figure(1) k+S+ : 5  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn +4^XFPq~  
    figure(2) [Z6]$$!#2  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn pj>b6^TI6C  
    'Y3>+7bI  
    非线性超快脉冲耦合的数值方法的Matlab程序 D3Lu]=G  
    e'aKI]>a  
    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。   |sz`w^#  
    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 'JY*K:-  
    VpSk.WY/ e  
    G3&ES3L  
    9PhdoREb  
    %  This Matlab script file solves the nonlinear Schrodinger equations tVQfR*=  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of p3O%|)yV  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear }/BwFB+(/  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 adtK$@Yeg  
    WmLl.Vv=  
    C=1;                           Rt~Aud[  
    M1=120,                       % integer for amplitude a%f{mP$m  
    M3=5000;                      % integer for length of coupler >R3~P~@30  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Qfo'w%px  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. d_#\^!9  
    T =40;                        % length of time:T*T0. ERQ a,h/  
    dt = T/N;                     % time step E } |g3  
    n = [-N/2:1:N/2-1]';          % Index >U~.I2sz  
    t = n.*dt;   6u/3"A]'  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. nMc3.fM  
    w=2*pi*n./T; {OP-9P=p  
    g1=-i*ww./2; t+Mr1e  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 3P Twpq1  
    g3=-i*ww./2; @8C^[fDL  
    P1=0; ,S;?3?a  
    P2=0; K1uN(T.Ju  
    P3=1; ,R0@`t1 p  
    P=0; W ]5kM~Q@  
    for m1=1:M1                 8 W8ahG}  
    p=0.032*m1;                %input amplitude gVCkj!{  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 _dppUUm  
    s1=s10; Pgf$GXE  
    s20=0.*s10;                %input in waveguide 2 u,[Yaw"L  
    s30=0.*s10;                %input in waveguide 3 M]!\X6<_  
    s2=s20; ;&e5.K+.Z  
    s3=s30; w(`X P  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Mo &Ia6^  
    %energy in waveguide 1 ,HS\(Z  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   !.iu_xJ  
    %energy in waveguide 2 R6dw#;6{I  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   aAO[Y"-:,Y  
    %energy in waveguide 3 },0fPkVsU  
    for m3 = 1:1:M3                                    % Start space evolution isHa4 D0  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS mB;W9[  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; =Y|TShKk  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; jEklf0Z  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform r S/Q  
       sca2 = fftshift(fft(s2)); e.G&hJ r  
       sca3 = fftshift(fft(s3)); :BCjt@K}  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   oLk>|J  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); e%x$Cb:znn  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); V'pNo&O=  
       s3 = ifft(fftshift(sc3)); Jjik~[<q:  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ih2H~c>O  
       s1 = ifft(fftshift(sc1)); U/,`xA;v>  
    end al=Dy60|z  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); k]Y+C@g  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); >!E:$;i@  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); /fA:Fnv  
       P1=[P1 p1/p10]; BMU~1[r  
       P2=[P2 p2/p10]; e`4OlM]  
       P3=[P3 p3/p10]; jnt0,y A  
       P=[P p*p]; 9C[3w[G~C  
    end Cst\_j  
    figure(1) n5 @H  
    plot(P,P1, P,P2, P,P3); G hLgV  
    nk1(/~`  
    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~!~