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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 U|QLc   
    3 f=_F  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of z^z_!@7v   
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of n$RhD93  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear P,-f]k[_  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 sdF;H[  
    k%|7H,7  
    %fid=fopen('e21.dat','w'); 5+*MqO>  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ;i*<HNQ  
    M1 =3000;              % Total number of space steps QOA7#H-m9  
    J =100;                % Steps between output of space 2Fk4jHj  
    T =10;                  % length of time windows:T*T0 ol QT r  
    T0=0.1;                 % input pulse width oc+TsVt  
    MN1=0;                 % initial value for the space output location hK F*{,'  
    dt = T/N;                      % time step #=mLQSiQ  
    n = [-N/2:1:N/2-1]';           % Index p4QQ5O$;  
    t = n.*dt;   -j1?l Y  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 :.wR*E  
    u20=u10.*0.0;                  % input to waveguide 2 eT33&:n4  
    u1=u10; u2=u20;                 `|maf=SnY5  
    U1 = u1;   h3 -y}.VjG  
    U2 = u2;                       % Compute initial condition; save it in U !nh7<VJ  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. \1Tu P}P  
    w=2*pi*n./T; GCaiogiBg  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T [B<htD&  
    L=4;                           % length of evoluation to compare with S. Trillo's paper z,pKy Inw  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 oasp/Y.p  
    for m1 = 1:1:M1                                    % Start space evolution 1vKAJ<4W  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS nn[OC=cDN  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; i\~@2  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform MIa#\tJj  
       ca2 = fftshift(fft(u2)); X{cFq W7  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation D d['e  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   1dDK(RBbQ  
       u2 = ifft(fftshift(c2));                        % Return to physical space ^n Gj 7b  
       u1 = ifft(fftshift(c1)); SI_u0j4%*  
    if rem(m1,J) == 0                                 % Save output every J steps. og0su  
        U1 = [U1 u1];                                  % put solutions in U array S7i,oP7  
        U2=[U2 u2]; u!4i+7}  
        MN1=[MN1 m1]; yN-o?[o  
        z1=dz*MN1';                                    % output location N_jpCCG~  
      end jQ>~  
    end :g&9v_}&K{  
    hg=abs(U1').*abs(U1');                             % for data write to excel \ @XvEx%  
    ha=[z1 hg];                                        % for data write to excel }eKY%WU>O  
    t1=[0 t']; qPal'c0  
    hh=[t1' ha'];                                      % for data write to excel file g$X4ZRSel  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ZC7ZlL _  
    figure(1) .J=<E  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn }4$k-,1S  
    figure(2) N{b ;kiZq  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn )gNS%t c*K  
    Z+p'3  
    非线性超快脉冲耦合的数值方法的Matlab程序 4~8!3JH39  
    9):h %o  
    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。   <!qN<#$y  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 2!@ER i  
    J}zN]|bz  
    ~F)[H'$A  
    +K2p2Dw(k  
    %  This Matlab script file solves the nonlinear Schrodinger equations dd?ZQ:n  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of `1xJ1 z#  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _;z IH5 H  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 L0^rw|Z%'  
    S/?!ESW6  
    C=1;                           Z'Uc}M'U  
    M1=120,                       % integer for amplitude G q&[T:  
    M3=5000;                      % integer for length of coupler c]Z@L~WW  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Nbyc,a[o  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. s?Wkh`b  
    T =40;                        % length of time:T*T0. K>a@AXC  
    dt = T/N;                     % time step QmiS/`AAv  
    n = [-N/2:1:N/2-1]';          % Index %DQ!#Nl*  
    t = n.*dt;   w?JRY  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. pnTuYT^%)  
    w=2*pi*n./T; (Ts#^qC  
    g1=-i*ww./2; Jxo#sV-  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; "|,;~k1  
    g3=-i*ww./2; A_pcv7=@  
    P1=0; v)c[-:"z  
    P2=0; BN]{o(EB  
    P3=1; >Hd Pcsl L  
    P=0; AQ<2 "s  
    for m1=1:M1                 #Y_v0.N  
    p=0.032*m1;                %input amplitude o[Gp*o\  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 5f}GV0=n  
    s1=s10; 9JtPP  
    s20=0.*s10;                %input in waveguide 2 &sA@!  
    s30=0.*s10;                %input in waveguide 3 =@\Li)Y  
    s2=s20; a +lTAe  
    s3=s30; &al\8  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   znq/ %7  
    %energy in waveguide 1 2EAY`}Rl6.  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   b%_[\((  
    %energy in waveguide 2 k62KZ5| D  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   5^0K5R6GQf  
    %energy in waveguide 3 A5q%yt I  
    for m3 = 1:1:M3                                    % Start space evolution `21$e  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS _/pdZM,V  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6Gj69Lr  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; +cf.In,{  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform kf -/rC)>  
       sca2 = fftshift(fft(s2)); q% pjY  
       sca3 = fftshift(fft(s3)); L=v"5)m2R  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ,!I'0x1OR  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); &{=`g+4n  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); \f-HfYG  
       s3 = ifft(fftshift(sc3)); oc0z1u  
       s2 = ifft(fftshift(sc2));                       % Return to physical space $ 0Up.  
       s1 = ifft(fftshift(sc1)); @7z_f!'u  
    end EG oe<.  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); k<.VR"I p  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); *#&s+h,^  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Z.{r%W{2  
       P1=[P1 p1/p10]; R2B0?fu  
       P2=[P2 p2/p10]; jHx)q|2\  
       P3=[P3 p3/p10]; 1 GB  
       P=[P p*p]; \CKf/:"  
    end > Du>vlT Y  
    figure(1) <uL0 M`u3  
    plot(P,P1, P,P2, P,P3); $8t\|O3  
    ~'3hK4  
    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~!~