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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 m*>gG{3;  
    ZBc8 ^QZ  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of w.-J2%J   
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of mqQC`Aqx:  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Ot~buf'|  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 6{[ uCxxl  
    ~HUO$*U4<  
    %fid=fopen('e21.dat','w'); wQOIUvd  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) rJCu6  
    M1 =3000;              % Total number of space steps VO,F[E~_  
    J =100;                % Steps between output of space =n_>7@9l  
    T =10;                  % length of time windows:T*T0 ?Pt*4NaT;  
    T0=0.1;                 % input pulse width j<d,7  
    MN1=0;                 % initial value for the space output location SA,+oq(  
    dt = T/N;                      % time step ]P4?jKI  
    n = [-N/2:1:N/2-1]';           % Index ;fm> \f  
    t = n.*dt;   FOSC#W9E  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 <*HsJwr)u  
    u20=u10.*0.0;                  % input to waveguide 2 2<uBC  
    u1=u10; u2=u20;                 %VO>6iVn  
    U1 = u1;   "bvob G  
    U2 = u2;                       % Compute initial condition; save it in U {6>:= ?7]R  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Tl-Ix&37  
    w=2*pi*n./T; I=4G+h5p  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T PED5>90  
    L=4;                           % length of evoluation to compare with S. Trillo's paper wF{M"$am  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 b}m@2DR'|m  
    for m1 = 1:1:M1                                    % Start space evolution RnUud\T/  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 249DAjn+  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; d+IN-lR(  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform u 236a\:  
       ca2 = fftshift(fft(u2)); #UqE %g`J  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation i dY Xv)R  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   m=D9V-P  
       u2 = ifft(fftshift(c2));                        % Return to physical space 8} |!p>  
       u1 = ifft(fftshift(c1)); D4U<Rn6N_5  
    if rem(m1,J) == 0                                 % Save output every J steps. E-HK=D&W/  
        U1 = [U1 u1];                                  % put solutions in U array <-=g)3_  
        U2=[U2 u2]; d@+u&xrd  
        MN1=[MN1 m1]; @8|i@S@4  
        z1=dz*MN1';                                    % output location C=P}@|K  
      end $`"$ZI6[  
    end O|0,= 5  
    hg=abs(U1').*abs(U1');                             % for data write to excel 6G>loNM^  
    ha=[z1 hg];                                        % for data write to excel YZ/2 :[b  
    t1=[0 t']; qXB5wDJg  
    hh=[t1' ha'];                                      % for data write to excel file ;% l0Ml>  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ;1Q @d  
    figure(1) k, jcLX.  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn D<Z]kR(  
    figure(2) wRe2sjM  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn JYa3xeC;  
    3u1\zse  
    非线性超快脉冲耦合的数值方法的Matlab程序 \-{2E  
    G5!!^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。   ic?(`6N8  
    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 !'kr:r}gg  
    -}"nb-RR\  
    He  LW*  
    BYb"[qPV  
    %  This Matlab script file solves the nonlinear Schrodinger equations @e^(V$ap  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 2:&QBwr+;  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear -n6e;p]  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 O\}w&BE:h  
    E&> 2=$~  
    C=1;                           dRXrI  
    M1=120,                       % integer for amplitude :hDv^D?3  
    M3=5000;                      % integer for length of coupler ]nm(V  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) a*!9RQ  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. i6xzHfaYG  
    T =40;                        % length of time:T*T0. X6n8Bi9Ik  
    dt = T/N;                     % time step t9&=; s  
    n = [-N/2:1:N/2-1]';          % Index "Q;Vy t  
    t = n.*dt;   \r- v]]_<d  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 8,]wOxwqi  
    w=2*pi*n./T; 4}*V=>z  
    g1=-i*ww./2; -hZw.eChQa  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; !r9~K^EI  
    g3=-i*ww./2; IgKrcpK#}?  
    P1=0; K,Hxe;-  
    P2=0; +D M,+{}  
    P3=1; #[y2nK3zF  
    P=0; (O'O #AD  
    for m1=1:M1                 Q*R9OF  
    p=0.032*m1;                %input amplitude 8FgF6ip  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 M#xol/)h  
    s1=s10; :-cqC|Y  
    s20=0.*s10;                %input in waveguide 2 :<xf'.  
    s30=0.*s10;                %input in waveguide 3 ro18%' RRI  
    s2=s20; #QiNSS  
    s3=s30; b:x*Hjf  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   _`xhP-,`S  
    %energy in waveguide 1 t[\6/`YH  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   14p{V} f3  
    %energy in waveguide 2 0D}k ^W  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   c)SQ@B@q  
    %energy in waveguide 3 A1x    
    for m3 = 1:1:M3                                    % Start space evolution N7Kkz /  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS UX)QdT45Mh  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; NP$ D9#   
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; {/!Yavx  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 3IQ-2 X--  
       sca2 = fftshift(fft(s2)); $A>]lLo0  
       sca3 = fftshift(fft(s3)); 6bBNC2K$-  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   p I@!2c:}  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); j +Ro?  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 0B(Y{*QB  
       s3 = ifft(fftshift(sc3)); (b+o$C  
       s2 = ifft(fftshift(sc2));                       % Return to physical space &&te(DC\  
       s1 = ifft(fftshift(sc1)); Bx0=D:j  
    end #x(3>}  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ^1X 6DH`  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); #Z}YQ $g  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); c5t7X-LB  
       P1=[P1 p1/p10]; Sh7ob2  
       P2=[P2 p2/p10]; NeniQeR   
       P3=[P3 p3/p10]; rnXoA, c/  
       P=[P p*p]; sDyt3xN  
    end ;et(Yi;9  
    figure(1) gr4JaV  
    plot(P,P1, P,P2, P,P3); C.+:FY.H  
    l!%V&HJV  
    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~!~