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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 8<o(z'&y  
    rVO+ vhih  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of AvwX 2?tc  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of P--#5W;^oB  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ei"FN3Rm  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1,/oS&?E  
    p'R}z|d)  
    %fid=fopen('e21.dat','w'); ^ o{O5&i]  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Axcm~ !uf  
    M1 =3000;              % Total number of space steps :xA'X+d/'  
    J =100;                % Steps between output of space >Qi2;t~G  
    T =10;                  % length of time windows:T*T0 'Kq%t M26!  
    T0=0.1;                 % input pulse width {:"bX~<^  
    MN1=0;                 % initial value for the space output location LsmC/+7r$1  
    dt = T/N;                      % time step YlYTH_L>E  
    n = [-N/2:1:N/2-1]';           % Index phNv^R+  
    t = n.*dt;   v3[ 2!UXq  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 1p tPey  
    u20=u10.*0.0;                  % input to waveguide 2 EBn7waBS  
    u1=u10; u2=u20;                 S4\T (  
    U1 = u1;   [#.QDe  
    U2 = u2;                       % Compute initial condition; save it in U d6Z;\f7[  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. P!-9cd1 C,  
    w=2*pi*n./T; N". af)5  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T uh GL1{  
    L=4;                           % length of evoluation to compare with S. Trillo's paper | 0&~fY  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 , n+dB2\  
    for m1 = 1:1:M1                                    % Start space evolution sqkPC_;A  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS toP7b  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; $V@IRBm  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform PB`94W  
       ca2 = fftshift(fft(u2)); X09& S4  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation gXF.e.uU  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   PsTwJLY   
       u2 = ifft(fftshift(c2));                        % Return to physical space x&kF;UC  
       u1 = ifft(fftshift(c1)); p( z.[  
    if rem(m1,J) == 0                                 % Save output every J steps. 0uj3kr?cv  
        U1 = [U1 u1];                                  % put solutions in U array C^ uXJ~8  
        U2=[U2 u2]; yJ?4B?p(  
        MN1=[MN1 m1]; x=9drKIw>  
        z1=dz*MN1';                                    % output location -()CgtSR  
      end eE7+fMP{  
    end oo /#]a  
    hg=abs(U1').*abs(U1');                             % for data write to excel _RAPXU~ 6-  
    ha=[z1 hg];                                        % for data write to excel )WD<Q x&  
    t1=[0 t']; Xo'_|-N+  
    hh=[t1' ha'];                                      % for data write to excel file 5I@< 6S&X  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format -l^u1z  
    figure(1) ]r|X[9  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn LB-4/G$  
    figure(2) t.3b\RV[  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn mgg/i@(  
    !x&/M*nBE  
    非线性超快脉冲耦合的数值方法的Matlab程序  8*lVO2  
    $2\ OBc=  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   +$ P0&YaQ  
    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 h19c*,0z!  
    rry 33  
    rZ *}jD[  
    t}]=5)9<  
    %  This Matlab script file solves the nonlinear Schrodinger equations =%p0r z|b  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of \y{C>! WX4  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear s<aJ pi{n4  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004   Lxs  
    r 5:DIA!  
    C=1;                           ;QS-a  
    M1=120,                       % integer for amplitude /u5MAl.<[  
    M3=5000;                      % integer for length of coupler fgq#Oi}  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) L_Ff*   
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. R9^Vk*`gFU  
    T =40;                        % length of time:T*T0. 7]62=p2R  
    dt = T/N;                     % time step M2{{B ^*$6  
    n = [-N/2:1:N/2-1]';          % Index 6gNsh  
    t = n.*dt;   3+0 $=ef  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. h# B%'9r  
    w=2*pi*n./T; [a`89'"z  
    g1=-i*ww./2; A+_361KH  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Ic P]EgB  
    g3=-i*ww./2; X=8y$Yy  
    P1=0; UXvUU^k"v  
    P2=0; H)ud?vB6  
    P3=1; I& DEF*  
    P=0; ]-&A )M6  
    for m1=1:M1                 RNiFLD%5  
    p=0.032*m1;                %input amplitude w9G (^jS6  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 Rq|7$O5  
    s1=s10; WRe9ki=R  
    s20=0.*s10;                %input in waveguide 2 `O5w M\Z  
    s30=0.*s10;                %input in waveguide 3 @ l41'?m  
    s2=s20; j KGfm9|zj  
    s3=s30; I r]#u]Ap  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));    At @H  
    %energy in waveguide 1 Y{ijSOl3  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   g Y|f[M|  
    %energy in waveguide 2 UP'~D]J  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Y23- Im  
    %energy in waveguide 3 *eK\W00  
    for m3 = 1:1:M3                                    % Start space evolution 0}$Zr*|;Y  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS >g+yw1nC  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; VKqIFM1b  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; }OL?k/w  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform o<cg9  
       sca2 = fftshift(fft(s2)); Pq u]?X  
       sca3 = fftshift(fft(s3)); $KHw=<:)/  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   LDc?/ Z1  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); C9OEB6  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); +N n $  
       s3 = ifft(fftshift(sc3)); l!qhK'']V"  
       s2 = ifft(fftshift(sc2));                       % Return to physical space jlXzfD T  
       s1 = ifft(fftshift(sc1)); `ECY:3"$KA  
    end RUco3fZ   
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); W T~UEK'  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 2@~.FBby7@  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 4} .PQ{  
       P1=[P1 p1/p10]; /<C}v~r  
       P2=[P2 p2/p10]; P|j|0o,8p  
       P3=[P3 p3/p10]; S#Q0aG j  
       P=[P p*p]; *hWpJEV  
    end *@)0TL( 03  
    figure(1) .Q!_.LX  
    plot(P,P1, P,P2, P,P3); [`J91=  
    F \0>/  
    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~!~