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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 正序阅读 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 q2HYiH^L  
    <dyewy*.L  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of tabT0  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of HF|oBX$_  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear fnx-s{c?  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [qsEUc+Z.'  
    \EseGgd21  
    %fid=fopen('e21.dat','w'); 0!v ->Dk  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) @cU&n6C@  
    M1 =3000;              % Total number of space steps % `Z! 4L  
    J =100;                % Steps between output of space G "P4-  
    T =10;                  % length of time windows:T*T0 ybp -$e  
    T0=0.1;                 % input pulse width E*i#?u  
    MN1=0;                 % initial value for the space output location &/,|+U[  
    dt = T/N;                      % time step r'gOVi4t1*  
    n = [-N/2:1:N/2-1]';           % Index F;^F+H  
    t = n.*dt;   `~eUee3b.~  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 |7x\m t  
    u20=u10.*0.0;                  % input to waveguide 2 K98i[,rP  
    u1=u10; u2=u20;                 gv5*!eI  
    U1 = u1;   ^n0]dizB  
    U2 = u2;                       % Compute initial condition; save it in U @JdZ5Q  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. YJ$1N!rG  
    w=2*pi*n./T; q+,Q<2J  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T ^pHq66d%Z  
    L=4;                           % length of evoluation to compare with S. Trillo's paper Sp@-p9#  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 G@j0rnn>B  
    for m1 = 1:1:M1                                    % Start space evolution T0]MuIJ).  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS -_$$Te  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; cu+FM  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ](|\whI  
       ca2 = fftshift(fft(u2)); nB .G  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation [` sL?&a  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   nT2)E&U6%  
       u2 = ifft(fftshift(c2));                        % Return to physical space ToYAW,U[d  
       u1 = ifft(fftshift(c1)); /*0K92NB  
    if rem(m1,J) == 0                                 % Save output every J steps. Bj7gQ%>H4  
        U1 = [U1 u1];                                  % put solutions in U array  T Q,?>6n  
        U2=[U2 u2]; @IXsy  
        MN1=[MN1 m1]; v$^Z6>vVI  
        z1=dz*MN1';                                    % output location %.Q !oYehj  
      end 6Cp]NbNrq  
    end >t7x>_~   
    hg=abs(U1').*abs(U1');                             % for data write to excel K(aJi,e>  
    ha=[z1 hg];                                        % for data write to excel y|wc ,n%L>  
    t1=[0 t']; {s;U~!3aY  
    hh=[t1' ha'];                                      % for data write to excel file *g^x*|f6  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Z(Jt~a3o  
    figure(1) @V!r"Bkg.  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn _o8 ?E&d  
    figure(2) 1@$Ko5  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ZRYEqSm  
    ++E3]X|  
    非线性超快脉冲耦合的数值方法的Matlab程序 V*~Zs'L'E  
    }u1O#L}F5  
    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。   &4_qF^9J  
    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 3 h<,  
    0bo/XUpi  
    vhhC> 7  
    o6p98Dpg   
    %  This Matlab script file solves the nonlinear Schrodinger equations ]LM-@G+Jz  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of `jOX6_z?I  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear }1rm  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 bcupo:N  
    4ni3kmvX  
    C=1;                           #^ ]n0!  
    M1=120,                       % integer for amplitude Si~vDQ7"  
    M3=5000;                      % integer for length of coupler G%Lt.?m[  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) B-r0"MX&  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 1x,tu}<u^  
    T =40;                        % length of time:T*T0. h\'n**f_x  
    dt = T/N;                     % time step SCTA=l.  
    n = [-N/2:1:N/2-1]';          % Index #BST lz  
    t = n.*dt;   L31|\x]  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. D$x_o!JT  
    w=2*pi*n./T; zLJ/5&  
    g1=-i*ww./2; 3g6j?yYqb  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; y8DhOlewQ  
    g3=-i*ww./2; jQ)T67  
    P1=0; +}a ]GTBgA  
    P2=0; 1</kTm/Qa  
    P3=1; .(WQYOMl0  
    P=0; %!1Q P[}K  
    for m1=1:M1                 }C|dyyr  
    p=0.032*m1;                %input amplitude B2O}1.  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 !3ctB3eJ  
    s1=s10; -! K-Htb-  
    s20=0.*s10;                %input in waveguide 2 [VWUqlNt>  
    s30=0.*s10;                %input in waveguide 3 kTvd+TP4  
    s2=s20; LupkrxV  
    s3=s30; ,f&5pw =  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   7t*"%]o  
    %energy in waveguide 1 1w&!H ]%{  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   9rA=pH%<>B  
    %energy in waveguide 2 _H/8_[xk  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   'f?$"U JF  
    %energy in waveguide 3 S1?-I_t+]  
    for m3 = 1:1:M3                                    % Start space evolution ',S'.U  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS rX1QMR7?  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; YSe.t_K2C  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ;"m ,:5%  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform &sd}ulEg`  
       sca2 = fftshift(fft(s2)); ~T89_L  
       sca3 = fftshift(fft(s3)); P$-X)c$&  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   n9xAPB }  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); ,zTy?OQ  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Zg.&V  
       s3 = ifft(fftshift(sc3)); [r[ =W!  
       s2 = ifft(fftshift(sc2));                       % Return to physical space Pp5^@A  
       s1 = ifft(fftshift(sc1)); @W9x$  
    end xagBORg+Bd  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); a 7,C>%I  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); z.I9wQ]X[  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); pLzk   
       P1=[P1 p1/p10]; Kc^;vT>3  
       P2=[P2 p2/p10]; *VZ5B<Ic  
       P3=[P3 p3/p10]; oo.2Dn6z  
       P=[P p*p]; 0a"c2J  
    end Xqm::1(-(  
    figure(1) I2nhqJy^  
    plot(P,P1, P,P2, P,P3); D= h)&  
    L;f!.FX#  
    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~!~