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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 qvhTc6oH  
    6^}GXfJAc  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ~@MIG  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 9:4P7  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 2}' &38wMT  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 03AYW)"}M  
    xlv:+  
    %fid=fopen('e21.dat','w'); % UY=VE\F  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Y Q3%vH5#y  
    M1 =3000;              % Total number of space steps /Y%) Y  
    J =100;                % Steps between output of space v )4 kS  
    T =10;                  % length of time windows:T*T0 FHqa|4Ie  
    T0=0.1;                 % input pulse width q1`uS^3`  
    MN1=0;                 % initial value for the space output location +#,t  
    dt = T/N;                      % time step ,k+jx53XV  
    n = [-N/2:1:N/2-1]';           % Index Oa CkU  
    t = n.*dt;   2mVH*\D  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 I)O%D3wfMW  
    u20=u10.*0.0;                  % input to waveguide 2 IcI y  
    u1=u10; u2=u20;                 z35n3q  
    U1 = u1;   }DY^a'wJ-  
    U2 = u2;                       % Compute initial condition; save it in U xL=g(FN(6L  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 24>{T5E  
    w=2*pi*n./T; ~iyd p  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T **dGK_^T0  
    L=4;                           % length of evoluation to compare with S. Trillo's paper ib*$3Fn~  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 UFC.!t-Z  
    for m1 = 1:1:M1                                    % Start space evolution &%C4rAd2  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS >c8zMd  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ^7~=+0cF]  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform OCY7Bls4  
       ca2 = fftshift(fft(u2)); l?Bv9k.^?  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation JwxI8Pi*y  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   C7eaioW$  
       u2 = ifft(fftshift(c2));                        % Return to physical space Pg|q{fc  
       u1 = ifft(fftshift(c1)); X7Cou6r  
    if rem(m1,J) == 0                                 % Save output every J steps. X}h{xl   
        U1 = [U1 u1];                                  % put solutions in U array wF$8#=  
        U2=[U2 u2]; 4VD'<`R[  
        MN1=[MN1 m1]; GDZe6*  
        z1=dz*MN1';                                    % output location 6(<AuhFu  
      end Y')in7g  
    end H /*^$>0Uo  
    hg=abs(U1').*abs(U1');                             % for data write to excel <),FI <~  
    ha=[z1 hg];                                        % for data write to excel b> &kL  
    t1=[0 t']; {- 7T\mj  
    hh=[t1' ha'];                                      % for data write to excel file RR*z3i`PP  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 'R,1Jmx  
    figure(1) w'?uJW  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn (y=P-nm  
    figure(2) 3QM.X^ANH  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn r]kLe2r:B  
    <b{Le{QJ*  
    非线性超快脉冲耦合的数值方法的Matlab程序 VL7zU->  
    W(a=ev2sa  
    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。   T[~ak"M  
    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 2Q-kD?PO,  
    G{YJ(6etZ  
    NrhU70y  
    6(<M.U_ft  
    %  This Matlab script file solves the nonlinear Schrodinger equations *.ZV.(  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of &z&Jl#t-)  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear D{PO!WzW  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9Z6O{ >  
    htkn#s~=  
    C=1;                           `cMa Fc-y/  
    M1=120,                       % integer for amplitude %~}9#0h)  
    M3=5000;                      % integer for length of coupler ! FhN(L[=j  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) HVh+Z k  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. q J@XVN4   
    T =40;                        % length of time:T*T0. & i)p^AmM  
    dt = T/N;                     % time step  Z\4l+.R`  
    n = [-N/2:1:N/2-1]';          % Index rnEWTk7&  
    t = n.*dt;   OAc+LdT  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. "72 _Sw  
    w=2*pi*n./T; $NT{ssh  
    g1=-i*ww./2; j""u:l^+x  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rP^2MH"  
    g3=-i*ww./2;  ceyZ4M  
    P1=0; +'y$XR~W{  
    P2=0; W5HC7o\4  
    P3=1; [gqV}Y"Md  
    P=0; jbMzcn~ehI  
    for m1=1:M1                 (VU: &.  
    p=0.032*m1;                %input amplitude ZMy,<wk  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 WSWaq\9]8  
    s1=s10; o%RyE]pw,  
    s20=0.*s10;                %input in waveguide 2 Y{f;qbEQH'  
    s30=0.*s10;                %input in waveguide 3 ]@C&Q,~q  
    s2=s20; 1`X{$mxw  
    s3=s30; C[|jJ9VE,  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   )zz"DH  
    %energy in waveguide 1 _LCK|H%v'  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   `>g: :  
    %energy in waveguide 2 8! pfy"  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   |r%6;8A]i  
    %energy in waveguide 3 305()  
    for m3 = 1:1:M3                                    % Start space evolution eM*@}3  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS '\[GquK;P  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; "  q0lh  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 5O]ph[7  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 118A6qyi  
       sca2 = fftshift(fft(s2)); ROW8YTYb  
       sca3 = fftshift(fft(s3)); P!0uAkt9C  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   v0apEjT  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 8%U+y0j6b  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); "tn]s>iAd=  
       s3 = ifft(fftshift(sc3)); Fnzv&  
       s2 = ifft(fftshift(sc2));                       % Return to physical space mC8c`# 1T  
       s1 = ifft(fftshift(sc1)); 5)AMl)  
    end mXAX%M U  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); P I)lJ\  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); )8!""n~  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 18zv]v %  
       P1=[P1 p1/p10]; ]wc'h>w  
       P2=[P2 p2/p10]; 1\$xq9  
       P3=[P3 p3/p10]; zw_Xh~4"b  
       P=[P p*p]; |zKFF?7#wE  
    end +%UfnbZ  
    figure(1) K_G( J>  
    plot(P,P1, P,P2, P,P3); dNUi|IYm$  
    6:fe.0H 9  
    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~!~