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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 $.``OxJk%  
    IeH^Wm&^  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of |^ ?`Q.|c$  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Bpm,mp4g\#  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear k&yQ98H$K"  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004  8>ESD}(  
    '^e0Ud,  
    %fid=fopen('e21.dat','w'); (VfwLo>#  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) - Sx0qi'%  
    M1 =3000;              % Total number of space steps l},dQ4R  
    J =100;                % Steps between output of space hH#lTye  
    T =10;                  % length of time windows:T*T0 z/)$D  
    T0=0.1;                 % input pulse width :,jPNuOA  
    MN1=0;                 % initial value for the space output location EG%I1F%  
    dt = T/N;                      % time step DQ%`v =  
    n = [-N/2:1:N/2-1]';           % Index ix:2Z-  
    t = n.*dt;   '^8g9E .4K  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 c$.UE  
    u20=u10.*0.0;                  % input to waveguide 2 E2h(w_l  
    u1=u10; u2=u20;                 HJc<Gwm  
    U1 = u1;   [+y &HNf  
    U2 = u2;                       % Compute initial condition; save it in U ,|6Y\L  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. "pOqd8>]  
    w=2*pi*n./T; ?0 HR(N(z!  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T @<|6{N<  
    L=4;                           % length of evoluation to compare with S. Trillo's paper :wFb5"  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 >ze>Xr'm5=  
    for m1 = 1:1:M1                                    % Start space evolution R_t~UTfI;  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS )uANmThOz  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Rk}\)r\  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 2TE\4j  
       ca2 = fftshift(fft(u2)); G!nl'5|y  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation [SK2x4  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ur?d6 a  
       u2 = ifft(fftshift(c2));                        % Return to physical space XAw2X;F%  
       u1 = ifft(fftshift(c1)); ~azF+}x90N  
    if rem(m1,J) == 0                                 % Save output every J steps. _2wAaJvA  
        U1 = [U1 u1];                                  % put solutions in U array ^cB49s+{e  
        U2=[U2 u2]; ${wU+E*  
        MN1=[MN1 m1]; =g/4{IL%  
        z1=dz*MN1';                                    % output location Ii|uGxEc  
      end W^^K0yn`@  
    end bjuYA/w<  
    hg=abs(U1').*abs(U1');                             % for data write to excel &,^mM' C  
    ha=[z1 hg];                                        % for data write to excel CR%D\I$o  
    t1=[0 t']; MomLda V9Q  
    hh=[t1' ha'];                                      % for data write to excel file !>CE(;E>z  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 2O?Vr" A  
    figure(1) /7c2OI=\  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn >_rzT9gX&  
    figure(2) j kSc&  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn W/#KX}4  
    f+*J ue  
    非线性超快脉冲耦合的数值方法的Matlab程序 `)0Rv|?  
    !y.ei1diw  
    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。    ` 2Wl  
    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 _Syre6k  
    J@oEV=L  
    7xX;MB &  
    "2*G$\  
    %  This Matlab script file solves the nonlinear Schrodinger equations t.3Ct@wK  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 9 yh9HE  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 6XQ*:N/4al  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 |Dl*w/n  
    !Sh^LYqn  
    C=1;                           6Hc H'nmeN  
    M1=120,                       % integer for amplitude MDMtOfe|  
    M3=5000;                      % integer for length of coupler k)?,xY\AV  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) \;nD)<)J  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. s/r5,IFR  
    T =40;                        % length of time:T*T0. \pjRv  
    dt = T/N;                     % time step Nr> c'TH  
    n = [-N/2:1:N/2-1]';          % Index *LY~l  
    t = n.*dt;   aO~s i=  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 8 m%>:}o  
    w=2*pi*n./T; *ah>-}-  
    g1=-i*ww./2; ( rA\_FOJ  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 2#>$%[   
    g3=-i*ww./2; *ge].E  
    P1=0; UN cYu9[  
    P2=0; \[Sm2/9v  
    P3=1; FQ ;4'B^k]  
    P=0; ZA *b9W  
    for m1=1:M1                 9oZ } h&  
    p=0.032*m1;                %input amplitude 8QkWgd7y  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 )e4WAlg8c  
    s1=s10; J!21`M-Ue  
    s20=0.*s10;                %input in waveguide 2 N&6_8=3z  
    s30=0.*s10;                %input in waveguide 3 qZT 4+&y  
    s2=s20; `_NnQ%  
    s3=s30; /#S4espE  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   nz,Mqol  
    %energy in waveguide 1 ig2{lEkF  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   .V5q$5j  
    %energy in waveguide 2 $nUd\B$.=  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   8m#}S\m  
    %energy in waveguide 3 ,pQ'w7  
    for m3 = 1:1:M3                                    % Start space evolution ?noETHz)  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS \iFMU#  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; {] t\`fjrg  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; c8bca`  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform XM$5S+e  
       sca2 = fftshift(fft(s2));  ltCwns  
       sca3 = fftshift(fft(s3)); 21[K[ %  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   !Z<mrr;T@  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); \Dvl%:8   
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 4 7)+'`  
       s3 = ifft(fftshift(sc3)); Bo\a  
       s2 = ifft(fftshift(sc2));                       % Return to physical space D..{|29,:  
       s1 = ifft(fftshift(sc1)); AijPN  
    end jI*}y[o  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 9[epr+f  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); R9b/?*%=9  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); EIq{C-(  
       P1=[P1 p1/p10]; l _kg3e4  
       P2=[P2 p2/p10]; otmIu`h  
       P3=[P3 p3/p10]; y1,?ZWTayr  
       P=[P p*p]; jRv;D#Hp  
    end _~X8/p/Qh  
    figure(1) ^%K1R;  
    plot(P,P1, P,P2, P,P3); n9<roH  
    A%NK0j$;}  
    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~!~