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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 prIJjy-F  
    V1G5Kph  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 0lcwc"_DZX  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ov\%*z2=  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear c^&:':Z%'  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 QZO<'q`L  
    L+lye Ir'  
    %fid=fopen('e21.dat','w'); K&=6DvfR  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) v] Xy^7?  
    M1 =3000;              % Total number of space steps y|9 LtQ  
    J =100;                % Steps between output of space i !SN"SY  
    T =10;                  % length of time windows:T*T0 ^;\6ju2  
    T0=0.1;                 % input pulse width rXe+#`m2  
    MN1=0;                 % initial value for the space output location K #JO#  
    dt = T/N;                      % time step abEdZ)$  
    n = [-N/2:1:N/2-1]';           % Index NB(  GE  
    t = n.*dt;   b+CvA(*  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 N a.e1A&?j  
    u20=u10.*0.0;                  % input to waveguide 2 )^E6VD&6  
    u1=u10; u2=u20;                  f|yq~3x)  
    U1 = u1;   REk^pZ3B  
    U2 = u2;                       % Compute initial condition; save it in U XFww|SG$  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Fy_~~nI0  
    w=2*pi*n./T; x^pHP|<3`  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 5(Xq58nhxI  
    L=4;                           % length of evoluation to compare with S. Trillo's paper g^\>hjNX  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 x_4{MD^%  
    for m1 = 1:1:M1                                    % Start space evolution %.{xo.`a[  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS aprgThoD  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; [ID#P Ule  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 8Y;>3z th7  
       ca2 = fftshift(fft(u2)); o 7&q  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation |qq29dS?  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   h#|Ac>fz  
       u2 = ifft(fftshift(c2));                        % Return to physical space )f%Q7  
       u1 = ifft(fftshift(c1)); M3)Id?|]6  
    if rem(m1,J) == 0                                 % Save output every J steps. +2s][^-KV  
        U1 = [U1 u1];                                  % put solutions in U array cW^u4%f't'  
        U2=[U2 u2]; oR<;Tr~{q  
        MN1=[MN1 m1]; N$8"X-na?  
        z1=dz*MN1';                                    % output location $[(FCS  
      end qKuHd~M{ 1  
    end mi sPJO&QD  
    hg=abs(U1').*abs(U1');                             % for data write to excel M;@/697G  
    ha=[z1 hg];                                        % for data write to excel \3j4=K'nE  
    t1=[0 t']; 93Qx+oK]  
    hh=[t1' ha'];                                      % for data write to excel file *eUxarI  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ]=]`Mnuxb  
    figure(1) `SYq/6$VEH  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 0:>C v<N  
    figure(2) '[[*(4 a3  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^c>ROpic  
    `%0k\,}V  
    非线性超快脉冲耦合的数值方法的Matlab程序 O'W[/\A56M  
    8PW3x-+  
    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。   =,W~^<\"  
    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 Y2y = P  
    mC`U"rlK~  
    _We4%  
    BH?fFe&J:`  
    %  This Matlab script file solves the nonlinear Schrodinger equations  OV$|!n  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of T7 XbbU  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear a[V4EX1E  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 J`A )WsKkb  
    'Z^KpW  
    C=1;                           &uu69)u  
    M1=120,                       % integer for amplitude A)o%\j  
    M3=5000;                      % integer for length of coupler bRc~e@  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) p/&s-G F  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. K>`*JJ,  
    T =40;                        % length of time:T*T0. 1|#j/  
    dt = T/N;                     % time step 1`EkN0iZ  
    n = [-N/2:1:N/2-1]';          % Index vtf`+q  
    t = n.*dt;   m9 f[nT  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. |K$EULzz  
    w=2*pi*n./T; ::G0v  
    g1=-i*ww./2; #N|A@B5 x  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Gv }~  
    g3=-i*ww./2; VWE`wan<  
    P1=0; qu0dWgK  
    P2=0; uF\f>E)/N%  
    P3=1; ln=:E$jX  
    P=0; *[wj )  
    for m1=1:M1                 [%BWCd8Q~P  
    p=0.032*m1;                %input amplitude n%:&N   
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 #jR1ti)p  
    s1=s10; Ng<oz*>U  
    s20=0.*s10;                %input in waveguide 2 H=7Nh6v  
    s30=0.*s10;                %input in waveguide 3 -Mufo.Jz1o  
    s2=s20; }h_= n>  
    s3=s30; -#"7F:N1  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Z"g6z#L&  
    %energy in waveguide 1 *v9 {f?  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   GF awmNZ  
    %energy in waveguide 2 7W\aX*]  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   E,:E u<  
    %energy in waveguide 3 0@PI=JZ%  
    for m3 = 1:1:M3                                    % Start space evolution i?pC[Ao-_  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS V(6ovJpA0  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; LDv>hzo  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; +%RB&:K7,  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform v?(9ZY]  
       sca2 = fftshift(fft(s2)); 8 n)3'ok  
       sca3 = fftshift(fft(s3)); gpzZs<ST  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   !7fVO2m T  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); LuW^Ga"E  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 1q;r4$n  
       s3 = ifft(fftshift(sc3)); B#;0{  
       s2 = ifft(fftshift(sc2));                       % Return to physical space d<B=p&~  
       s1 = ifft(fftshift(sc1)); M-+= t8  
    end #sp8 !8|y  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); WL/9r *jW  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); b_j8g{/9  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |F^h >^ x  
       P1=[P1 p1/p10]; AIa#t#8${  
       P2=[P2 p2/p10]; n"c3C)  
       P3=[P3 p3/p10]; ~`Xu 6+1o  
       P=[P p*p]; 2k3yf_N  
    end TdH~ sz  
    figure(1) 4Z<  
    plot(P,P1, P,P2, P,P3); \H5{[ZUn  
    T hLR<\  
    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~!~