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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 {3V%  
    BbCt_z'  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of <W$Ig@4[.d  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of c UJUZ@ol  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Y$tgz)  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 {'(1c)q>  
    ^ W/,Z`  
    %fid=fopen('e21.dat','w'); ,B^NH7A:  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) C3m](%?   
    M1 =3000;              % Total number of space steps kaKV{;UM  
    J =100;                % Steps between output of space \W^+aNbv=8  
    T =10;                  % length of time windows:T*T0 d5b \kRr  
    T0=0.1;                 % input pulse width Yh^~4S?  
    MN1=0;                 % initial value for the space output location y2XeD=_'  
    dt = T/N;                      % time step BkZmE,  
    n = [-N/2:1:N/2-1]';           % Index cwe@W PE2  
    t = n.*dt;   HizMjJ|  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 {9 PeBc  
    u20=u10.*0.0;                  % input to waveguide 2 x+mf QcSD&  
    u1=u10; u2=u20;                 ;JNI $DR  
    U1 = u1;   k3:8T#N>!O  
    U2 = u2;                       % Compute initial condition; save it in U vocXk_  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. yP&SA+  
    w=2*pi*n./T; a.oZ}R7'Y  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T QH?}uX'x)G  
    L=4;                           % length of evoluation to compare with S. Trillo's paper OJ2O?Te8  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 Glt%%TJb   
    for m1 = 1:1:M1                                    % Start space evolution z3 zN^ZT  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS !'ylh8}  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; hM": ?Rx  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform SI/@Bbd=  
       ca2 = fftshift(fft(u2)); nWrkn m  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation k1EAmA l  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Wa/&H$d\u@  
       u2 = ifft(fftshift(c2));                        % Return to physical space "q-,140_  
       u1 = ifft(fftshift(c1)); yUZ;keQ_Tw  
    if rem(m1,J) == 0                                 % Save output every J steps. '[XtARtY`  
        U1 = [U1 u1];                                  % put solutions in U array !W^b:qjJ  
        U2=[U2 u2]; ?2;gmZd7  
        MN1=[MN1 m1]; upD 2vtU  
        z1=dz*MN1';                                    % output location =z=$S]qN  
      end (3H'!P7|~  
    end  3,7SGt r  
    hg=abs(U1').*abs(U1');                             % for data write to excel dc ]+1 A  
    ha=[z1 hg];                                        % for data write to excel 8Z^9r/%*Z  
    t1=[0 t']; AbWnDqv  
    hh=[t1' ha'];                                      % for data write to excel file (|(#W+l~  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format W~TT`%[  
    figure(1) 'dnTu@mUT  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn (l|:$%[0  
    figure(2) .x 1&   
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn c[/h7!/aH  
    \~3g*V  
    非线性超快脉冲耦合的数值方法的Matlab程序 c4T8eTKU  
    \xQ10\u  
    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。   @0XqUcV  
    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 4h|48</  
    r306`)kX  
    > xc7Hr~  
    G=[ =[o\  
    %  This Matlab script file solves the nonlinear Schrodinger equations q~3dbj  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of **zh>Y}6  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 8veYs`  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Jgf73IX[  
    {}vB# !  
    C=1;                           UuNcBzB2d  
    M1=120,                       % integer for amplitude %T.4Aj  
    M3=5000;                      % integer for length of coupler ]cz*k/*0  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) n1X.]|6'  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. rv(Qz|K@  
    T =40;                        % length of time:T*T0. 7~t,Pt)  
    dt = T/N;                     % time step mP1EWh|  
    n = [-N/2:1:N/2-1]';          % Index t+R8{9L-  
    t = n.*dt;   S{ v [65  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. i.0}d5Y  
    w=2*pi*n./T; +) pO82  
    g1=-i*ww./2; sC8C><y  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rPK)=[MZ  
    g3=-i*ww./2; Z#-:zD7_  
    P1=0; '?q \mi  
    P2=0; {=(GY@yU/  
    P3=1; 1 LgzqRq  
    P=0; O23dtH  
    for m1=1:M1                 \6UK:'5{  
    p=0.032*m1;                %input amplitude eiL  ;  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 r ek89.p  
    s1=s10; rt\i@}  
    s20=0.*s10;                %input in waveguide 2 {Jv m *   
    s30=0.*s10;                %input in waveguide 3 [SluYmW  
    s2=s20; KL2#Bm_  
    s3=s30; .A: #l?  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   {x3"/sF  
    %energy in waveguide 1 DEGEr-  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   D[.;-4"_  
    %energy in waveguide 2 *x^W`i   
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   `@8QQB  
    %energy in waveguide 3 ";jj`  
    for m3 = 1:1:M3                                    % Start space evolution 'USol<  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 3SRz14/W_R  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; -}liG  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 5jj<sj!S  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform .%{3#\  
       sca2 = fftshift(fft(s2)); !n<vN@V*3d  
       sca3 = fftshift(fft(s3));  V~V_+  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   9{gY|2R_  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); _z:7Dj#  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ;\N{z6  
       s3 = ifft(fftshift(sc3)); "3kIQsD|j  
       s2 = ifft(fftshift(sc2));                       % Return to physical space {uO=Wkp~7  
       s1 = ifft(fftshift(sc1)); LwpO_/qV  
    end @M[t|  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 3BBw:)V  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); M.|@|If4?  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); nLn3kMl4  
       P1=[P1 p1/p10]; C_SJ4Sh  
       P2=[P2 p2/p10]; HZp}<7NR(7  
       P3=[P3 p3/p10]; 2}Ga   
       P=[P p*p]; I]HrtI  
    end t'msgC6=>u  
    figure(1) c/fU0cA@  
    plot(P,P1, P,P2, P,P3); n H)6mOYp  
    X.u&4SH  
    转自:http://blog.163.com/opto_wang/
     
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    离线ciomplj
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~