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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 H+@?K6{h  
    ~PU}==*q  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ^+gD;a|t  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of NbCIL8f]  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Bgp%hK  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 I|;C} lfp  
    K4I/a#S'@6  
    %fid=fopen('e21.dat','w'); I]3!M`IMG  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Hw6 2'%  
    M1 =3000;              % Total number of space steps H6Gs&yk3  
    J =100;                % Steps between output of space I :bT"N  
    T =10;                  % length of time windows:T*T0 V 'fri/Z  
    T0=0.1;                 % input pulse width gv i!|!M=  
    MN1=0;                 % initial value for the space output location rV?@Kgxi  
    dt = T/N;                      % time step 1N5lI97j  
    n = [-N/2:1:N/2-1]';           % Index qv4r !x  
    t = n.*dt;    -rT#Wi  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 563ExibH  
    u20=u10.*0.0;                  % input to waveguide 2 @hrIu" '!  
    u1=u10; u2=u20;                 fKtlfQG  
    U1 = u1;   L|;sB=$'{  
    U2 = u2;                       % Compute initial condition; save it in U `DM)tm3&m  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Dd-a*6|x  
    w=2*pi*n./T; H^vA}F`  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T bQ&%6'ck  
    L=4;                           % length of evoluation to compare with S. Trillo's paper C~. T[Mlu  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 Prc1U)nfo  
    for m1 = 1:1:M1                                    % Start space evolution 'Z%1Ly^b  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS {.DY\;Q  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; WLta{A?  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform NW*#./WdF8  
       ca2 = fftshift(fft(u2)); ]Zc\si3i&  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation tCPK_Wws?Z  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   4]-7S l,  
       u2 = ifft(fftshift(c2));                        % Return to physical space 6Tc! =lk  
       u1 = ifft(fftshift(c1)); 2U"2L^oKI  
    if rem(m1,J) == 0                                 % Save output every J steps. "" _B3'  
        U1 = [U1 u1];                                  % put solutions in U array `0MQL@B  
        U2=[U2 u2]; BHErc\ITP  
        MN1=[MN1 m1];  5PC:4  
        z1=dz*MN1';                                    % output location ]\k& l ['  
      end c6y>]8_  
    end <P@O{Xi+K  
    hg=abs(U1').*abs(U1');                             % for data write to excel o02G:!gB  
    ha=[z1 hg];                                        % for data write to excel vo2GFo  
    t1=[0 t']; G)_Zls2 ;  
    hh=[t1' ha'];                                      % for data write to excel file L]&y[/\E1  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ?{5}3a bB`  
    figure(1) ~[~#PO  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn hb %F"Q  
    figure(2) {z;4t&5  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn (Jk[%_b>_  
    VWzuV&;P  
    非线性超快脉冲耦合的数值方法的Matlab程序 \w(0k^<7  
    :2')`xT  
    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。   |2rOV&@l9  
    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 LnsYtkb r  
     obPG]*3  
    (hIo0 .  
    9]1LwX!M2  
    %  This Matlab script file solves the nonlinear Schrodinger equations K@ &;f( Y  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of Q:T9&_|  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ]9JH.fF  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 7u5H o`  
    o)DO[  
    C=1;                           ?5,I`9  
    M1=120,                       % integer for amplitude %Nob B  
    M3=5000;                      % integer for length of coupler g-NrxyTBlx  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) pK"Z9y&  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. _={mKKoHs  
    T =40;                        % length of time:T*T0. y7GgTC/H  
    dt = T/N;                     % time step IY mkZ?cW  
    n = [-N/2:1:N/2-1]';          % Index qEl PYN*wF  
    t = n.*dt;   jpTk@  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. m&be55M;  
    w=2*pi*n./T; U}5]Vm$]  
    g1=-i*ww./2; rls{~ZRl  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; UISsiiG(  
    g3=-i*ww./2; kc}|L9  
    P1=0;  x\VP X  
    P2=0; hJz]N$@W  
    P3=1; 9U=6l]Np  
    P=0; 0($On`#  
    for m1=1:M1                 *&R|0I{>  
    p=0.032*m1;                %input amplitude j#Lj<jX!xR  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 DnW/q  
    s1=s10; #TH(:I=[  
    s20=0.*s10;                %input in waveguide 2 wx!2/I>  
    s30=0.*s10;                %input in waveguide 3 !T8sWMY  
    s2=s20; JeA_mtSQ|  
    s3=s30; lLglF4  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   &fU48n1Uh  
    %energy in waveguide 1 jR@>~t[}o  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   &n0Ag]$P  
    %energy in waveguide 2 c"t&,OU:  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   T1x67 b u  
    %energy in waveguide 3 sb?!U"v.'  
    for m3 = 1:1:M3                                    % Start space evolution aH8]$e8_,\  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS t}OzF cyqN  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; yMD0Tj5ZQ  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; Pt-O1$C[  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform ,Ik~E&Ku2'  
       sca2 = fftshift(fft(s2)); E0DquVrz  
       sca3 = fftshift(fft(s3)); /WK1(B:  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   T, PN6d  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); }Gx@1)??  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); E]r<t#  
       s3 = ifft(fftshift(sc3)); c>+68<H  
       s2 = ifft(fftshift(sc2));                       % Return to physical space t'.:"H8BI  
       s1 = ifft(fftshift(sc1)); n1PvZ~^3  
    end nHp$5|r<  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 'SrDc'?  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); l k /Ke  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); S1C#5=  
       P1=[P1 p1/p10]; \pSRG=`  
       P2=[P2 p2/p10]; *Gj`1# Z$  
       P3=[P3 p3/p10]; N3oa!PE  
       P=[P p*p]; ZW@cw}  
    end :2:%  
    figure(1) hPCSAo!|  
    plot(P,P1, P,P2, P,P3); vmo!  
    c%+uji6  
    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~!~