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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 :I)WSXP9h  
    }5I+VY7a  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of .0gF&>I}  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of o/6 'g)r*  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear (n>gC  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 lCznH?[  
    ux 7^PTgcO  
    %fid=fopen('e21.dat','w'); *$4EXwt'  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) H`XE5Hk)P%  
    M1 =3000;              % Total number of space steps @ 7WWoy  
    J =100;                % Steps between output of space  oRbG6Vv/  
    T =10;                  % length of time windows:T*T0 <Y9 L3O`[  
    T0=0.1;                 % input pulse width %xH2jf  
    MN1=0;                 % initial value for the space output location ];n3H~2  
    dt = T/N;                      % time step 7"iUyZ(  
    n = [-N/2:1:N/2-1]';           % Index )uJu.foE  
    t = n.*dt;   ]l~TI8gC  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 z(yJ/~m  
    u20=u10.*0.0;                  % input to waveguide 2 oOj7y>Nm  
    u1=u10; u2=u20;                 "G+g(?N]j  
    U1 = u1;   h>A~..  
    U2 = u2;                       % Compute initial condition; save it in U ;]/emw=a  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ZjEc\{ s  
    w=2*pi*n./T; rda/  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T pm.Zc'23  
    L=4;                           % length of evoluation to compare with S. Trillo's paper j-% vLL/  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 `wzb}"gLsM  
    for m1 = 1:1:M1                                    % Start space evolution z3\WcW7|  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 63EwV p/|  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; n*Q~<`T  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform Qel2OI`b  
       ca2 = fftshift(fft(u2)); LZ ?z5U:  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation vs`"BQYf  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   *T+Bjj;w  
       u2 = ifft(fftshift(c2));                        % Return to physical space Wvg+5Q  
       u1 = ifft(fftshift(c1)); vfn _Nq;  
    if rem(m1,J) == 0                                 % Save output every J steps. LMF@-j%  
        U1 = [U1 u1];                                  % put solutions in U array \@3B%RW0  
        U2=[U2 u2]; p;P"mp\'  
        MN1=[MN1 m1]; ^^O @ [_  
        z1=dz*MN1';                                    % output location zP F0M(  
      end Xv~v=.HNhk  
    end LxcC5/@\~(  
    hg=abs(U1').*abs(U1');                             % for data write to excel -{^IT`  
    ha=[z1 hg];                                        % for data write to excel Tgf#I*(^]  
    t1=[0 t']; %O=U|tuc$  
    hh=[t1' ha'];                                      % for data write to excel file d[p-zn.  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format .d4L@{V  
    figure(1) D #`o  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn Ui^~A  
    figure(2) wd 4]Z0;  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn }r+(Z.BHM  
    vzr?#FG  
    非线性超快脉冲耦合的数值方法的Matlab程序 I 19 /  
    ;E!(W=]*F  
    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。   !P_8D*^9  
    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 {`Jr$*;  
    3 W%Bsqn  
    \E!a=cL!  
    'UW(0 PXw  
    %  This Matlab script file solves the nonlinear Schrodinger equations .:`+4n  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of "IjCuR;#  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ;aY.CgX  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 )37.H^7  
    pKnM=N1f  
    C=1;                           W`qiPLk  
    M1=120,                       % integer for amplitude r&MHww1i  
    M3=5000;                      % integer for length of coupler ?3 #W7sF  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Y%i=u:}fm  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. vq.~8c1  
    T =40;                        % length of time:T*T0. Ub(8ko:8$  
    dt = T/N;                     % time step C,;hNg[  
    n = [-N/2:1:N/2-1]';          % Index >R9_ ;  
    t = n.*dt;   HZG^o^o1l+  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. j.b7<Vr4;  
    w=2*pi*n./T; QXQ'QEG  
    g1=-i*ww./2; sM4Qu./  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; n' XvPV|  
    g3=-i*ww./2; @jKiE%OP  
    P1=0; YV6@SXy  
    P2=0; ,D6hJ_:  
    P3=1; ^h c&rD)_  
    P=0; ptCFW_UV  
    for m1=1:M1                 Qh0tU<jG  
    p=0.032*m1;                %input amplitude |SO?UIWp  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 (Ov{gj^  
    s1=s10; L,m'/}$  
    s20=0.*s10;                %input in waveguide 2 +5zLQ>]z  
    s30=0.*s10;                %input in waveguide 3 XMR$I&;G8  
    s2=s20; "5 /i  
    s3=s30; ~)Z MGx  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   7jj.maK  
    %energy in waveguide 1 :Z}d#Rbl  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));    Xf4   
    %energy in waveguide 2 gH0' Ok'  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   DaA9fJ7a   
    %energy in waveguide 3 FuWMVT`Y  
    for m3 = 1:1:M3                                    % Start space evolution HFtl4P  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS z vM=k-Ec  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; MM+xm{4l  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; go6XUe  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Ve]ufn6  
       sca2 = fftshift(fft(s2)); efc<lSUR  
       sca3 = fftshift(fft(s3)); f>*D@TrU  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   k2"DFXsv  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); h~!KNF*XW  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); (9"w{pnlLc  
       s3 = ifft(fftshift(sc3)); %gd {u\h^  
       s2 = ifft(fftshift(sc2));                       % Return to physical space 3?R56$-+  
       s1 = ifft(fftshift(sc1)); _F2 R x@Y  
    end \),DW)  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 5-=&4R\k  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); #><P28m  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); I 3ZlKI  
       P1=[P1 p1/p10]; r I-A)b4  
       P2=[P2 p2/p10]; V!|:rwG2  
       P3=[P3 p3/p10]; /K@_O\+;Q  
       P=[P p*p]; UdIl5P  
    end !LG 5q/}&  
    figure(1) feSj3,<!  
    plot(P,P1, P,P2, P,P3); y7x&/2  
    ;Sc}e/WJj  
    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~!~