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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 t'Eb#Nup3  
    +rsl( 08FY  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of Bhu@ 2KdA  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ^0~c 7`k`V  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear >bA$SN  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Yn4)Zhkk  
    aM{@1m Bm  
    %fid=fopen('e21.dat','w'); UV']NH h  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) FL`1yD^2  
    M1 =3000;              % Total number of space steps w3<"g&n|  
    J =100;                % Steps between output of space :'y{dbKp"  
    T =10;                  % length of time windows:T*T0 dv'E:R(a  
    T0=0.1;                 % input pulse width s[3![ "^Y  
    MN1=0;                 % initial value for the space output location J1tzHa6  
    dt = T/N;                      % time step m0|Ae@g~3  
    n = [-N/2:1:N/2-1]';           % Index n{64g+  
    t = n.*dt;   au~]  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 9^PRX  
    u20=u10.*0.0;                  % input to waveguide 2 *M wfod  
    u1=u10; u2=u20;                 )WVItqQKV  
    U1 = u1;   \5Vp6^  
    U2 = u2;                       % Compute initial condition; save it in U BbrT f"`  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. fW.GNX8  
    w=2*pi*n./T; _{e&@ d  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T %j *k  
    L=4;                           % length of evoluation to compare with S. Trillo's paper (_w %  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 _Z+jQFKJ\8  
    for m1 = 1:1:M1                                    % Start space evolution `6Ureui2?  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ,u}<Ws8N  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; S5~`T7Ra  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform L\b]k,Ksf  
       ca2 = fftshift(fft(u2)); X`yNR;>  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ~$4]HDg  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   G la@l<  
       u2 = ifft(fftshift(c2));                        % Return to physical space Z|ZBKcmg  
       u1 = ifft(fftshift(c1)); <i}q=%W!1  
    if rem(m1,J) == 0                                 % Save output every J steps. d"H<e}D  
        U1 = [U1 u1];                                  % put solutions in U array {)B9Z I{+A  
        U2=[U2 u2]; ORowx,(hX  
        MN1=[MN1 m1]; sDLS*467  
        z1=dz*MN1';                                    % output location _0,"vFdj  
      end .pZo(*  
    end ~`t%M?l  
    hg=abs(U1').*abs(U1');                             % for data write to excel ?R;nL{  
    ha=[z1 hg];                                        % for data write to excel >ik1]!j]Lv  
    t1=[0 t']; ybZ}  
    hh=[t1' ha'];                                      % for data write to excel file i8Fs0U4"  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format I*D<J$ 9N  
    figure(1) XzT78  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn k)`$%[K8  
    figure(2) ~J0,)_b%*  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn n{dP@_>WS  
    .zvlRt.zl  
    非线性超快脉冲耦合的数值方法的Matlab程序 W|ReLM\  
    aS,a_b]  
    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。   +0]'| tF>  
    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 2m_'z  
    :T_'n,  
    8 +"10q-  
    *(k%MTG  
    %  This Matlab script file solves the nonlinear Schrodinger equations ~|&="K4,:  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of yeh8z:5Z O  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 'pan9PW  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 1g1?zk8zO  
    bxAsV/j  
    C=1;                           hUVk54~l  
    M1=120,                       % integer for amplitude @l'G[jN5  
    M3=5000;                      % integer for length of coupler E;6~R M:  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) H(G!t`K  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. Mx8Gu^FW.d  
    T =40;                        % length of time:T*T0. nO~b=qO  
    dt = T/N;                     % time step %X;7--S%?g  
    n = [-N/2:1:N/2-1]';          % Index |/VL35b  
    t = n.*dt;   75ZH  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 9#uIC7M  
    w=2*pi*n./T; =HVfJ"vK  
    g1=-i*ww./2; 2B-.}OJ  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; *B1x`=  
    g3=-i*ww./2; -'6<   
    P1=0; 7Rnm%8?T  
    P2=0; : (gZgMT  
    P3=1; ! .AhzU1%Y  
    P=0; GuT6K}~|D  
    for m1=1:M1                 LfEvc2 v=g  
    p=0.032*m1;                %input amplitude czI{qi5N  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 )!e3.C|V1W  
    s1=s10; Go1(@  
    s20=0.*s10;                %input in waveguide 2 tQrS3Hz'nA  
    s30=0.*s10;                %input in waveguide 3 Z==!C=SBv  
    s2=s20; Hle\ON  
    s3=s30; &y7 0  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   .d~\Ysve  
    %energy in waveguide 1 8lwFAiC8  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   CM9XPr  
    %energy in waveguide 2 /HkFlfPd  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ' WQdr(  
    %energy in waveguide 3 PL@~Ys0  
    for m3 = 1:1:M3                                    % Start space evolution (? \?it-  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ?q _^Rj$  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; }X]\VSF{  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; j$Nf%V 6Y  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform mQ}Gh_'ps  
       sca2 = fftshift(fft(s2)); H?tUCbw  
       sca3 = fftshift(fft(s3)); 1AF%-<`?s  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ;1 |x  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); O|I+],  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Sh&iQ_vq  
       s3 = ifft(fftshift(sc3)); y7z(&M@  
       s2 = ifft(fftshift(sc2));                       % Return to physical space rVH6QQF=\  
       s1 = ifft(fftshift(sc1)); 2ev*CX6.  
    end '.(~  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); T~Ly^|Ihz  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); J!hFN]M<<  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); EyY],W1 Y  
       P1=[P1 p1/p10]; X4wH/q^  
       P2=[P2 p2/p10]; =A@>I0(7  
       P3=[P3 p3/p10]; vT c7an6fy  
       P=[P p*p]; ;F5"}x  
    end s\gp5MT  
    figure(1) R4{-Qv#8 q  
    plot(P,P1, P,P2, P,P3); :"QfF@Z{  
    E9+HS  
    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~!~