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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 97~>gFU77#  
    I0qJr2[X~  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of sWB@'P:x  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 0+u >"7T  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ,Xr`tQ<@  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 9dm<(I}  
    H_Xk;fM  
    %fid=fopen('e21.dat','w'); ^;F5ymb3U  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ]0BX5Z'  
    M1 =3000;              % Total number of space steps 6nR EuT'k  
    J =100;                % Steps between output of space n`@dk_%yI  
    T =10;                  % length of time windows:T*T0 f( Dtv  
    T0=0.1;                 % input pulse width z`.<dNg  
    MN1=0;                 % initial value for the space output location ,fqM>Q  
    dt = T/N;                      % time step 6kMkFZ}+  
    n = [-N/2:1:N/2-1]';           % Index xR8.1T?8  
    t = n.*dt;   >2= Y 35j  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 RWX!d54&  
    u20=u10.*0.0;                  % input to waveguide 2 <1B+@  
    u1=u10; u2=u20;                 ~mwIr  
    U1 = u1;   8!HB$vdw7  
    U2 = u2;                       % Compute initial condition; save it in U 7 \[fjCg\w  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. bwcr/J( Nb  
    w=2*pi*n./T; t\ a|Gp W  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 2i;ox*SfpU  
    L=4;                           % length of evoluation to compare with S. Trillo's paper cA|vH^:  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 gFrNk Uqp  
    for m1 = 1:1:M1                                    % Start space evolution >]&Ow9-  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS Yi)s=Q:  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; t%J1(H  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform Z[ &d2'  
       ca2 = fftshift(fft(u2)); ek U%^R<  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Jz3,vV fQ:  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   M] +.xo+A  
       u2 = ifft(fftshift(c2));                        % Return to physical space vU5}E\Ny  
       u1 = ifft(fftshift(c1)); ;<thEWH;Y  
    if rem(m1,J) == 0                                 % Save output every J steps. KV$4}{  
        U1 = [U1 u1];                                  % put solutions in U array D6|-nl  
        U2=[U2 u2]; ^sFO[cYo  
        MN1=[MN1 m1]; ipl,{  
        z1=dz*MN1';                                    % output location Gi#-TP\  
      end V0# Ocq,  
    end k<CbI V  
    hg=abs(U1').*abs(U1');                             % for data write to excel Hb::;[bm:  
    ha=[z1 hg];                                        % for data write to excel Dte5g),R  
    t1=[0 t']; erbk (  
    hh=[t1' ha'];                                      % for data write to excel file Gk/cP`  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format %?aq1 =B  
    figure(1) >T c\~l  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn j;7E+Yp  
    figure(2) s@5~Hy eI  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn {7c'%e  
    YYPJ (o\  
    非线性超快脉冲耦合的数值方法的Matlab程序 m{?f,Q=u@  
    yjMN>L'  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   JAP(J~  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 s,8zj<dUv  
    ;^0rY)&  
    |FM*1Q[1  
    '21gUYm  
    %  This Matlab script file solves the nonlinear Schrodinger equations S4[ #[w`=  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of k4hk* 0Jq  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3Jt# Mp  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 (_<,Oj#*S  
    S*|/txE'~Y  
    C=1;                           =-X-${/  
    M1=120,                       % integer for amplitude M@<9/xPS  
    M3=5000;                      % integer for length of coupler vNrn]v=|}7  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) i}P{{kMJ  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. %Nv w`H  
    T =40;                        % length of time:T*T0. `]XI Q\ *  
    dt = T/N;                     % time step X<Z(,B  
    n = [-N/2:1:N/2-1]';          % Index fByf~iv,  
    t = n.*dt;   XD|g G  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. l v hJ  
    w=2*pi*n./T; uC#@qpzy  
    g1=-i*ww./2; ;H.V-~:P)  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; mfaU_Vo&  
    g3=-i*ww./2; _p+E(i 9  
    P1=0; jVQ89vf ~  
    P2=0; @sA!o[gH  
    P3=1; FE&:?  
    P=0; 9J?s:"j  
    for m1=1:M1                  0.0-rd>  
    p=0.032*m1;                %input amplitude >h#w~@e::  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 {vCtp   
    s1=s10; t(-,mw  
    s20=0.*s10;                %input in waveguide 2 nHk^trGm  
    s30=0.*s10;                %input in waveguide 3 $ P?^GB>u  
    s2=s20; _ `&l46  
    s3=s30; $Oy&PO e  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));    16~E  
    %energy in waveguide 1 D_0Vu/v  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   C-;w}  
    %energy in waveguide 2 ){"?@1vP  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   OQB7C0+ &  
    %energy in waveguide 3 W_JO~P  
    for m3 = 1:1:M3                                    % Start space evolution E'DHO2 Y  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS T-6<qh  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 3u$1W@T(  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; qrw  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 6X%g-aTs  
       sca2 = fftshift(fft(s2)); n"6L\u  
       sca3 = fftshift(fft(s3)); =!^ gQ0~4  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   v /c]=/  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); T!KwRxJ23  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); S* O. ?  
       s3 = ifft(fftshift(sc3)); ZDbe]9#Xh  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ChG7>4:\  
       s1 = ifft(fftshift(sc1)); ^zQI_ydG  
    end yvoz 3_!  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); o5?Y   
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); II}M|qHaK  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); s) shq3O  
       P1=[P1 p1/p10]; aYb97}kI  
       P2=[P2 p2/p10]; ;ISnI  
       P3=[P3 p3/p10]; 3yKmuu!  
       P=[P p*p]; Tgr,1) T  
    end 2icQ (H;  
    figure(1) U\tx{CsSz  
    plot(P,P1, P,P2, P,P3); yW= +6@A4  
    *??lwvJp  
    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~!~