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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 Sjp ]TWj  
    D{rM  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of v>/_U  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 4n} a%ocv^  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Ay0.D FL  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 SS6K7  
    I8f='  
    %fid=fopen('e21.dat','w'); dJ {q}U  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) ]j0/.pG  
    M1 =3000;              % Total number of space steps h + <Jv   
    J =100;                % Steps between output of space L;-V Yo#  
    T =10;                  % length of time windows:T*T0 .Ta(v3om%  
    T0=0.1;                 % input pulse width CE@[Z  
    MN1=0;                 % initial value for the space output location g OK   
    dt = T/N;                      % time step UM<!bNz`  
    n = [-N/2:1:N/2-1]';           % Index Z&of-[)  
    t = n.*dt;   cH6++r  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 -B& Nou  
    u20=u10.*0.0;                  % input to waveguide 2 +c$:#9$ |  
    u1=u10; u2=u20;                 Wv||9[Rd  
    U1 = u1;   VWc)AfKe  
    U2 = u2;                       % Compute initial condition; save it in U  {H*  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. mKsJ[)#.  
    w=2*pi*n./T; :DrF)1C  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T zGNmc7  
    L=4;                           % length of evoluation to compare with S. Trillo's paper _2TL>1KZt  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 erh ez  
    for m1 = 1:1:M1                                    % Start space evolution NFyKTA6  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS =Z ql6D  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; qKrxln/T  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform [RF6mWQ  
       ca2 = fftshift(fft(u2)); x4K A8  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 6{quO# !  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   qOy0QZ#0  
       u2 = ifft(fftshift(c2));                        % Return to physical space oL~?^`cGZ  
       u1 = ifft(fftshift(c1)); 2u$rloc$b  
    if rem(m1,J) == 0                                 % Save output every J steps. *M/ :W =,t  
        U1 = [U1 u1];                                  % put solutions in U array >p'{!k  
        U2=[U2 u2]; pzZ+!d  
        MN1=[MN1 m1]; ~1{ppc+  
        z1=dz*MN1';                                    % output location 3l"8_zLP  
      end a7685Y  
    end O?O=]s u  
    hg=abs(U1').*abs(U1');                             % for data write to excel 4fL`.n1^  
    ha=[z1 hg];                                        % for data write to excel BOWOH  
    t1=[0 t']; bObsj]  
    hh=[t1' ha'];                                      % for data write to excel file dI|D c  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format D^gS.X^  
    figure(1) %lD+57=  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn %DA&txX}w  
    figure(2) R a"hdxH  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 7MGvw-Tpb7  
    Qj'Ik`o  
    非线性超快脉冲耦合的数值方法的Matlab程序 dyk(/# *7W  
    '4SDAa2f  
    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。   :yRv:`r3Lt  
    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 oKCv$>Y  
    #IJe q0TVB  
    A$]s{`  
    jwUX?`6jX  
    %  This Matlab script file solves the nonlinear Schrodinger equations ]T'7+5w  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of a{@}vZx>3  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear T];dFv-GT  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [(gXjt-  
    ;s;3cC!  
    C=1;                           ~>HzAo9e  
    M1=120,                       % integer for amplitude 0)M8Tm0$  
    M3=5000;                      % integer for length of coupler s<rV1D  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) ,ryL( "G  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. gq"d$Xh$x7  
    T =40;                        % length of time:T*T0. tbWf m5$  
    dt = T/N;                     % time step YM};85K  
    n = [-N/2:1:N/2-1]';          % Index  * k<@  
    t = n.*dt;   hf^<lJh~=  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. V$sY3,J7A%  
    w=2*pi*n./T; @Ns[qn;9  
    g1=-i*ww./2; UoPY:(?;i  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; P#,;)HF  
    g3=-i*ww./2; X6",Xr! {  
    P1=0; zh|9\lf  
    P2=0; *ziR&Fr!  
    P3=1; l#`G4Vf  
    P=0; IvT><8<G  
    for m1=1:M1                 o<G#%9j  
    p=0.032*m1;                %input amplitude 0ZM(heQ  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 g;v;xlY`N  
    s1=s10; Xl$, f`f~  
    s20=0.*s10;                %input in waveguide 2 tAF?. \x"g  
    s30=0.*s10;                %input in waveguide 3 nYFrp)DLK  
    s2=s20; 5nUJ9sqA  
    s3=s30; pF4Z4?W  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   <S041KF.{6  
    %energy in waveguide 1 MUAs(M;  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   2ozh!8aL  
    %energy in waveguide 2 Rd&DH_<+^  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   An$2='=/  
    %energy in waveguide 3 Xv|=RNz  
    for m3 = 1:1:M3                                    % Start space evolution Vv45w#w;  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 3iIy_nWC  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; nuXL{tg6  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 3f] ;y<Km  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform #3QPcoxa  
       sca2 = fftshift(fft(s2)); IQRuqp KL  
       sca3 = fftshift(fft(s3)); Jsysk $R  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   z@i4  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); d<6F'F^w.7  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); mAtqF %V  
       s3 = ifft(fftshift(sc3)); D2?H"PH  
       s2 = ifft(fftshift(sc2));                       % Return to physical space  @Fb1D"!  
       s1 = ifft(fftshift(sc1)); %'yrIR  
    end .VCY|KZ  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); _r*\ BM8y  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); ,|{`(y/v  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); E4L?4>V@\  
       P1=[P1 p1/p10]; U}RBgPX!  
       P2=[P2 p2/p10]; ;^5k_\  
       P3=[P3 p3/p10]; {aUnOyX_  
       P=[P p*p]; + cfEyiub  
    end `8ac;b  
    figure(1) N)H "'#-  
    plot(P,P1, P,P2, P,P3); >ESVHPj]  
    P[ 2!D)A  
    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~!~