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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 8U\ +b?}  
    a&Z|3+ZA  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of C"0gAN  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ~Bu~?ZJmd  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear JziMjR  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Fb-NG.Z#  
    tx5@r;  
    %fid=fopen('e21.dat','w');  NPf,9c;  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Z39^nGO  
    M1 =3000;              % Total number of space steps gB kb0  
    J =100;                % Steps between output of space w(mn@Qc  
    T =10;                  % length of time windows:T*T0 p&ow\A O  
    T0=0.1;                 % input pulse width ^!kv gm<{$  
    MN1=0;                 % initial value for the space output location drb_GT  
    dt = T/N;                      % time step 7a@V2cr@  
    n = [-N/2:1:N/2-1]';           % Index %iJ6;V 4  
    t = n.*dt;   h]MSjC.X  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ?$r+#'asd(  
    u20=u10.*0.0;                  % input to waveguide 2 U ][.ioc  
    u1=u10; u2=u20;                 HjV^6oP  
    U1 = u1;   >n` OLHg;  
    U2 = u2;                       % Compute initial condition; save it in U Ea P#~x  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ODEy2).  
    w=2*pi*n./T; X)nOY*  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T CQv [Od  
    L=4;                           % length of evoluation to compare with S. Trillo's paper %*jpQOw  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 L;BYPZR  
    for m1 = 1:1:M1                                    % Start space evolution w)!(@}vd  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS RA\H?1;8C  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; n.7 $*9)#  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform y`(z_5ClT  
       ca2 = fftshift(fft(u2)); :mg#&MZj<  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation d(]LRIn~1  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   4@8i,q>  
       u2 = ifft(fftshift(c2));                        % Return to physical space }i/{8Ou W  
       u1 = ifft(fftshift(c1)); ?B h}  
    if rem(m1,J) == 0                                 % Save output every J steps. v $ pA Rt  
        U1 = [U1 u1];                                  % put solutions in U array 3QXGbu}:h!  
        U2=[U2 u2]; ;M'R/JlUN  
        MN1=[MN1 m1]; kWoy%?|RRa  
        z1=dz*MN1';                                    % output location tX)]ZuEi$  
      end xRaYm  
    end ^[ id8  
    hg=abs(U1').*abs(U1');                             % for data write to excel x,p|n  
    ha=[z1 hg];                                        % for data write to excel kxf'_Nzy  
    t1=[0 t']; H;$w^Tr  
    hh=[t1' ha'];                                      % for data write to excel file +;*])N%q  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format F92n)*[  
    figure(1) F htf4  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 7Y!^88,f.  
    figure(2) ("{AY?{{  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn <BO|.(ys  
    Wt4!XV  
    非线性超快脉冲耦合的数值方法的Matlab程序 ,xR^8G 8  
    G`)I _uO  
    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。   4vy!'r@   
    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 'nCBLc8  
    Dnd  
    ZZeqOu7^  
    Gt 2rJ<>  
    %  This Matlab script file solves the nonlinear Schrodinger equations M8g=t[\  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of HVk3F| ]V  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear n P69W  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ^U`[P@T  
    8:0l5cZE  
    C=1;                           >\>HRyt%  
    M1=120,                       % integer for amplitude *1elUI2Rg  
    M3=5000;                      % integer for length of coupler [IHT)%>E8&  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) QDgOprha  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. >\@6i s  
    T =40;                        % length of time:T*T0. vn kktD'n  
    dt = T/N;                     % time step ?j $z[_K  
    n = [-N/2:1:N/2-1]';          % Index @c{Z?>dUc#  
    t = n.*dt;   yJKezIL\z  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 9VP|a-  
    w=2*pi*n./T; NIYAcLa@n8  
    g1=-i*ww./2; *^NC5=A(d  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; S&R~*  
    g3=-i*ww./2; qed; UyN  
    P1=0; )Wc#?K  
    P2=0; ~ xXB !K~C  
    P3=1; Xbap' /t  
    P=0; YjsaTdZ!&  
    for m1=1:M1                 &[kwM3 95  
    p=0.032*m1;                %input amplitude nkG 6.  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ^@tn+'.  
    s1=s10; }~A-ELe:  
    s20=0.*s10;                %input in waveguide 2 0"<g g5  
    s30=0.*s10;                %input in waveguide 3 al" 1T-  
    s2=s20; JBg",2w |C  
    s3=s30; MiRMjQ2  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   -@i2]o  
    %energy in waveguide 1 :v&GA s6H  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   QtX ->6P>  
    %energy in waveguide 2 ;GvyL>|-~  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   hz )L+  
    %energy in waveguide 3 (6.0gB$aTu  
    for m3 = 1:1:M3                                    % Start space evolution ss-Be  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS N5~g:([k  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ;((gmg7,  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 7OW;o mT`  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform O >'o;0  
       sca2 = fftshift(fft(s2)); Q_@ Z.{  
       sca3 = fftshift(fft(s3)); \DfvNeF  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   q A G0t{K  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); M/B_-8B_D  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);  {kmaMP  
       s3 = ifft(fftshift(sc3)); .4?M.Z4[  
       s2 = ifft(fftshift(sc2));                       % Return to physical space G19FSLrtA  
       s1 = ifft(fftshift(sc1)); {Y IVHl  
    end ;rk}\M$+  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); =D3Y q?  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); W]rXt,{ &  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); FUHa"$Bg  
       P1=[P1 p1/p10]; =0m[  
       P2=[P2 p2/p10]; 3 :f5xF  
       P3=[P3 p3/p10]; [*50Ng>P`  
       P=[P p*p]; nY(jN D  
    end tCA |sN  
    figure(1) *d(wO l5[  
    plot(P,P1, P,P2, P,P3); u8o!ncy  
    0w(<pNA  
    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~!~