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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 P gK> Z,  
    j9]H~:g$d  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of a2\r^fY/  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Ed=]RR 4R  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ~k[q:$T  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ohj(1jt  
    RbGq$vYol/  
    %fid=fopen('e21.dat','w'); 5zR9N>!c  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) t (>}  
    M1 =3000;              % Total number of space steps [W{WfJ-HwG  
    J =100;                % Steps between output of space i%eq!q  
    T =10;                  % length of time windows:T*T0 |#_`aT"  
    T0=0.1;                 % input pulse width T.kQ] h2ZG  
    MN1=0;                 % initial value for the space output location mhZ60RW  
    dt = T/N;                      % time step J_ S]jE{  
    n = [-N/2:1:N/2-1]';           % Index 5<?s86GHh'  
    t = n.*dt;   > qhoGg  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 1hnw+T<<W  
    u20=u10.*0.0;                  % input to waveguide 2 uy^vQ/  
    u1=u10; u2=u20;                 HHU0Nku@ho  
    U1 = u1;   (#`1[n+b`x  
    U2 = u2;                       % Compute initial condition; save it in U <qpDAz4k  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. Zn]njf1x  
    w=2*pi*n./T; -p\uW 0XA  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T [h^>Iq (Z  
    L=4;                           % length of evoluation to compare with S. Trillo's paper ~KF>Jow?Y  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 .uGvmD <;x  
    for m1 = 1:1:M1                                    % Start space evolution i1E~F  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS zPKx: I3  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 2IGoAt>V  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ohPCYt  
       ca2 = fftshift(fft(u2)); Ug1n4X3FKn  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation _K5R?"H0  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   rbw5.NU  
       u2 = ifft(fftshift(c2));                        % Return to physical space #ovmX  
       u1 = ifft(fftshift(c1)); 9;*-y$@  
    if rem(m1,J) == 0                                 % Save output every J steps. sa26u`?  
        U1 = [U1 u1];                                  % put solutions in U array ]gHi5]\NC  
        U2=[U2 u2]; eVy>  
        MN1=[MN1 m1]; m5/d=k0l  
        z1=dz*MN1';                                    % output location eAPNF?0yh  
      end CMI V"-  
    end {+V]saYP  
    hg=abs(U1').*abs(U1');                             % for data write to excel bXw!fYm&  
    ha=[z1 hg];                                        % for data write to excel GV"HkE;  
    t1=[0 t']; +4Uxq{.K  
    hh=[t1' ha'];                                      % for data write to excel file $V0G[!4  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format ZFNn(n  
    figure(1) ^UEExj f  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 2sryhS'(H  
    figure(2) QxaW x  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn d}2$J1`  
    {r,MRZaa  
    非线性超快脉冲耦合的数值方法的Matlab程序 L~PBD?l  
    2Vn~o_ga  
    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。   f*IC ZM  
    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 i 6@c@n  
    XFiP8aX<  
    RrG5`2  
    ipThw p9  
    %  This Matlab script file solves the nonlinear Schrodinger equations E9"P~ nz  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of X*^^W_LH.  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear g$N/pg2>cT  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 N#Y|MfLc  
    WX9ABh&5  
    C=1;                           dpPu&m+  
    M1=120,                       % integer for amplitude Tt.#O~2:9  
    M3=5000;                      % integer for length of coupler ;;#_[Zl  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) \[57Dmo  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ~Gz b^  
    T =40;                        % length of time:T*T0. BM,]Wjfdj  
    dt = T/N;                     % time step aA|<W g  
    n = [-N/2:1:N/2-1]';          % Index p!OCF]r  
    t = n.*dt;   ]#fmih^  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. &P@dx=6d  
    w=2*pi*n./T; (1pR=  
    g1=-i*ww./2; B,_/'DneQK  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; m);0sb  
    g3=-i*ww./2; {|E'  
    P1=0; '[z529HN  
    P2=0; t6+c"=P#  
    P3=1; KS3>c7  
    P=0; 9[5qN!P;y  
    for m1=1:M1                 fK %${   
    p=0.032*m1;                %input amplitude K|{IX^3)V  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 iiw\  
    s1=s10; *:+&Sx L  
    s20=0.*s10;                %input in waveguide 2 %tOGs80_{  
    s30=0.*s10;                %input in waveguide 3 `Pcbc\"*y  
    s2=s20; D["~G v  
    s3=s30; RI[=N:C^  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   .T63:  
    %energy in waveguide 1 'BiR ,M$mY  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   %wDE+&M  
    %energy in waveguide 2 U{JD\G 8m  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Ki,SFww8r  
    %energy in waveguide 3 cR *5iqA  
    for m3 = 1:1:M3                                    % Start space evolution vR)f'+_Nz  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 3b d(.he2u  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; RnaxRnXVR  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; F+m%PVW:  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform j TyR+#Wn  
       sca2 = fftshift(fft(s2)); ev'` K=n8  
       sca3 = fftshift(fft(s3)); :]rb}1nLB  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   c;13V(Djy  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); wqnHaWd*  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); e2><Y<  
       s3 = ifft(fftshift(sc3)); ;J>upI   
       s2 = ifft(fftshift(sc2));                       % Return to physical space ms]r1x"  
       s1 = ifft(fftshift(sc1)); b4R;#rm  
    end Mjon++>Z  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); a7fFp 9l!  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); Lhz*o6)  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); rsaN<6#_^Q  
       P1=[P1 p1/p10]; #hZ`r5GvTj  
       P2=[P2 p2/p10]; 9zL(PkC%\  
       P3=[P3 p3/p10]; @BmI1  
       P=[P p*p]; li37*  
    end #aua6V!"  
    figure(1) N8E  
    plot(P,P1, P,P2, P,P3); Im g$D*BM  
    wU5.t -|`  
    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~!~