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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 S\g7wXH  
    X]MM7hMuR  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of F>kn:I"X)  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of \w[ZY$/  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear H0 n@kKr  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 8sF0]J[g{  
    b%f2"e0g  
    %fid=fopen('e21.dat','w'); NvHy'  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) >m6,xxTR  
    M1 =3000;              % Total number of space steps {C0^D*U:  
    J =100;                % Steps between output of space u|>U`[Zpj  
    T =10;                  % length of time windows:T*T0 MQH8Q$5D  
    T0=0.1;                 % input pulse width |ezO@  
    MN1=0;                 % initial value for the space output location ajW$d!  
    dt = T/N;                      % time step FJ,\?ooGf  
    n = [-N/2:1:N/2-1]';           % Index S%s|P=u  
    t = n.*dt;   'A(-MTd%  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 m\Fb ,  
    u20=u10.*0.0;                  % input to waveguide 2 Ldj^O9p(  
    u1=u10; u2=u20;                 &R FM d=  
    U1 = u1;   +6)kX4  
    U2 = u2;                       % Compute initial condition; save it in U %%,hR'+|  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. pF*~)e  
    w=2*pi*n./T; hPi :31-0  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T i =fOdp  
    L=4;                           % length of evoluation to compare with S. Trillo's paper hOLy*%  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 l)PFzIz=V  
    for m1 = 1:1:M1                                    % Start space evolution h:Mn$VR,  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ($ B ]9*  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; `MYKXBM  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ~v(M6dz~vk  
       ca2 = fftshift(fft(u2)); OK2/k_jXN'  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation 8j+:s\  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   19w,'}CGk  
       u2 = ifft(fftshift(c2));                        % Return to physical space 9k+&fyy  
       u1 = ifft(fftshift(c1)); J(&M<<%  
    if rem(m1,J) == 0                                 % Save output every J steps. ny_ kr`$42  
        U1 = [U1 u1];                                  % put solutions in U array S}p&\w H  
        U2=[U2 u2]; -f;j1bQ  
        MN1=[MN1 m1]; vb.Y8[  
        z1=dz*MN1';                                    % output location L!b0y7yR  
      end {{[jC"4AY  
    end k1Mxsd  
    hg=abs(U1').*abs(U1');                             % for data write to excel GKsL~;8"  
    ha=[z1 hg];                                        % for data write to excel B/9<b{6  
    t1=[0 t']; JXRf4QmG  
    hh=[t1' ha'];                                      % for data write to excel file 0@e}hv;  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format am'p^Z @  
    figure(1) )4F/T,{;m  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 0O['-x  
    figure(2) qfP"UAc{/  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn d,J<SG&L&  
    B[/['sD  
    非线性超快脉冲耦合的数值方法的Matlab程序 ,ORG"]_F  
    >]XaUQ-  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   7MuK/q.  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 vPl6Das r  
    xlPcg7  
    < ;,S"e  
    N}x/&e  
    %  This Matlab script file solves the nonlinear Schrodinger equations &b@!DAwAJ  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of qvfAG 0p  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Ubw!/|mi  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ?<yq 2`\4O  
    Puth8$  
    C=1;                           [>M*_1F  
    M1=120,                       % integer for amplitude 4z0R\tjT  
    M3=5000;                      % integer for length of coupler ;/)Mcx]n  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) ),y!<\oQ  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 5Du>-.r  
    T =40;                        % length of time:T*T0. |p8"9jN@}c  
    dt = T/N;                     % time step  10l1a4  
    n = [-N/2:1:N/2-1]';          % Index X~)V)'R  
    t = n.*dt;   6Er0o{iI  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ghJ,s|lH  
    w=2*pi*n./T; d[>N6?JA/  
    g1=-i*ww./2; ReB(T7Vk=  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; rz[uuY7  
    g3=-i*ww./2; f?>-yMR|  
    P1=0; @^:7UI_  
    P2=0; 5;K-,"UQ  
    P3=1; BudWbZ5>Ep  
    P=0; JW%/^'  
    for m1=1:M1                 z"s%#/#  
    p=0.032*m1;                %input amplitude 1W}nYU  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 %];h|[ax]  
    s1=s10; .cH{WZ  
    s20=0.*s10;                %input in waveguide 2 q(jkit~`A  
    s30=0.*s10;                %input in waveguide 3 9#EHXgz  
    s2=s20; ?LV-W  
    s3=s30; <9d-Hz  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   !}L~@[v,uL  
    %energy in waveguide 1 S`W'G&bCj  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   VT5cxB<  
    %energy in waveguide 2 #A|D\IhF  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   lZS_n9Sc  
    %energy in waveguide 3 Xew1LPI  
    for m3 = 1:1:M3                                    % Start space evolution Hlt8al3  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS n2jvXLJq  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; MR?*GI's  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 'Ffy8z{&3  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 'd2qa`H'}B  
       sca2 = fftshift(fft(s2)); D8@n kSP  
       sca3 = fftshift(fft(s3)); {XDY:`vZ}  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   {w |dM#  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); hr_9;,EPh  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); E,<\T6/%q  
       s3 = ifft(fftshift(sc3)); 7|+|\ 7l#  
       s2 = ifft(fftshift(sc2));                       % Return to physical space mX<Fuu}E*Z  
       s1 = ifft(fftshift(sc1)); +&7[lsD*  
    end 7g A08M[O  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); s.R-<Y 3  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); >op:0on]}  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); z_:eM7]jv  
       P1=[P1 p1/p10]; }XGMa?WR  
       P2=[P2 p2/p10]; 96"yNqBf  
       P3=[P3 p3/p10]; !cEbz b  
       P=[P p*p]; H{\.g=01  
    end ` j&0VIU>>  
    figure(1) M('s|>\l  
    plot(P,P1, P,P2, P,P3); ,]PyDq6  
    eK Z@ FEZ  
    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~!~