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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 cO,V8#H  
    J\3} il N  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of [+g@@\X4  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 5vf t}f  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear hX m} d\  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 y.p6%E_`  
    LUck>l\l  
    %fid=fopen('e21.dat','w'); S |>$0P4W(  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) T-C#xmY(  
    M1 =3000;              % Total number of space steps AwU c{h l<  
    J =100;                % Steps between output of space ^,lZ58 2  
    T =10;                  % length of time windows:T*T0 87KrSZ  
    T0=0.1;                 % input pulse width 4|N\Q=,  
    MN1=0;                 % initial value for the space output location GQ2PmnV +  
    dt = T/N;                      % time step ]<gCq/V#  
    n = [-N/2:1:N/2-1]';           % Index ~AanU1U<  
    t = n.*dt;   HhmVV"g  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 _AYC|R|  
    u20=u10.*0.0;                  % input to waveguide 2 c%@~%IGF  
    u1=u10; u2=u20;                 k%}89glm  
    U1 = u1;   2BDan^:-Av  
    U2 = u2;                       % Compute initial condition; save it in U $-Pqs ^g  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. P4j8`}&/  
    w=2*pi*n./T; M J,ZXJXs  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T BD7@Mj*|  
    L=4;                           % length of evoluation to compare with S. Trillo's paper _]xt65TL  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 4iNbK~5j  
    for m1 = 1:1:M1                                    % Start space evolution .^lb LN^2  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 3;MjO*-  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; +}QBzGW`  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform NOr <,  
       ca2 = fftshift(fft(u2)); {R-82%X  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation yv)nW::D(  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   BwJ^_:(p~  
       u2 = ifft(fftshift(c2));                        % Return to physical space Y^2Qxo3"3  
       u1 = ifft(fftshift(c1)); rN1U.FRe/  
    if rem(m1,J) == 0                                 % Save output every J steps. LkGf|yd_  
        U1 = [U1 u1];                                  % put solutions in U array Tz[?gF.Do  
        U2=[U2 u2]; q^1aPz  
        MN1=[MN1 m1]; 0[:9 Hb6  
        z1=dz*MN1';                                    % output location ml.;wB|  
      end 4r[pMJiq  
    end MJ*]fC3/  
    hg=abs(U1').*abs(U1');                             % for data write to excel <D!c ~*[  
    ha=[z1 hg];                                        % for data write to excel dA1 C)gLi  
    t1=[0 t']; ;DD>k bd  
    hh=[t1' ha'];                                      % for data write to excel file n2d8;B#  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format {(Og/[  
    figure(1) AB"1(PbG  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn d)0LVa(  
    figure(2) g T XW2S  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ?orhJS  
    a,~D+s;^  
    非线性超快脉冲耦合的数值方法的Matlab程序 }B"|z'u  
    +z|UpI  
    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。   3G%wZ,)C  
    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 V+O0k: o  
    TTZ['HP oI  
    _7lt(f[S  
    Y:%m;b$]  
    %  This Matlab script file solves the nonlinear Schrodinger equations hB?,7-  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of kqD*TJA  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 1iJ0Hut}d  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 `u#;MUg  
    q*[!>\ Z8  
    C=1;                           A{z>D`d  
    M1=120,                       % integer for amplitude OG`|td  
    M3=5000;                      % integer for length of coupler #9D/jYK1X  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) "[*S?QO(L  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. u3Usq=Ij{  
    T =40;                        % length of time:T*T0. "mPSA Z  
    dt = T/N;                     % time step w dGpt_  
    n = [-N/2:1:N/2-1]';          % Index s]y-pZ  
    t = n.*dt;   7deAr$?Wx  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 7`IUMYl#~  
    w=2*pi*n./T; -,QKTxwo>  
    g1=-i*ww./2; X!o[RJY  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; W?qpnPW  
    g3=-i*ww./2; 7q%|4Z-~  
    P1=0; C}b|2y  
    P2=0; 5^i.;>(b  
    P3=1; =[]x\&@t  
    P=0; ?}'N_n ys  
    for m1=1:M1                 7 9Qc`3a  
    p=0.032*m1;                %input amplitude Nfv="t9e  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 m$fQ`XzU  
    s1=s10; 0A#*4ap  
    s20=0.*s10;                %input in waveguide 2 7_9+=. +X5  
    s30=0.*s10;                %input in waveguide 3 UrO=!Gk  
    s2=s20; _urG_~q  
    s3=s30; o 'C~~Vg).  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   {y,nFxLq  
    %energy in waveguide 1 +I|Rk&  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   #^|| ]g/N  
    %energy in waveguide 2 WD15pq l  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   "^;#f+0  
    %energy in waveguide 3 CO-Iar  
    for m3 = 1:1:M3                                    % Start space evolution t< sp%zXZ  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS }m6f^fs}  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; }@Xh xZu  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ,*/Pg 52?  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 7MY)\aH  
       sca2 = fftshift(fft(s2)); ,{k<JA {  
       sca3 = fftshift(fft(s3)); 8h2D+1,PZC  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   vqq6B/r@Fu  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); WgE@89  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); 807al^s x  
       s3 = ifft(fftshift(sc3)); sffhPX\I  
       s2 = ifft(fftshift(sc2));                       % Return to physical space jm+ V$YBP  
       s1 = ifft(fftshift(sc1)); }@d>,1DU  
    end `9/0J-7*  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); d9O:,DKf  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); SOVj Eo4'3  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); ~gP7s_ qr{  
       P1=[P1 p1/p10]; R]Hz8 _X  
       P2=[P2 p2/p10]; 'X9AG6K1  
       P3=[P3 p3/p10]; Te# ]Cn|  
       P=[P p*p]; jDR')ascn  
    end _B)s=Snx  
    figure(1) G.E[6G3  
    plot(P,P1, P,P2, P,P3); C 8N%X2R  
    )X/*($SuA  
    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~!~