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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 P5^<c\Mr,Y  
    D[ -Gzqh  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 9e*v&A2Y'  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of G uLU7a  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear FV->226o%  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 i`}nv,  
    N-O"y3W}  
    %fid=fopen('e21.dat','w'); &n)=OConge  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) L)`SNN\ipR  
    M1 =3000;              % Total number of space steps 8qY\T0  
    J =100;                % Steps between output of space Z*Fxr;)d  
    T =10;                  % length of time windows:T*T0  A/zZ%h  
    T0=0.1;                 % input pulse width / .ddx<  
    MN1=0;                 % initial value for the space output location LyB &u( )  
    dt = T/N;                      % time step e0ea2 2  
    n = [-N/2:1:N/2-1]';           % Index DiLZ5^`]  
    t = n.*dt;   d?uN6JH9  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 sD[G?X  
    u20=u10.*0.0;                  % input to waveguide 2 YA vOV-L  
    u1=u10; u2=u20;                 U)n+j}vi  
    U1 = u1;   :QV-!  
    U2 = u2;                       % Compute initial condition; save it in U Z+*t=?L,,G  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. C;C= g1I}  
    w=2*pi*n./T; T3W?-,  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T /Dl{I7W   
    L=4;                           % length of evoluation to compare with S. Trillo's paper ~RRp5x _  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 )Zcw G(o0  
    for m1 = 1:1:M1                                    % Start space evolution vl{G;[6  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 1D6F WYV8  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; .(7 end<  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ph;ds+b  
       ca2 = fftshift(fft(u2)); X_6h8n}i  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation -9Ll'fbq  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   l".LtUf-  
       u2 = ifft(fftshift(c2));                        % Return to physical space CQ`$' oy?W  
       u1 = ifft(fftshift(c1)); X{j`H\'L  
    if rem(m1,J) == 0                                 % Save output every J steps. ?IWLH-fkP  
        U1 = [U1 u1];                                  % put solutions in U array =/J{>S>(i  
        U2=[U2 u2]; nF8|*}w  
        MN1=[MN1 m1]; ;6T>p  
        z1=dz*MN1';                                    % output location iIe\mV  
      end VX!UT=;  
    end gW[(gf.oo  
    hg=abs(U1').*abs(U1');                             % for data write to excel 2th>+M~A  
    ha=[z1 hg];                                        % for data write to excel Z?7XuELKV  
    t1=[0 t']; p%8v+9+h2  
    hh=[t1' ha'];                                      % for data write to excel file = %O@%v  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format + ~6Nq(kV  
    figure(1) 3j]P\T  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn oY#62&wk4  
    figure(2) Aw38T w  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn yMQZulCWE  
    ]W-7 U_  
    非线性超快脉冲耦合的数值方法的Matlab程序 %SHjJCS3  
    *Z+8L*k97  
    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。   Z uh!{_x;  
    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 a2{ nrGD  
    P2q'P&  
    [HV>4,,3"  
    a<W[???m/M  
    %  This Matlab script file solves the nonlinear Schrodinger equations  o IUjd  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 5L'bF2SI  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear jP]I>Tq  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 X/5\L.g2  
    |m^qA](M  
    C=1;                           WxN@&g(  
    M1=120,                       % integer for amplitude AS} FRNIVx  
    M3=5000;                      % integer for length of coupler ^sWsP`DV  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) yK$.wd 2,  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 9vAY|b^  
    T =40;                        % length of time:T*T0. W' DpI7  
    dt = T/N;                     % time step _* xjG \!  
    n = [-N/2:1:N/2-1]';          % Index Y55Yo5<j/+  
    t = n.*dt;   lcv&/ A  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. F|eKt/>e  
    w=2*pi*n./T; \Kx@?,  
    g1=-i*ww./2; PWwz<AI+  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; t3~ZGOn  
    g3=-i*ww./2; O[N}@%HMW  
    P1=0; 44uM:;  
    P2=0; `30og]F0YJ  
    P3=1; rj.]M6#  
    P=0; f`8]4ms"  
    for m1=1:M1                 [@l:C\2  
    p=0.032*m1;                %input amplitude +}XFkH~  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 1@ e22\  
    s1=s10; sd@JQ%O  
    s20=0.*s10;                %input in waveguide 2 k63]Qf=5?N  
    s30=0.*s10;                %input in waveguide 3 Q: H`TSR]  
    s2=s20; y?ps+ce93  
    s3=s30; F~NmLm  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   }`O_  
    %energy in waveguide 1 \m>mE/N  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   r[>=iim  
    %energy in waveguide 2 m.F \Mn  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Rmq8lU  
    %energy in waveguide 3 v4?qI >/  
    for m3 = 1:1:M3                                    % Start space evolution q'07  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS .,)C^hs@  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Ur`jmB  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; F__(iXxC  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Fq]ht*  
       sca2 = fftshift(fft(s2)); 'nK(cKDIG  
       sca3 = fftshift(fft(s3)); ICJp-  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   gUfLw  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); /[[_}\xI%  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);  d"E@e21  
       s3 = ifft(fftshift(sc3)); i2a""zac  
       s2 = ifft(fftshift(sc2));                       % Return to physical space #cN0ciCT'  
       s1 = ifft(fftshift(sc1)); F,t ,Ja  
    end )1PZ#  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); sH//*y  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); l!U_7)s/  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 2wHvHH!  
       P1=[P1 p1/p10]; #].n0[  
       P2=[P2 p2/p10]; ^ -s'Ad3  
       P3=[P3 p3/p10]; Im NTk  
       P=[P p*p]; *, /ADtL  
    end FME&v Uh/  
    figure(1) {uurM` f}:  
    plot(P,P1, P,P2, P,P3); `/zx2Tkk  
    lJ+05\pE  
    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~!~