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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 95!xTf  
    M}5C;E*  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ,Xh4(Gn#b  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of _+;x 4K;  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _>`0!mG  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 ./g0T{&  
    GS{9MGl  
    %fid=fopen('e21.dat','w'); 9xKFX|*$  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) cn\_;TYiJ  
    M1 =3000;              % Total number of space steps g]ihwm~  
    J =100;                % Steps between output of space e.jgV=dT-  
    T =10;                  % length of time windows:T*T0 uyA9`~p=#  
    T0=0.1;                 % input pulse width NFSPw` f  
    MN1=0;                 % initial value for the space output location TRq~n7Y7C  
    dt = T/N;                      % time step 8EE7mEmLH  
    n = [-N/2:1:N/2-1]';           % Index Ci*5E$+\  
    t = n.*dt;   x9ws@=[:  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 & aLR'*]6  
    u20=u10.*0.0;                  % input to waveguide 2 T5Fah#-4  
    u1=u10; u2=u20;                 xxiLi46/  
    U1 = u1;   Ml3F\ fAW  
    U2 = u2;                       % Compute initial condition; save it in U ld?M,Qd  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. OS9v.pz  
    w=2*pi*n./T; r"Bf@va  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 14&EdTG.  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 08` @u4  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 lR(&Wc\j  
    for m1 = 1:1:M1                                    % Start space evolution drZw#b  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS )5t_tPv  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; L9kP8&&KK  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform W#wM PsB  
       ca2 = fftshift(fft(u2)); + mcN6/  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation uJO*aA{K  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   i!HGM=f  
       u2 = ifft(fftshift(c2));                        % Return to physical space gky_]7Av  
       u1 = ifft(fftshift(c1)); fr?eOigbl  
    if rem(m1,J) == 0                                 % Save output every J steps. qb<gh D=j  
        U1 = [U1 u1];                                  % put solutions in U array O>Sbb2q?"  
        U2=[U2 u2]; `WB|h)Y  
        MN1=[MN1 m1]; Gs6 #aL}]R  
        z1=dz*MN1';                                    % output location pE< ' '`  
      end h>/ViB@"W|  
    end l}^#kHSyd  
    hg=abs(U1').*abs(U1');                             % for data write to excel |l|]Tw  
    ha=[z1 hg];                                        % for data write to excel G](K2=  
    t1=[0 t']; ;H=6u  
    hh=[t1' ha'];                                      % for data write to excel file xr/ k.Fz  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format _"bx#B*  
    figure(1) s7e'9Bx  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn } :mI6zsNj  
    figure(2) ^ \?9W  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn }B- A*TI<h  
    }rE|\p>  
    非线性超快脉冲耦合的数值方法的Matlab程序 H6O\U2+  
    Y'5ck(  
    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。   i/~J0qQ  
    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 GN<I|mGLJK  
    0o]K6 b  
    #dft-23  
    rA`\we)  
    %  This Matlab script file solves the nonlinear Schrodinger equations  {5udol5?  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ~c^-DAgB  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear agYK aM1N  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 z!+<m<  
    yjq )}y,tF  
    C=1;                           9zyN8v2  
    M1=120,                       % integer for amplitude s]iOC6v  
    M3=5000;                      % integer for length of coupler XbC8t &Q],  
    N = 512;                      % Number of Fourier modes (Time domain sampling points)  M9K).P=  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. DX"; v J  
    T =40;                        % length of time:T*T0. IT(c'}  
    dt = T/N;                     % time step h 3&:"*A2  
    n = [-N/2:1:N/2-1]';          % Index %\cC]<>  
    t = n.*dt;   z aF0nov  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. mSfhl(<L  
    w=2*pi*n./T; Lvq]SzOw  
    g1=-i*ww./2; A 5 X+Z  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; )ta5y7np  
    g3=-i*ww./2; zmFFBf"<  
    P1=0; |pqpF?h5|  
    P2=0; cPcV[6)5K9  
    P3=1; -G;1U  
    P=0; 9pcf jx..  
    for m1=1:M1                 ".%LBs~$  
    p=0.032*m1;                %input amplitude =]a@)6y  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 fn OkH  
    s1=s10; =!^iiHF  
    s20=0.*s10;                %input in waveguide 2 /wE_eK.  
    s30=0.*s10;                %input in waveguide 3 s%oAsQ_y  
    s2=s20; \z9?rvT:  
    s3=s30; R3n&o%$*  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   >U<nEnB$?  
    %energy in waveguide 1 4C%>/*%8>  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   k~f+LO  
    %energy in waveguide 2 #sU~fq  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   h50StZ8Yr  
    %energy in waveguide 3 8>Z$/1Mh  
    for m3 = 1:1:M3                                    % Start space evolution aT#{t {gkA  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Vb^s 'k  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; $ud>Z;X=P  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; 41o!2(e$  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform >iH).:j  
       sca2 = fftshift(fft(s2)); w3qf7{b  
       sca3 = fftshift(fft(s3)); t`T\d\  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   jF{gDK  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); V6MT>T  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); yH%+cmp7  
       s3 = ifft(fftshift(sc3)); 9K46>_TyH  
       s2 = ifft(fftshift(sc2));                       % Return to physical space C;q}3c*L  
       s1 = ifft(fftshift(sc1)); SU O;  
    end &ORv bnd6  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Q *]`t@ q  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 5 ?~-Vv31s  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); |Xm4(FN\  
       P1=[P1 p1/p10]; ; axa ZV  
       P2=[P2 p2/p10]; >zg8xA1zL  
       P3=[P3 p3/p10]; &JhIn%=-  
       P=[P p*p]; #A/J^Ko  
    end a^c ,=X3  
    figure(1) n,jE#Z.D  
    plot(P,P1, P,P2, P,P3); Mc7<[a  
    G^rh*cb K  
    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~!~