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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_BY+#  
    Sas &P:# r  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ZT \=:X*e  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of aOj(=s  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear dZ1/w0<M2  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Vlk]  
    -f+U:/'.>v  
    %fid=fopen('e21.dat','w'); BO3#*J5S\  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 2,nVo^13}  
    M1 =3000;              % Total number of space steps l20fA-T _I  
    J =100;                % Steps between output of space _qZ?|;o^  
    T =10;                  % length of time windows:T*T0 U=<d;2N#  
    T0=0.1;                 % input pulse width *Z+8L*k97  
    MN1=0;                 % initial value for the space output location Z uh!{_x;  
    dt = T/N;                      % time step a2{ nrGD  
    n = [-N/2:1:N/2-1]';           % Index P2q'P&  
    t = n.*dt;   ? ^E B"{  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 &K1\"  
    u20=u10.*0.0;                  % input to waveguide 2 .fQ/a`AsU  
    u1=u10; u2=u20;                 &g{b5x{iD  
    U1 = u1;   u;[*Z  
    U2 = u2;                       % Compute initial condition; save it in U OJkiTs{  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ranLHm.nB  
    w=2*pi*n./T; Guc~] B  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T rM sd)  
    L=4;                           % length of evoluation to compare with S. Trillo's paper 5iG+O4n%  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 xS4B"/  
    for m1 = 1:1:M1                                    % Start space evolution Jj~c&LxrO  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS +, SUJ|  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; :|GC~JElo5  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform @dy<=bh~  
       ca2 = fftshift(fft(u2)); zjzW;bo( d  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation `qNhB\  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   (#dwIBBFt  
       u2 = ifft(fftshift(c2));                        % Return to physical space \Kx@?,  
       u1 = ifft(fftshift(c1)); ?f\;z<e|  
    if rem(m1,J) == 0                                 % Save output every J steps. *@XJ7G[  
        U1 = [U1 u1];                                  % put solutions in U array AjTkQ)  
        U2=[U2 u2]; -R~!N#y  
        MN1=[MN1 m1]; Auq)  
        z1=dz*MN1';                                    % output location "|2|Vju%  
      end hU:M]O0uw  
    end 3Ishe"  
    hg=abs(U1').*abs(U1');                             % for data write to excel Tn$/9<Q  
    ha=[z1 hg];                                        % for data write to excel y5td o'Ex  
    t1=[0 t']; q,ry3Nr4n  
    hh=[t1' ha'];                                      % for data write to excel file 36NENzK  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format rQ^X3J*`  
    figure(1) Hcp)Q76X  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn "Y9PS_u(~  
    figure(2) 0>  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn x >u \  
    k *a?Ey$  
    非线性超快脉冲耦合的数值方法的Matlab程序 Px!M^ T!Pi  
    O#}'QZd'  
    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。   zL1*w@6  
    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 [hLSK-K 9  
    .,)C^hs@  
    Ur`jmB  
    F__(iXxC  
    %  This Matlab script file solves the nonlinear Schrodinger equations Fq]ht*  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 'nK(cKDIG  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ICJp-  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 X3z$f(lF%)  
    y>:-6)pv  
    C=1;                            d"E@e21  
    M1=120,                       % integer for amplitude i2a""zac  
    M3=5000;                      % integer for length of coupler #cN0ciCT'  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) F,t ,Ja  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. )1PZ#  
    T =40;                        % length of time:T*T0. sH//*y  
    dt = T/N;                     % time step l!U_7)s/  
    n = [-N/2:1:N/2-1]';          % Index 2wHvHH!  
    t = n.*dt;   #].n0[  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. ^ -s'Ad3  
    w=2*pi*n./T; Im NTk  
    g1=-i*ww./2; *, /ADtL  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; FME&v Uh/  
    g3=-i*ww./2; {uurM` f}:  
    P1=0; (*.t~6c?5  
    P2=0; TRQ@=.  
    P3=1; 3DNw=Ic0k  
    P=0; uQ^r1 $#  
    for m1=1:M1                 wVI 1sR  
    p=0.032*m1;                %input amplitude YbMeSU/sX  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 q/ x(:yol  
    s1=s10; "bO\Wt#Mf  
    s20=0.*s10;                %input in waveguide 2 %i7bkdcwk  
    s30=0.*s10;                %input in waveguide 3 yPgDb[V+  
    s2=s20; %J*z!Fe8s  
    s3=s30; D1&%N{  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   iKy_DV;J  
    %energy in waveguide 1 0K\Xxo.=  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   B{\cV-X$0  
    %energy in waveguide 2 K~j&Q{yws@  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   9uV'# sR  
    %energy in waveguide 3 '#~$Od4&=  
    for m3 = 1:1:M3                                    % Start space evolution 1_D|;/aI  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS _JlbVe[<  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; zp"Lp>i  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; RUJkfi=$  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Dc,h( 2  
       sca2 = fftshift(fft(s2)); 0mJvoz\j8  
       sca3 = fftshift(fft(s3)); X!}  t``  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   (x} >tm  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); JArSJ:}  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); (!-gX" <b  
       s3 = ifft(fftshift(sc3)); [dG&"%5vD  
       s2 = ifft(fftshift(sc2));                       % Return to physical space ,o $F~KPu  
       s1 = ifft(fftshift(sc1)); 8MHYk>O~{G  
    end j2V"w&>b}  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); `[hc{ynO|  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); }T@^wY_Ow  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));  oCE=!75  
       P1=[P1 p1/p10]; )E--E+j  
       P2=[P2 p2/p10]; /az}<r8  
       P3=[P3 p3/p10]; X?,ly3,  
       P=[P p*p]; hE|Z~5\Y,>  
    end ?2hS<qXX  
    figure(1) axJuJ`+Y  
    plot(P,P1, P,P2, P,P3); fj2pD Cic  
    k)Y}X)\36  
    转自:http://blog.163.com/opto_wang/
     
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    离线ciomplj
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    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~