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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 bmddh2  
    A><%"9pZ  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of Ox43(S0~  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of uTJ?@ ^nq  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear $S cjEG:6  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 #6m//0 u  
    O "h+i>|l  
    %fid=fopen('e21.dat','w'); h/w- &7t  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) I~T?tm  
    M1 =3000;              % Total number of space steps nocH~bAf2  
    J =100;                % Steps between output of space KJkcmF}Q  
    T =10;                  % length of time windows:T*T0 FRF}V@~  
    T0=0.1;                 % input pulse width rC*nZ*  
    MN1=0;                 % initial value for the space output location 4-n.4j|  
    dt = T/N;                      % time step 3 \WdA$Wx  
    n = [-N/2:1:N/2-1]';           % Index ;~q)^.K3  
    t = n.*dt;   NAocmbfNz  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 ^e 6(#SqR  
    u20=u10.*0.0;                  % input to waveguide 2 ohyUvxvj  
    u1=u10; u2=u20;                 ,^,J[F  
    U1 = u1;   mLYB6   
    U2 = u2;                       % Compute initial condition; save it in U lJ,s}l7  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. |Z/ySAFM  
    w=2*pi*n./T; -T(V6&'Qi  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T gR>#LM&dG  
    L=4;                           % length of evoluation to compare with S. Trillo's paper @<sP1`1  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 V7v,)a" L  
    for m1 = 1:1:M1                                    % Start space evolution Bms?`7}N  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS \%VoX` B  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; Y{'G2)e  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform Kj>_XaFCg!  
       ca2 = fftshift(fft(u2)); gy[uq m_ T  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation }R'oAE}$  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   )G|U B8]  
       u2 = ifft(fftshift(c2));                        % Return to physical space ljCgIfZ_4  
       u1 = ifft(fftshift(c1)); n(+:l'#HJ  
    if rem(m1,J) == 0                                 % Save output every J steps. ZtT`_G&  
        U1 = [U1 u1];                                  % put solutions in U array rYqvG  
        U2=[U2 u2]; Y#5S;?bR  
        MN1=[MN1 m1]; Q&LkST-i  
        z1=dz*MN1';                                    % output location <Jk|Bmw;  
      end _B[(/wY  
    end Z~gqTB]H  
    hg=abs(U1').*abs(U1');                             % for data write to excel m4 (Fuu  
    ha=[z1 hg];                                        % for data write to excel U#P#YpD;==  
    t1=[0 t']; 3N21[i2/m  
    hh=[t1' ha'];                                      % for data write to excel file M>#{~zr  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format h^)2:0#{I  
    figure(1) o_5@R+&  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn U|QDV16f  
    figure(2) -d~'tti  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn WveFB%@`;  
    "8I4]'  
    非线性超快脉冲耦合的数值方法的Matlab程序 !]nCeo  
    (qrT0D6  
    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。   {m?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 =EJ"edw]%0  
    )qIK7;  
    (!(bysi9  
    FRW.  
    %  This Matlab script file solves the nonlinear Schrodinger equations $9~1s/('  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of qGqu/$bh  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ;a`X|N9  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 >A/=eW/q  
    #rwR)9iC0  
    C=1;                           F8I <4S  
    M1=120,                       % integer for amplitude >>r:L3<!  
    M3=5000;                      % integer for length of coupler `dZ|}4[1  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) $%-?S]6)  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. mI%/k7:sf  
    T =40;                        % length of time:T*T0. -Me\nu8(RF  
    dt = T/N;                     % time step p3o?_ !Z  
    n = [-N/2:1:N/2-1]';          % Index ._Xtb,p{  
    t = n.*dt;   v2'J L(=  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. gib]#n1!p  
    w=2*pi*n./T; 'Ap 5Aq  
    g1=-i*ww./2; %U 7B0-  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; @gc"-V*-/  
    g3=-i*ww./2; Vvj]2V3  
    P1=0; Tjqn::~D  
    P2=0; %K7}yy&9C  
    P3=1; h~p}08  
    P=0; ?s]`G'=>V`  
    for m1=1:M1                 =.a ]?&Yyh  
    p=0.032*m1;                %input amplitude O@rb4(  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 `9l\ ~t(M  
    s1=s10; KF)i66  
    s20=0.*s10;                %input in waveguide 2 ,GIqRT4K  
    s30=0.*s10;                %input in waveguide 3 &?6w 2[}  
    s2=s20; t,,^^ll  
    s3=s30; mtHz6+  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ~~,<+X:  
    %energy in waveguide 1 )[*O^bPowI  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   k Dt)S$N4n  
    %energy in waveguide 2 ex458^N_  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   }q W aE  
    %energy in waveguide 3 beE%%C]X  
    for m3 = 1:1:M3                                    % Start space evolution  /GUuu  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS wlM ?gQXU[  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 8)8oR&(f  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; p%1m&/ `F  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform (qN(#~  
       sca2 = fftshift(fft(s2)); qGCg3u6  
       sca3 = fftshift(fft(s3)); ;7k7/f:  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   4 G[hU4L  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); [Gy'0P(EQ  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); zP}v2  
       s3 = ifft(fftshift(sc3)); N-E`go  
       s2 = ifft(fftshift(sc2));                       % Return to physical space c&-$?f r  
       s1 = ifft(fftshift(sc1)); {W<-f?  
    end Ai18]QD-  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); 6~W E#z_  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); wf%Ep#^6}  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); %)Dd{|c  
       P1=[P1 p1/p10]; @0,dyg<$>  
       P2=[P2 p2/p10]; cV,Dl`1r  
       P3=[P3 p3/p10];  q)+ n2FM  
       P=[P p*p]; uTGvXKL7  
    end WI_mJ/2  
    figure(1) %0]b5u  
    plot(P,P1, P,P2, P,P3); `|Z@UPHzG  
    JSK5x(GlH  
    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~!~