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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 N \Wd 0b  
    =^D{ZZw{  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of $ix*xm. 4m  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of `ek On@T0  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ;x~[om21;  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 l0g`;BI_  
    /{7we$+,p  
    %fid=fopen('e21.dat','w'); y |0I3n]e  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 8~s-@3J  
    M1 =3000;              % Total number of space steps @[] A&)B  
    J =100;                % Steps between output of space PdNxuy  
    T =10;                  % length of time windows:T*T0 f8X/kz  
    T0=0.1;                 % input pulse width M~ ^ {S[o  
    MN1=0;                 % initial value for the space output location Z d]2>h  
    dt = T/N;                      % time step eVx &S a  
    n = [-N/2:1:N/2-1]';           % Index 4t;m^Iv  
    t = n.*dt;   J&jNONu?  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 !YJ^BI    
    u20=u10.*0.0;                  % input to waveguide 2 G*$a81dAX  
    u1=u10; u2=u20;                 !&=%#i  
    U1 = u1;   0Fi&7%  
    U2 = u2;                       % Compute initial condition; save it in U ( O>oN~  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. H%:u9DlEK/  
    w=2*pi*n./T; &ivPY  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T fX 41o#  
    L=4;                           % length of evoluation to compare with S. Trillo's paper FeM,$&G:  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 05>xQx?"m4  
    for m1 = 1:1:M1                                    % Start space evolution ^"?b!=n!  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS J@I-tS  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; >RMp`HxDf  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform Fo1|O&>  
       ca2 = fftshift(fft(u2)); ;*8nd-\  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation :/ yR  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   >5|;8v-r  
       u2 = ifft(fftshift(c2));                        % Return to physical space VSI.c`=,  
       u1 = ifft(fftshift(c1)); M+N7JpR  
    if rem(m1,J) == 0                                 % Save output every J steps. $CY B&|d  
        U1 = [U1 u1];                                  % put solutions in U array )5M9Ro7  
        U2=[U2 u2]; rLm:qu(F1  
        MN1=[MN1 m1]; [!v| M  
        z1=dz*MN1';                                    % output location ?8LRd5LH  
      end yv!,iK9  
    end +J~q:b.  
    hg=abs(U1').*abs(U1');                             % for data write to excel !"Q8KV  
    ha=[z1 hg];                                        % for data write to excel [Bz'c1  
    t1=[0 t']; u+RdC;_  
    hh=[t1' ha'];                                      % for data write to excel file H#joc0?P  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format 7 i |_PP_  
    figure(1)  9g*MBe:  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn &Z^,-Y  
    figure(2) ?+bDFM}  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn pSq3\#Twr  
    CbA2?(1o1  
    非线性超快脉冲耦合的数值方法的Matlab程序 v$`AN4)}  
    sDH|k@K  
    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`l97$\  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 "16-K%}  
    L|3wG Y9E  
    8'2lc  
    ~!,Q<?  
    %  This Matlab script file solves the nonlinear Schrodinger equations O_p:`h:;M  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of BlV k?n  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear f(O`t}Ed  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Rp2~d  
    .+H8c.  
    C=1;                           _`JY A  
    M1=120,                       % integer for amplitude !S/hH%C  
    M3=5000;                      % integer for length of coupler =9 TAs? =  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) #@m*yJg<  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. at/v.U |F  
    T =40;                        % length of time:T*T0. %rQ5 <U  
    dt = T/N;                     % time step 1 D fB9n  
    n = [-N/2:1:N/2-1]';          % Index fWR]L47n  
    t = n.*dt;   bT@7&  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. #pxc6W /  
    w=2*pi*n./T; =#i#IF42?  
    g1=-i*ww./2; GRC=G&G  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 3:rH1vG.m  
    g3=-i*ww./2; 2&W(@wT$  
    P1=0; <%JRZYZ  
    P2=0; Qr;es,f  
    P3=1; >NN|vj  
    P=0; >?,arER  
    for m1=1:M1                 Dk|<&uVV  
    p=0.032*m1;                %input amplitude V 'Gi2gNaP  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 YZCPS6PuE  
    s1=s10; N1UE u,j  
    s20=0.*s10;                %input in waveguide 2 : 5@cj j  
    s30=0.*s10;                %input in waveguide 3 U/M(4H3>H  
    s2=s20; ;<#fZ0(l;  
    s3=s30; O\L(I079  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   s &v<5W2P  
    %energy in waveguide 1 xXK7i\ny  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   kRgyvA,*;  
    %energy in waveguide 2 `5`Pv'`  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   $&m^WrZaY  
    %energy in waveguide 3 181-m7W  
    for m3 = 1:1:M3                                    % Start space evolution Y9m'RFZr  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS Kg>+5~+E?q  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Y.yM1 z  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; I0O)MR<  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform :&`Yz   
       sca2 = fftshift(fft(s2)); oJ`ih&Q8  
       sca3 = fftshift(fft(s3)); Vzz0)`*hQ  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   -o F#a 8  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); "2CiW6X[M  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); M~7?m/Wj  
       s3 = ifft(fftshift(sc3));  "t8mQ;n  
       s2 = ifft(fftshift(sc2));                       % Return to physical space +I2P{7  
       s1 = ifft(fftshift(sc1)); B[-%A!3 F  
    end dH!k {3bL  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); b]mRn{r?  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); =[`wyQe`_  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); E8>npDFv.  
       P1=[P1 p1/p10]; C^r3r6  
       P2=[P2 p2/p10]; #l-,2C~  
       P3=[P3 p3/p10]; -nO('(t  
       P=[P p*p]; oC U8;z  
    end ~SJOynSz,  
    figure(1) Yh:*.@  
    plot(P,P1, P,P2, P,P3); 7 .+kcqX  
    P-No;/!B#  
    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~!~