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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 IA(+}V  
    nep-?7x  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ];7/DM#Np  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 48W-Tf6v|  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear (cpaMn@)g  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 !<AY0fpY  
    ffibS0aM  
    %fid=fopen('e21.dat','w'); ?]Z EK8c  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 1}DUe. a  
    M1 =3000;              % Total number of space steps 'boAv%1_sa  
    J =100;                % Steps between output of space ]>"q>XgnI  
    T =10;                  % length of time windows:T*T0 oP`yBX  
    T0=0.1;                 % input pulse width YA'_Ba(v)  
    MN1=0;                 % initial value for the space output location wJb"X=i*  
    dt = T/N;                      % time step 1Zi(5S)  
    n = [-N/2:1:N/2-1]';           % Index h_?#.z0ih;  
    t = n.*dt;   d\ {a&\v  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 +f]\>{o4  
    u20=u10.*0.0;                  % input to waveguide 2 FK!UUy;  
    u1=u10; u2=u20;                 i#1~<U  
    U1 = u1;   3!<} -sW4  
    U2 = u2;                       % Compute initial condition; save it in U =F>nqklc  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. :eR[lR^4*  
    w=2*pi*n./T; @"$rR+r'  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T W*D].|  
    L=4;                           % length of evoluation to compare with S. Trillo's paper uL[%R2  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 $ix*xm. 4m  
    for m1 = 1:1:M1                                    % Start space evolution `ek On@T0  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ;x~[om21;  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; $KGpcl  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform A Q e~F  
       ca2 = fftshift(fft(u2)); H,5 ##@X  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation EHC^ [5  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   cQ<* (KU  
       u2 = ifft(fftshift(c2));                        % Return to physical space GP._C=]?c  
       u1 = ifft(fftshift(c1)); Vo-]&u&cr  
    if rem(m1,J) == 0                                 % Save output every J steps. *iW$>Yjb  
        U1 = [U1 u1];                                  % put solutions in U array WKB@9Vfju  
        U2=[U2 u2]; Qx%]u8s  
        MN1=[MN1 m1]; r" )zR,  
        z1=dz*MN1';                                    % output location sxBRg=  
      end 0-{l4;o  
    end ^FZ7)T  
    hg=abs(U1').*abs(U1');                             % for data write to excel A1u|L^  
    ha=[z1 hg];                                        % for data write to excel D_MNF =7  
    t1=[0 t']; OJH:k~]0!  
    hh=[t1' ha'];                                      % for data write to excel file <(<19t5.  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format }bxx]rDl  
    figure(1) xw%'R-  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn uY5Gn.Y  
    figure(2) ;zl/  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn ^"?b!=n!  
    J@I-tS  
    非线性超快脉冲耦合的数值方法的Matlab程序 >RMp`HxDf  
    Fo1|O&>  
    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$7TnMug  
    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 l .wf= /  
    {=Ku9\  
    0Q_@2  
    1q[vNP=g&  
    %  This Matlab script file solves the nonlinear Schrodinger equations $CY B&|d  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of )5M9Ro7  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear rLm:qu(F1  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 }M I9?\"q  
    ?8LRd5LH  
    C=1;                           yv!,iK9  
    M1=120,                       % integer for amplitude U.@j !UrZ  
    M3=5000;                      % integer for length of coupler fDa$TbhjI  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) @$(/6]4p  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.  xedbr  
    T =40;                        % length of time:T*T0. 7v~\c%1V  
    dt = T/N;                     % time step =k(~PB^>  
    n = [-N/2:1:N/2-1]';          % Index 1jhGshhp  
    t = n.*dt;   #VwA?$4g`  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 2Rp'ju~O)/  
    w=2*pi*n./T; |5}~n"R5  
    g1=-i*ww./2; y&.[Nt '+  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; v$`AN4)}  
    g3=-i*ww./2; vkXdKL(q  
    P1=0; B !hrr  
    P2=0; t7%!~s=,M  
    P3=1; TZ7{cekQ  
    P=0; Yz?1]<X  
    for m1=1:M1                 ~!,Q<?  
    p=0.032*m1;                %input amplitude #6tb{ws3  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ~la=rh3  
    s1=s10; E&/D%}Wl  
    s20=0.*s10;                %input in waveguide 2 3d{v5. C#X  
    s30=0.*s10;                %input in waveguide 3 gJy Ft8Z<  
    s2=s20; w:z@!<  
    s3=s30; !S/hH%C  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   =9 TAs? =  
    %energy in waveguide 1 #@m*yJg<  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   at/v.U |F  
    %energy in waveguide 2 %rQ5 <U  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   PUUBn"U-  
    %energy in waveguide 3 ;n*N9-|.  
    for m3 = 1:1:M3                                    % Start space evolution bT@7&  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS #pxc6W /  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; =#i#IF42?  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; GRC=G&G  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform 3:rH1vG.m  
       sca2 = fftshift(fft(s2)); 2&W(@wT$  
       sca3 = fftshift(fft(s3)); <%JRZYZ  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ,~Y5vnaOQ  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); #EpDIL  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); F6T@YSP  
       s3 = ifft(fftshift(sc3)); JlF0L%Rc  
       s2 = ifft(fftshift(sc2));                       % Return to physical space =*q:R9V  
       s1 = ifft(fftshift(sc1)); *|x2"?d-F:  
    end Z;@F.r  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Q^v8n1  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); j\nnx8`7  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); rbnu:+!  
       P1=[P1 p1/p10]; <?P UF,  
       P2=[P2 p2/p10]; i&^?p|eKa  
       P3=[P3 p3/p10]; R0fZ9_d7}  
       P=[P p*p]; EjB<`yT  
    end lX`)Avqa  
    figure(1) unmuY^+<  
    plot(P,P1, P,P2, P,P3); &b}!KD1  
    b9(d@2MtK  
    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~!~