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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 *Z; r B  
    IytDvz*|  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of YtpRy% R  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of (vnoP< 0  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear #~S>K3(  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =HS4I.@c_5  
    \ADLMj`F|  
    %fid=fopen('e21.dat','w'); T{tn.sT  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Q(e{~ ]*  
    M1 =3000;              % Total number of space steps tvGlp)?.  
    J =100;                % Steps between output of space x}|+sS,g  
    T =10;                  % length of time windows:T*T0 YQYX,b  
    T0=0.1;                 % input pulse width JCD?qeTg  
    MN1=0;                 % initial value for the space output location IT18v[-G  
    dt = T/N;                      % time step l#$TYJi  
    n = [-N/2:1:N/2-1]';           % Index >azEed<B  
    t = n.*dt;   t!:)L+$3  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 lH6fvz  
    u20=u10.*0.0;                  % input to waveguide 2 lm*g Gy1i  
    u1=u10; u2=u20;                 5B?i(2&#  
    U1 = u1;   ?!y"OrHg  
    U2 = u2;                       % Compute initial condition; save it in U )b0];&hw]  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. BPewc9RxV  
    w=2*pi*n./T; `7\H41%\pp  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T Z9VR]cf?  
    L=4;                           % length of evoluation to compare with S. Trillo's paper ?A&%Cwj  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 n]iyFZ`9  
    for m1 = 1:1:M1                                    % Start space evolution 7]Rk+q2:  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS N 2Ssf$  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 'fn$'CeM(  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform zSXA=   
       ca2 = fftshift(fft(u2)); )NIv  "Q  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ke]Yfwk  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Cfv]VQQE  
       u2 = ifft(fftshift(c2));                        % Return to physical space |vz9Hs$@l  
       u1 = ifft(fftshift(c1)); 0X>T+A[E  
    if rem(m1,J) == 0                                 % Save output every J steps. =) }nLS3t  
        U1 = [U1 u1];                                  % put solutions in U array hl]S'yr  
        U2=[U2 u2]; ve fU'  
        MN1=[MN1 m1]; NbkK&bz  
        z1=dz*MN1';                                    % output location PJK9704 6  
      end :j,}{)5=  
    end RB;BQoGX  
    hg=abs(U1').*abs(U1');                             % for data write to excel > c:Zx!  
    ha=[z1 hg];                                        % for data write to excel +?AW>&68y  
    t1=[0 t']; qrE0H  
    hh=[t1' ha'];                                      % for data write to excel file x<>YUw8`  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format N}mh}  
    figure(1) WFDCPQ@  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn p[qg&VKB  
    figure(2) Ao"C<.gUYP  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn #&BS ?@  
    y/tSGkMv  
    非线性超快脉冲耦合的数值方法的Matlab程序 12OlrU  
    oKa>.e7.  
    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。   ;==j|/ERe  
    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 vQHpf>o  
    mNDuwDd$S  
    %*K;np-q{  
    iRve)   
    %  This Matlab script file solves the nonlinear Schrodinger equations ?1w"IjUS  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of f^e&hyC   
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +|&0fGv;d9  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 GTAf   
    g~)3WfC$[  
    C=1;                           DFy1 bg  
    M1=120,                       % integer for amplitude -N# #w=  
    M3=5000;                      % integer for length of coupler ^P$7A]!  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) moG~S]  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. X"<|Z]w  
    T =40;                        % length of time:T*T0. WcEt%mGQ,  
    dt = T/N;                     % time step ~kb{K;  
    n = [-N/2:1:N/2-1]';          % Index {7X~!e|w  
    t = n.*dt;   A[JM4x   
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. kEP<[K  
    w=2*pi*n./T; h<NRE0-  
    g1=-i*ww./2; ,YB1 y)x  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;  zy>}L #  
    g3=-i*ww./2; "% Y u wMY  
    P1=0; u)~s4tP4  
    P2=0; vYnftJK&  
    P3=1; A*i_|]Q  
    P=0; ]sL45k2W  
    for m1=1:M1                 uJ8{HB  
    p=0.032*m1;                %input amplitude h(N=V|0  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 +tU Q  
    s1=s10; S#2[%o  
    s20=0.*s10;                %input in waveguide 2 '5rU e\k  
    s30=0.*s10;                %input in waveguide 3 Gru ALx7  
    s2=s20; X| <yq  
    s3=s30; ; k}H(QI  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   mx}E$b$<CY  
    %energy in waveguide 1 L|\Diap  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   E {>`MNj  
    %energy in waveguide 2 KlO(o#&N  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   Ekjf^Uo  
    %energy in waveguide 3 =DMbz`t  
    for m3 = 1:1:M3                                    % Start space evolution &t_h'JX&  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 7>,rvW:]  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; TB#N k5  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; PAoX$q  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Ef,Cd[]b  
       sca2 = fftshift(fft(s2)); k?j Fh6%  
       sca3 = fftshift(fft(s3)); j04/[V)  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   %g w{[ /[A  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); TSQh X~RN  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); VQ<5%+  
       s3 = ifft(fftshift(sc3)); }\Z5{OA  
       s2 = ifft(fftshift(sc2));                       % Return to physical space f:vD`Fz1  
       s1 = ifft(fftshift(sc1)); aQ|hi F}  
    end ps+:</;Z  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); [`nY2[A$  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); F$yeF^\g  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 9p*-?kPb  
       P1=[P1 p1/p10]; 9L  HuS  
       P2=[P2 p2/p10]; :e2X/tl#  
       P3=[P3 p3/p10]; 5-w:c>  
       P=[P p*p]; l%<c6;  
    end =P]GPEz_  
    figure(1) @vAFfYU9<.  
    plot(P,P1, P,P2, P,P3); 7\%$>< K  
    `bqzg  
    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~!~