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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 lL*"N|Y  
    Qb@i_SX(fs  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of *z__$!LR  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of _f@nUv*  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear Z L'krV  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 AdWP  
    Xj$'i/=-+c  
    %fid=fopen('e21.dat','w'); h"dn:5G:=  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) j# n  
    M1 =3000;              % Total number of space steps Hx NoV.q  
    J =100;                % Steps between output of space 0A F}wz>  
    T =10;                  % length of time windows:T*T0 c"pu"t@/Z  
    T0=0.1;                 % input pulse width ddw^oU  
    MN1=0;                 % initial value for the space output location g5t`YcL  
    dt = T/N;                      % time step #NWS)^&1b  
    n = [-N/2:1:N/2-1]';           % Index |b+CXEzo  
    t = n.*dt;   Y``]66\Fp  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 g1&q6wCg|  
    u20=u10.*0.0;                  % input to waveguide 2 4E@_Fn_#  
    u1=u10; u2=u20;                 !"dAwG?S  
    U1 = u1;   {GG;/Ns{f-  
    U2 = u2;                       % Compute initial condition; save it in U newURb,-!  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. WU~L#Ih.V  
    w=2*pi*n./T; Nq#B4Zx  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T c.}#.-b8  
    L=4;                           % length of evoluation to compare with S. Trillo's paper j>Cp4  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 j5G=ZI86y  
    for m1 = 1:1:M1                                    % Start space evolution 7,FhKTV1/  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS `( _N9.>B  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; ilwIqj  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform _c,{}sn  
       ca2 = fftshift(fft(u2)); )^m"fQ+  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation PBgU/zVn  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   I[bWd{i:  
       u2 = ifft(fftshift(c2));                        % Return to physical space 0+Q; a  
       u1 = ifft(fftshift(c1)); "8/BVW^bv  
    if rem(m1,J) == 0                                 % Save output every J steps. ,&s%^I+CC  
        U1 = [U1 u1];                                  % put solutions in U array Vj6 w7hz  
        U2=[U2 u2]; m=V69 a#  
        MN1=[MN1 m1]; L4v26*P  
        z1=dz*MN1';                                    % output location JwdvY]  
      end apWv+A  
    end f*Yr*yC  
    hg=abs(U1').*abs(U1');                             % for data write to excel a$$aM2.2  
    ha=[z1 hg];                                        % for data write to excel O8/r-?4.  
    t1=[0 t']; h}=  
    hh=[t1' ha'];                                      % for data write to excel file t_ id/  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format FA1h!Vit  
    figure(1) C&;m56  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn K?*p|&Fi?8  
    figure(2) d?)Ic1][  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn 9}' 92  
    c6tH'oV  
    非线性超快脉冲耦合的数值方法的Matlab程序 [H {2<!  
    SDko#  
    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。   $~NB .SY  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 r)oR `\7  
    WMnxN34  
    CRu {Ie5B  
    {}"a_L&[;  
    %  This Matlab script file solves the nonlinear Schrodinger equations DtkOb,wY  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of ;Hn>Ew  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear CQH^VTQ  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +<fT\Oq#  
    c=33O,_  
    C=1;                           t""d^a#Dp  
    M1=120,                       % integer for amplitude Gp2C wyv  
    M3=5000;                      % integer for length of coupler Q$A;Fk}-  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) qEM,~:lTn  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. B]:?4Ov  
    T =40;                        % length of time:T*T0. =1zRm >m  
    dt = T/N;                     % time step ?gG%FzfQ/  
    n = [-N/2:1:N/2-1]';          % Index q>[}JtXK  
    t = n.*dt;   9b)'vr*Hy7  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. (/A 6kp?  
    w=2*pi*n./T; _^`TG]F  
    g1=-i*ww./2; rAS2qt  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; Gk!CU"`sP  
    g3=-i*ww./2; g:Fo7*i  
    P1=0; spma\,o  
    P2=0; 3 ]w a8|  
    P3=1; kg^5D3!2{Q  
    P=0; <"nF`'olV  
    for m1=1:M1                 @*iT%p_L  
    p=0.032*m1;                %input amplitude 3]67U}`  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 + De-U.  
    s1=s10; Wt!8.d} =  
    s20=0.*s10;                %input in waveguide 2 :.SwO<j  
    s30=0.*s10;                %input in waveguide 3 vWjHHw  
    s2=s20; @^nE^;  
    s3=s30; n\u3$nGL1`  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   B*n_ VBd  
    %energy in waveguide 1 U[6 ~ad a  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   oWBjPsQ  
    %energy in waveguide 2 t LM/STb6  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   )npvy>C'(  
    %energy in waveguide 3 |v:fP;zc  
    for m3 = 1:1:M3                                    % Start space evolution )zu m.6pT  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS 51`*VR]`K  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; bM"d$tl$?'  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; U[NQ"  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform pPJE.[)V/  
       sca2 = fftshift(fft(s2)); wPaMYxO/  
       sca3 = fftshift(fft(s3)); V@\A<q%jTs  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   SeBl*V  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); s(y=u>  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Q'0:k{G  
       s3 = ifft(fftshift(sc3)); G1ED=N_#  
       s2 = ifft(fftshift(sc2));                       % Return to physical space z 9~|Su  
       s1 = ifft(fftshift(sc1)); r_pZK(G%  
    end M)CQ|P  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); lLN5***47J  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); wQ '_, d  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Z=^~]Mfa  
       P1=[P1 p1/p10]; $mn+  
       P2=[P2 p2/p10]; 9HZR%s[J  
       P3=[P3 p3/p10]; 6d;RtCENo  
       P=[P p*p]; 'y|p)r"  
    end ,b74 m  
    figure(1) B4w/cIj_  
    plot(P,P1, P,P2, P,P3); -8z@FLUK-  
    PF0AU T  
    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~!~