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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 *s/F4?*  
    ClEtw   
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of HH]LvK  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of 1,/oS&?E  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @U9ov >E  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [[)HPHSQ  
    %@IR7v~  
    %fid=fopen('e21.dat','w'); +yYz;, \  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) l^SKd  
    M1 =3000;              % Total number of space steps cL}g7D  
    J =100;                % Steps between output of space s*Fmu7o43  
    T =10;                  % length of time windows:T*T0 rj6wKf z  
    T0=0.1;                 % input pulse width "{&!fD~w  
    MN1=0;                 % initial value for the space output location dtnAMa5$T  
    dt = T/N;                      % time step APF-*/K?  
    n = [-N/2:1:N/2-1]';           % Index -PX {W)Aw  
    t = n.*dt;   ruA!+@or  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 !W6]+  
    u20=u10.*0.0;                  % input to waveguide 2 >Rr]e`3wG  
    u1=u10; u2=u20;                 NTn-4iJy  
    U1 = u1;   a~{mRh  
    U2 = u2;                       % Compute initial condition; save it in U e06r5%|.%  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. 8 /\rmf\  
    w=2*pi*n./T; rSa 3u*xB  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T JU~l  
    L=4;                           % length of evoluation to compare with S. Trillo's paper :_vf1>[  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 z7GLpTa  
    for m1 = 1:1:M1                                    % Start space evolution 7wZKK0;T  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS z,^baU  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; a|OX4  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform YUc&X^O  
       ca2 = fftshift(fft(u2)); x&kF;UC  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation p( z.[  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   0uj3kr?cv  
       u2 = ifft(fftshift(c2));                        % Return to physical space b>o38(  
       u1 = ifft(fftshift(c1)); yJ?4B?p(  
    if rem(m1,J) == 0                                 % Save output every J steps. v_b%2;<1  
        U1 = [U1 u1];                                  % put solutions in U array R@ihN?k  
        U2=[U2 u2]; RCsd  
        MN1=[MN1 m1]; a*o=,!  
        z1=dz*MN1';                                    % output location QupCr/Hs  
      end $L3UDX+F  
    end G"C'/  
    hg=abs(U1').*abs(U1');                             % for data write to excel &L;0%  
    ha=[z1 hg];                                        % for data write to excel -l^u1z  
    t1=[0 t']; k3u3X~u  
    hh=[t1' ha'];                                      % for data write to excel file qi$6y?  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Qxt ,@<IK  
    figure(1) N 0`)WLW  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn U t0oh  
    figure(2) pWeKN`  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn [ibnI2I]`  
    g }5lGz4  
    非线性超快脉冲耦合的数值方法的Matlab程序 2x t 8F  
    {&m^*YN/  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   `vUilh ^c  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Z?dz@d%C  
    JH5ckgdZ  
    r IY_1  
    )88z=5.  
    %  This Matlab script file solves the nonlinear Schrodinger equations eR =P  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of }ob#LC,  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear <Knl6$B  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =M>pL+#  
    l(*`,-pv:  
    C=1;                           6"z:s-V  
    M1=120,                       % integer for amplitude [>v.#:YM^  
    M3=5000;                      % integer for length of coupler vDqmD{%4N  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) l7nc8K  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. 0]fzjiaGt  
    T =40;                        % length of time:T*T0. oBpHmMzA  
    dt = T/N;                     % time step pFx7URZA  
    n = [-N/2:1:N/2-1]';          % Index G D$o |l]\  
    t = n.*dt;   3Oy?_a$  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. x}{/) ?vC  
    w=2*pi*n./T; Jzo|$W  
    g1=-i*ww./2; X6kCYTJYF  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; VMZ\9IwI  
    g3=-i*ww./2; ( hp 52Vse  
    P1=0; JN,4#,  
    P2=0; 2h%/exeS;  
    P3=1; "@#^/m)  
    P=0; 7'LKyy !"3  
    for m1=1:M1                 ">@]{e*  
    p=0.032*m1;                %input amplitude i^f*Em1  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 k+t?EZ6L  
    s1=s10; W9+H /T7!  
    s20=0.*s10;                %input in waveguide 2 p D-k<8|  
    s30=0.*s10;                %input in waveguide 3 j  Jt"=  
    s2=s20; 3MH9%*w'0  
    s3=s30; EyO=M~nsS  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   b bCH(fYbu  
    %energy in waveguide 1 *eK\W00  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   >k }ea5+  
    %energy in waveguide 2 %-1-y]R|  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ^ ~'&K e  
    %energy in waveguide 3 P{-j ^'y  
    for m3 = 1:1:M3                                    % Start space evolution Tr*3:J }  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS C-u'Me)H  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; 6V-u<FJ  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; mSdByT+dG  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform >"5 f B  
       sca2 = fftshift(fft(s2)); )31{.c/  
       sca3 = fftshift(fft(s3)); nvY%{Zf$}  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   ;UUpkOQO(  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); lY -2e>  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); Td(eNe_4T  
       s3 = ifft(fftshift(sc3)); Vq-W|<7C=  
       s2 = ifft(fftshift(sc2));                       % Return to physical space Di) %vU  
       s1 = ifft(fftshift(sc1)); 1 etl:gcEC  
    end u a%@Ay1|  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); [J{\Ke0<e1  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); &YpViC4K.  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); !>RDHu2n  
       P1=[P1 p1/p10]; Is&0h|  
       P2=[P2 p2/p10]; QiKci%=SX  
       P3=[P3 p3/p10]; pW5ch"HE  
       P=[P p*p]; AS5' j  
    end n#$sLXVy  
    figure(1) h @AKfE!\~  
    plot(P,P1, P,P2, P,P3); ;YN`E  
    zbY2gq@?  
    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~!~