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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 Wt(Kd5k0'2  
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    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ?F1wh2o q  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of -=}b;Kf -  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 7O:"~L  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 +hpSxdAz4  
    ~+<<bzY  
    %fid=fopen('e21.dat','w'); THJ 3-Ug  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 9-b 8`|s  
    M1 =3000;              % Total number of space steps C}9Kx }q  
    J =100;                % Steps between output of space @2u#93Y  
    T =10;                  % length of time windows:T*T0 }0Y`|H\v  
    T0=0.1;                 % input pulse width k'x #t(  
    MN1=0;                 % initial value for the space output location 6Hda]y  
    dt = T/N;                      % time step : aH%bk  
    n = [-N/2:1:N/2-1]';           % Index cu<y8 :U<  
    t = n.*dt;   0E yAMu  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 F%}7cm2  
    u20=u10.*0.0;                  % input to waveguide 2 Uh*@BmDA  
    u1=u10; u2=u20;                 NK~PcdGl  
    U1 = u1;   mzu<C)9d,  
    U2 = u2;                       % Compute initial condition; save it in U w3d34*0$  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. o,J^ e_  
    w=2*pi*n./T; mdaYYD=c%  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T `T=1<Twc  
    L=4;                           % length of evoluation to compare with S. Trillo's paper B.}cB'|  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 zLL)VFCJW  
    for m1 = 1:1:M1                                    % Start space evolution ]Ym=+lgi  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS XwtAF3oz  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 5:$Xtq  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform +|9f%f6vp  
       ca2 = fftshift(fft(u2)); 6i| ~7md,  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation [$;,Ua-mt  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   O MvT;Vgg  
       u2 = ifft(fftshift(c2));                        % Return to physical space ]'tJ S]  
       u1 = ifft(fftshift(c1)); @*SA$9/l  
    if rem(m1,J) == 0                                 % Save output every J steps. l:)S 3  
        U1 = [U1 u1];                                  % put solutions in U array YIO.yN"0  
        U2=[U2 u2]; ~?CS_B *  
        MN1=[MN1 m1]; "ct58Y@   
        z1=dz*MN1';                                    % output location -n-Z/5~ X  
      end ?T <rt  
    end hox< vr4  
    hg=abs(U1').*abs(U1');                             % for data write to excel JDKLKHOMZ  
    ha=[z1 hg];                                        % for data write to excel eKyqU9  
    t1=[0 t']; oJh"@6u6K  
    hh=[t1' ha'];                                      % for data write to excel file %P;[fJ `G  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format :kt/$S^-  
    figure(1) :s]\k%"  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn  jC4O`  
    figure(2) fq=:h\\G  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn {l@WCR  
    jI A#!4  
    非线性超快脉冲耦合的数值方法的Matlab程序 2 ZK%)vq0  
    Mb1wYh  
    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。   G%$}WA]|  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 Ok,HD7  
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    g8'~e{= (  
    %  This Matlab script file solves the nonlinear Schrodinger equations 2 eHx"Ha  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of `H"vR: ~{  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear p_r4^p\  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 6<PW./rk:  
    F )7j@h^  
    C=1;                           +<{m45  
    M1=120,                       % integer for amplitude h9jc,X u5X  
    M3=5000;                      % integer for length of coupler p(?g-  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) op.d;lO@  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. .lr5!Stb  
    T =40;                        % length of time:T*T0. ) P%4:P  
    dt = T/N;                     % time step \C7q4p?8  
    n = [-N/2:1:N/2-1]';          % Index Qh8C,"a  
    t = n.*dt;   R(`]n!V2  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. \?d TH:v/E  
    w=2*pi*n./T; `,P >mp)uU  
    g1=-i*ww./2; Wj tft%  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ,_bp)-OG  
    g3=-i*ww./2; .:N:pWe  
    P1=0; r>O|L%xpv  
    P2=0; (kY@7)d'e  
    P3=1; ol}`Wwy  
    P=0; %I0}4$  
    for m1=1:M1                 ]'g:B p  
    p=0.032*m1;                %input amplitude Fpf><Rn  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 o[^Q y(2~  
    s1=s10; (0}j]p'w  
    s20=0.*s10;                %input in waveguide 2 zofx+g\(W  
    s30=0.*s10;                %input in waveguide 3 &(7$&Q  
    s2=s20; B!uxs  
    s3=s30; B:nK)"{  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   Yt*vqm[WV  
    %energy in waveguide 1 U!Mf]3  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   s??czM2O  
    %energy in waveguide 2 Y;eoT J  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   ,cD1{T\  
    %energy in waveguide 3 gyFr"9';c  
    for m3 = 1:1:M3                                    % Start space evolution 0 u2Ny&6w  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS }*Zo6{B-  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; .1{l[[= W  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; K~3Ebr  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Cm410=b  
       sca2 = fftshift(fft(s2)); C`EY5"N r  
       sca3 = fftshift(fft(s3)); %qi%$  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   yW`e |!  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); O5OXw]  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); (Vap7.6;_  
       s3 = ifft(fftshift(sc3)); 3HKxYvc C  
       s2 = ifft(fftshift(sc2));                       % Return to physical space C=[Ae,  
       s1 = ifft(fftshift(sc1)); /ao<A\KR  
    end ](nH{aY!  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); x?=B\8m  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 1daL y  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); Gk 6fO  
       P1=[P1 p1/p10]; GMe0;StT  
       P2=[P2 p2/p10]; 7H#2WFQ7  
       P3=[P3 p3/p10]; H`5Ct  
       P=[P p*p]; ;j!UY.i  
    end bBG/gQ  
    figure(1) M}KZG'7  
    plot(P,P1, P,P2, P,P3); 1!1DuQ  
    FJF3B)Va|  
    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~!~