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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 正序阅读 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 i"pOYZW1  
    o8v,17 8  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of ~qIr'?D  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of =LGSywWM9  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear gXM+N(M-  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 $15H_X*!  
    9!kp3x/`  
    %fid=fopen('e21.dat','w'); ?~(#~3x  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) Xo&\~b#-  
    M1 =3000;              % Total number of space steps /7fd"U$Lh  
    J =100;                % Steps between output of space f re5{=@  
    T =10;                  % length of time windows:T*T0 F ^aD#  
    T0=0.1;                 % input pulse width 7(a1@VH  
    MN1=0;                 % initial value for the space output location "z;R"sv\  
    dt = T/N;                      % time step gVI`&W__,  
    n = [-N/2:1:N/2-1]';           % Index t\TxK7i  
    t = n.*dt;   _N)&<'lB<  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 Px9 K  
    u20=u10.*0.0;                  % input to waveguide 2 #TC}paIpj  
    u1=u10; u2=u20;                  ST0TWE'  
    U1 = u1;   O0s!3hKu  
    U2 = u2;                       % Compute initial condition; save it in U i]L=M 5^C  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ]!~?j3-k Q  
    w=2*pi*n./T; os&FrtDg  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T lI+^}-<  
    L=4;                           % length of evoluation to compare with S. Trillo's paper +!!G0Zj/  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 .N@+Ms3  
    for m1 = 1:1:M1                                    % Start space evolution TbN{ex*  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS SynRi/BRmw  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; /wl]kGF  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform ~8"oH5  
       ca2 = fftshift(fft(u2)); |lg jI!iK  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation z Tz_"N I  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   "v( pluN|  
       u2 = ifft(fftshift(c2));                        % Return to physical space o4J@M{xb_  
       u1 = ifft(fftshift(c1)); -sZb+2tDa  
    if rem(m1,J) == 0                                 % Save output every J steps. aM(#J7;  
        U1 = [U1 u1];                                  % put solutions in U array k_ywwkG9lU  
        U2=[U2 u2]; E*wG5] at  
        MN1=[MN1 m1]; I,`;#Q)nx  
        z1=dz*MN1';                                    % output location 8DY:a['-d  
      end MGxkqy?  
    end he:z9EG}  
    hg=abs(U1').*abs(U1');                             % for data write to excel jD}h`(bE  
    ha=[z1 hg];                                        % for data write to excel B]: |;d  
    t1=[0 t']; /BD'{tZ]Sl  
    hh=[t1' ha'];                                      % for data write to excel file ]!@=2kG4  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format -mn/Yv  
    figure(1) *|<~IQg  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn u[Si=)`VPk  
    figure(2) D~URY_[A  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn C"B'Dj  
    p<#aXs jy  
    非线性超快脉冲耦合的数值方法的Matlab程序 kh:_,g  
    0I<L<^s3^U  
    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。    _cj=}!I  
    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 _DT,iF*6  
    DR:DXJc  
    G5K?Q+n   
    &qWB\m  
    %  This Matlab script file solves the nonlinear Schrodinger equations D,[Nn_N  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of II|;_j  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear @ =~k[o  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 *w O~RnP  
    UZrEFpi  
    C=1;                           *Egg*2P;"Q  
    M1=120,                       % integer for amplitude s }OL)rW=}  
    M3=5000;                      % integer for length of coupler a$Y{ut0t(  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) wet[f{c  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. g,!.`[e'ex  
    T =40;                        % length of time:T*T0. iLNUydiS  
    dt = T/N;                     % time step 1[u{y{9 q  
    n = [-N/2:1:N/2-1]';          % Index doHE]gC2Uz  
    t = n.*dt;   PnInsf%;  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. =~Qg(=U0U  
    w=2*pi*n./T; 2[uFAgf@  
    g1=-i*ww./2; ]@<VLP?  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 3S]Q IZ1  
    g3=-i*ww./2; 1iLo$  
    P1=0; =b>TFB=*N  
    P2=0; /|P{t{^WM  
    P3=1; 3nc\6v%  
    P=0; KV|D]}  
    for m1=1:M1                 "aCB}  
    p=0.032*m1;                %input amplitude !rAH@y.l  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 V| kN 1 A  
    s1=s10; zIu/!aw  
    s20=0.*s10;                %input in waveguide 2 6QbDU[  
    s30=0.*s10;                %input in waveguide 3 @KU;' th  
    s2=s20; >yXhP6  
    s3=s30; zhd1)lgY  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   CJ%'VijhD  
    %energy in waveguide 1 0F%8d@Y2  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   rTR"\u7&H  
    %energy in waveguide 2 8h@L_*Kr  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   }F!Uu KR  
    %energy in waveguide 3 ^uN[rHZ*u  
    for m3 = 1:1:M3                                    % Start space evolution kk6 !krZ  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS `y^\c#k  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; }Oc+EV-Z  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; OUF%DMl4  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform :i?6#_2IC  
       sca2 = fftshift(fft(s2)); <nD@4J-A0  
       sca3 = fftshift(fft(s3)); SJa>!]U'xI  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   %aMC[i  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); =FV(m S  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); EFh^C.S8  
       s3 = ifft(fftshift(sc3)); 1.3dy]vG  
       s2 = ifft(fftshift(sc2));                       % Return to physical space Kc2y  
       s1 = ifft(fftshift(sc1)); gjN'D!'E1D  
    end lGWz  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); +~iiy;i(  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); )1M2}11uS  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); g`S;xs  
       P1=[P1 p1/p10]; QY&c=bWAX"  
       P2=[P2 p2/p10]; *->*p35  
       P3=[P3 p3/p10]; rC_1f3A  
       P=[P p*p]; Kmaz"6A  
    end E~fb#6  
    figure(1) E]/2 u3p  
    plot(P,P1, P,P2, P,P3); {G x=QNd  
    6Yodx$  
    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~!~