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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 (hZ:X)E>  
    d}0qJoH4  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of 1-;?0en&0  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of zDBD.5R;  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear a, Kky ^B  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 aSnp/g  
    |DG@ht  
    %fid=fopen('e21.dat','w'); 0~E 6QhV:  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) %|Hp Bs#'  
    M1 =3000;              % Total number of space steps -]"T^w ib  
    J =100;                % Steps between output of space nTnRGf\T  
    T =10;                  % length of time windows:T*T0 j64 4V|z  
    T0=0.1;                 % input pulse width M?:\9DDd  
    MN1=0;                 % initial value for the space output location =d20Xa  
    dt = T/N;                      % time step 6n w&$I  
    n = [-N/2:1:N/2-1]';           % Index Etnb3<^[t  
    t = n.*dt;   M23& <}Q8  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 N7.  @FK  
    u20=u10.*0.0;                  % input to waveguide 2 CUhV$A#oo  
    u1=u10; u2=u20;                 ]O{_O&w  
    U1 = u1;   Q)6va}2ai  
    U2 = u2;                       % Compute initial condition; save it in U P\B3 y+)  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. # 3.)H9  
    w=2*pi*n./T; E3\ZJjG  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T N=ifIVc  
    L=4;                           % length of evoluation to compare with S. Trillo's paper m4**>!I  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 LcUlc)YH5  
    for m1 = 1:1:M1                                    % Start space evolution ?eWJa  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS _`aR_ %Gx  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; X5E '*W  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform (:}<xxl  
       ca2 = fftshift(fft(u2)); APHPN:v  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation Y1r ,2k  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   1mUTtYU  
       u2 = ifft(fftshift(c2));                        % Return to physical space qC j*>D  
       u1 = ifft(fftshift(c1)); @l,{x|00  
    if rem(m1,J) == 0                                 % Save output every J steps. dq 8+m(7k  
        U1 = [U1 u1];                                  % put solutions in U array @InJ_9E  
        U2=[U2 u2]; bXl8v  
        MN1=[MN1 m1]; mU]s7` %<>  
        z1=dz*MN1';                                    % output location kMS5h~D[  
      end i[=C_+2  
    end <d! 6[,W;  
    hg=abs(U1').*abs(U1');                             % for data write to excel ZlM_ m >,o  
    ha=[z1 hg];                                        % for data write to excel 4I ,o&TK  
    t1=[0 t']; (t74a E pi  
    hh=[t1' ha'];                                      % for data write to excel file uX0 Bp8P  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format Jk*QcEE=  
    figure(1) 6UB6;-  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn \dNhzd#  
    figure(2) h6FgS9H  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn :0dfB&7  
    cs5ix"1A  
    非线性超快脉冲耦合的数值方法的Matlab程序 w a.f![  
    (HSw%e  
    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。   uHrb:X!q  
    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 I =b'j5c  
    bA+[{  
    nt`<y0ta  
    ?H0m<jO8~  
    %  This Matlab script file solves the nonlinear Schrodinger equations | XLFV  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of T{;=#rG<  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear |$Xf;N37t  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 [Pqn 3I[  
    }z{wQ\  
    C=1;                           %#4 +!  
    M1=120,                       % integer for amplitude 4(sttd_  
    M3=5000;                      % integer for length of coupler + o{*r#  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) a^/K?lAB8  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. MBv/  
    T =40;                        % length of time:T*T0. 5%qH 7[dx  
    dt = T/N;                     % time step p\ok_*b  
    n = [-N/2:1:N/2-1]';          % Index JP_kQ  
    t = n.*dt;   M/)B" q  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. f~v"zT  
    w=2*pi*n./T; TRCI\  
    g1=-i*ww./2; j #es2;  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 777rE[\@b  
    g3=-i*ww./2; X=#It&m%s  
    P1=0; x {vIT- f  
    P2=0; .hgH9$\  
    P3=1; omT(3)TP  
    P=0; mOSCkp{<e  
    for m1=1:M1                 \086O9  
    p=0.032*m1;                %input amplitude iGQ n/Xdo  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 K /8qB~J*  
    s1=s10; y\z*p&I  
    s20=0.*s10;                %input in waveguide 2 >OTl2F}4 !  
    s30=0.*s10;                %input in waveguide 3 Q.>/*8R;  
    s2=s20; +|M{I= 8  
    s3=s30; k)Zn>  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   ktWZBQY  
    %energy in waveguide 1 p*!q}%U  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   ,=x RoXYB}  
    %energy in waveguide 2 K~$35c3M  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   M.t@@wq  
    %energy in waveguide 3 5C* ?1& !  
    for m3 = 1:1:M3                                    % Start space evolution `TkbF9N+  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS AO^]>/7ed  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; >0 7shNX  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; "C& Jwm?  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform +L n M\n  
       sca2 = fftshift(fft(s2)); M-vC>u3Y  
       sca3 = fftshift(fft(s3)); dUZ$wbV%h  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   p ^](3Vi(  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); @N]5&4NL  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); q< b"M$  
       s3 = ifft(fftshift(sc3)); !4_!J (q%  
       s2 = ifft(fftshift(sc2));                       % Return to physical space *qbRP"#[$  
       s1 = ifft(fftshift(sc1)); 3m3 EXz  
    end QT7_x`#J~o  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); (%Ng'~J\|  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); e7h\(`J0lj  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));  w}"!l G  
       P1=[P1 p1/p10]; /^~p~HKtx  
       P2=[P2 p2/p10]; pAMo XJ`  
       P3=[P3 p3/p10]; U>bP}[&S  
       P=[P p*p]; jm4)gmC  
    end \I:UC %  
    figure(1) OX`?<@6  
    plot(P,P1, P,P2, P,P3); IC\E,m  
    +J%6bn)U  
    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~!~