切换到宽版
  • 广告投放
  • 稿件投递
  • 繁體中文
    • 8766阅读
    • 1回复

    [分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

    上一主题 下一主题
    离线tianmen
     
    发帖
    58
    光币
    15
    光券
    0
    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 4ye`;hXy  
    $@u^Jt, ?  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of -aH?7HV}  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of -9H!j4]T?  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear 3'sWlhf;  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 QN}3S0  
    S\v&{  
    %fid=fopen('e21.dat','w'); +4:+qGAJ{  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) M[ ~2,M&H  
    M1 =3000;              % Total number of space steps 6t7;}t]t  
    J =100;                % Steps between output of space B GEJiLH  
    T =10;                  % length of time windows:T*T0 )HzITsFZKT  
    T0=0.1;                 % input pulse width !aW*dD61  
    MN1=0;                 % initial value for the space output location vY0V{u?J  
    dt = T/N;                      % time step Xg!|F[i  
    n = [-N/2:1:N/2-1]';           % Index XJxs4a1[t  
    t = n.*dt;   z[lRb]:i[  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 5>1Y="B  
    u20=u10.*0.0;                  % input to waveguide 2 :LIKp;  
    u1=u10; u2=u20;                 rt@-Pw!B  
    U1 = u1;   y`B!6p 5j  
    U2 = u2;                       % Compute initial condition; save it in U "mP*}VF  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. e}Af"LI  
    w=2*pi*n./T; Pu%>j'A  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T $MJDB  
    L=4;                           % length of evoluation to compare with S. Trillo's paper Y3MR:{}  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 0ZID @^  
    for m1 = 1:1:M1                                    % Start space evolution 2GD mZl  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS ^d5./M8Bd  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; 5k%N<e` `  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform xZ @O"*{  
       ca2 = fftshift(fft(u2)); AXU!-er$  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation S~a:1 _Wl  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   Etr8lm E  
       u2 = ifft(fftshift(c2));                        % Return to physical space ZvnZ}t >?  
       u1 = ifft(fftshift(c1)); DT(Zv2  
    if rem(m1,J) == 0                                 % Save output every J steps. %*Z2Gef?H  
        U1 = [U1 u1];                                  % put solutions in U array Lx:9@3'7'  
        U2=[U2 u2]; -< dMD_  
        MN1=[MN1 m1]; )V$!  
        z1=dz*MN1';                                    % output location N>6yacTB  
      end 2W:?#h3  
    end XF f+efh  
    hg=abs(U1').*abs(U1');                             % for data write to excel sO4}kxZ  
    ha=[z1 hg];                                        % for data write to excel norc!?L  
    t1=[0 t']; Hj4w i|  
    hh=[t1' ha'];                                      % for data write to excel file Ye=7Y57Nr  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format d$pf[DJQo  
    figure(1) _~S^#ut+  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn !qGx(D{\  
    figure(2) W$MEbf%1  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn xc]C#q  
    #&2N,M!Q  
    非线性超快脉冲耦合的数值方法的Matlab程序 SSsQu^A  
    iJKm27 ">  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   yE|} r  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 K^qUlyv  
    \,bFm,kC?  
    %:;[M|.  
    Hv7D+ j8M  
    %  This Matlab script file solves the nonlinear Schrodinger equations i!}nGJGg  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of gK#fuQ$hH  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ZRq}g:  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 s)DNLx  
    BM$tywC  
    C=1;                           wZ3 vF)2s  
    M1=120,                       % integer for amplitude ~CdseSo 9  
    M3=5000;                      % integer for length of coupler 6k=Wt7C  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) rIWN!@.J  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. -MW(={#   
    T =40;                        % length of time:T*T0. 9oxf)pjw  
    dt = T/N;                     % time step ]-Y]Q%A4  
    n = [-N/2:1:N/2-1]';          % Index <QW1fE  
    t = n.*dt;   f}ij=Y9  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. RJs G]`  
    w=2*pi*n./T; eKFc W5O  
    g1=-i*ww./2; :2Rci`lp  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; ?O>JtEz~lQ  
    g3=-i*ww./2; .L{+O6*c  
    P1=0; |e; z"-3  
    P2=0; {f-/,g~  
    P3=1; =^AZx)Kwd  
    P=0; YM.IRj2/1  
    for m1=1:M1                 *9{Wn7pck/  
    p=0.032*m1;                %input amplitude {*Wwu f.  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 +:Q/<^Z  
    s1=s10; 5b4V/d* '  
    s20=0.*s10;                %input in waveguide 2 )7%]<2V%  
    s30=0.*s10;                %input in waveguide 3 W]Tt8  
    s2=s20; (5DGs_>  
    s3=s30; qkG;YGio  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   #`)-$vUv^f  
    %energy in waveguide 1 `k%#0E*H  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   7{6.  
    %energy in waveguide 2 /z?7ic0  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   PEn^.v@  
    %energy in waveguide 3 /(pD^D  
    for m3 = 1:1:M3                                    % Start space evolution wp GnS  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS QT l._j@  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; DCzPm/#b  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; ! E#.WX  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform svRaU7<UDN  
       sca2 = fftshift(fft(s2)); ,u^0V"hJ  
       sca3 = fftshift(fft(s3)); A*U'SCg(G  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   /F}\V ^  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); 4m(>"dHP  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); \bQ!> l\  
       s3 = ifft(fftshift(sc3)); G$`4.,g  
       s2 = ifft(fftshift(sc2));                       % Return to physical space JG4*B|3  
       s1 = ifft(fftshift(sc1)); YYr&r.6  
    end GfPz^F=ie.  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); (BQ3M-  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); $$f$$  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); gWH9=%!  
       P1=[P1 p1/p10]; >!F,y3"5S  
       P2=[P2 p2/p10]; f\r4[gU@  
       P3=[P3 p3/p10]; 3U.qN0]  
       P=[P p*p]; g E+OQWu  
    end /lQ0`^yB  
    figure(1) % j{pz  
    plot(P,P1, P,P2, P,P3); "?&bh@P&  
    dq/?&X  
    转自:http://blog.163.com/opto_wang/
     
    分享到
    离线ciomplj
    发帖
    319
    光币
    1
    光券
    0
    只看该作者 1楼 发表于: 2014-06-22
    谢谢哈~!~