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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 .Exvuo`F  
    |#_p0yPy  
    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of v":q_w<k  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of :GIBB=D9  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear _z#" BN  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 <G}Lc  
    N~,Ipf  
    %fid=fopen('e21.dat','w'); _3aE]\O[  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 9K@ I  
    M1 =3000;              % Total number of space steps P gA<pfEHE  
    J =100;                % Steps between output of space ;}SGJ7  
    T =10;                  % length of time windows:T*T0 AJ}FHym_ZQ  
    T0=0.1;                 % input pulse width )7& -DI1  
    MN1=0;                 % initial value for the space output location 9I/l+IS"X  
    dt = T/N;                      % time step +g g_C'"  
    n = [-N/2:1:N/2-1]';           % Index 4z(~)#'^  
    t = n.*dt;   b WNa6x  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 K[icVT2v~  
    u20=u10.*0.0;                  % input to waveguide 2 G*4I;'6  
    u1=u10; u2=u20;                 W\~ie}D{  
    U1 = u1;   L ?/AKg  
    U2 = u2;                       % Compute initial condition; save it in U fM ID}S  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. ms0V1`  
    w=2*pi*n./T; 3*<@PXpK&  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T 8lM=v> Xc  
    L=4;                           % length of evoluation to compare with S. Trillo's paper h}a}HabA  
    dz=L/M1;                       % space step, make sure nonlinear<0.05  $U?]^  
    for m1 = 1:1:M1                                    % Start space evolution C$[iduS  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS 7"'RE95  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; h,$CJdDY]  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform nriSVGi  
       ca2 = fftshift(fft(u2)); th73eC'  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation ~2k.x*$  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   i?!9%U!z4  
       u2 = ifft(fftshift(c2));                        % Return to physical space r<ww%2HTS  
       u1 = ifft(fftshift(c1)); v)Y)tu>  
    if rem(m1,J) == 0                                 % Save output every J steps. q\<l"b z  
        U1 = [U1 u1];                                  % put solutions in U array p?L%'  
        U2=[U2 u2]; MAYb.>X#>  
        MN1=[MN1 m1]; QQW}.>N  
        z1=dz*MN1';                                    % output location =H)]HxEEM  
      end :"Xnu%1  
    end uaO.7QSwN  
    hg=abs(U1').*abs(U1');                             % for data write to excel q%x i>H.:{  
    ha=[z1 hg];                                        % for data write to excel 2L&c91=wE  
    t1=[0 t']; aM $2lR])J  
    hh=[t1' ha'];                                      % for data write to excel file /[_aK0U3  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format e#/&A5#Ya  
    figure(1) sY!JB7!j  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn 9HJYrzf{%  
    figure(2) _$R=F/88  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn o6A$)m5V  
    Nqj@p<y/q  
    非线性超快脉冲耦合的数值方法的Matlab程序 b3%x&H<j  
    Kn->R9Tl  
    在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。   ?TpjU*Cxy  
    Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 =W7-;&  
    |aLK_]!  
    ei4LE XQ16  
    [@9S-$Xa  
    %  This Matlab script file solves the nonlinear Schrodinger equations `:=1*7)?  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of 5)< Y3nU~  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear z" tz-~  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 4tm%F\Izy  
    eOb--@~8  
    C=1;                           4vbGXb}!  
    M1=120,                       % integer for amplitude Q &W>h/  
    M3=5000;                      % integer for length of coupler B(M-;F  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) b|-)p+ba  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. `T*Y1@FV  
    T =40;                        % length of time:T*T0. [RKk-8I  
    dt = T/N;                     % time step pG"wQ  
    n = [-N/2:1:N/2-1]';          % Index .hH_1Mo8  
    t = n.*dt;   MDytA0M  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. :jv(-RTI  
    w=2*pi*n./T; _OG9wi(Fpx  
    g1=-i*ww./2; aUNA` L  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; #~'d Y\&  
    g3=-i*ww./2; =l:V9u-I^  
    P1=0; u)Kiwa  
    P2=0; [KR%8[e  
    P3=1; BR|0uJ.M  
    P=0; *jhgCm  
    for m1=1:M1                 I;rW!Hb  
    p=0.032*m1;                %input amplitude ifS#9N|8  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 ?<jWEz=  
    s1=s10; ((`\i=-o5  
    s20=0.*s10;                %input in waveguide 2 nam]eW  
    s30=0.*s10;                %input in waveguide 3 FNUs .d"  
    s2=s20; |9XoRGgXU  
    s3=s30; m4~ |z  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   EeMKo  
    %energy in waveguide 1 =iB[sLEJ  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   zlP{1z;nV  
    %energy in waveguide 2 G~y:ZEnN[  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   +JYb)rn$^  
    %energy in waveguide 3 Wi=zu[[qc  
    for m3 = 1:1:M3                                    % Start space evolution  lha;|  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS _'w:Sx?d7  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; ! 7V>gWhR  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; IT:WiMDQ}  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform Ba?1q%eG  
       sca2 = fftshift(fft(s2)); *bo| F%NAz  
       sca3 = fftshift(fft(s3)); 7yu-xnt3s  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   (<_kq;XtN0  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); uxn+.fA  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); w/ ~\NI  
       s3 = ifft(fftshift(sc3)); hpXW t Q  
       s2 = ifft(fftshift(sc2));                       % Return to physical space =c \(]xX  
       s1 = ifft(fftshift(sc1)); \},H\kK+^  
    end s:l H4B  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); ^U,iDK_  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); jY\z+lW6A  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); 'y!qrmMRr  
       P1=[P1 p1/p10]; ].d%R a:{  
       P2=[P2 p2/p10]; q}p$S2`  
       P3=[P3 p3/p10]; &I=o1F2B)  
       P=[P p*p]; o]tfvGvU*  
    end G^ k8Or2  
    figure(1) <gi~:%T  
    plot(P,P1, P,P2, P,P3); ZRYlm$C  
    a$?d_BX  
    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~!~