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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 d=o|)kV  
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    %  This Matlab script file solves the coupled nonlinear Schrodinger equations of .9 mwRYgD  
    %  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of ,=O`'l >K  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear  iE=Yh  
    %   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 gV$j ]  
    l9lBhltOH  
    %fid=fopen('e21.dat','w'); k<Z^93 S  
    N = 128;                       % Number of Fourier modes (Time domain sampling points) 'C8VD+p  
    M1 =3000;              % Total number of space steps  U":hJ*F)  
    J =100;                % Steps between output of space ]>E*s3h  
    T =10;                  % length of time windows:T*T0 0^az<!!O#  
    T0=0.1;                 % input pulse width ;&q}G1  
    MN1=0;                 % initial value for the space output location J0*hJ-/u  
    dt = T/N;                      % time step L3JFQc/oh~  
    n = [-N/2:1:N/2-1]';           % Index % obR2%  
    t = n.*dt;   X^ckTIdR  
    u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 _Db=I3.HJ  
    u20=u10.*0.0;                  % input to waveguide 2 rL3<r  
    u1=u10; u2=u20;                 n$ $^(-g@)  
    U1 = u1;   Py$Q]s?\1  
    U2 = u2;                       % Compute initial condition; save it in U GwQW I ]  
    ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. $,v '>  
    w=2*pi*n./T; bXF>{%(}E  
    g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T -G e5gQ=  
    L=4;                           % length of evoluation to compare with S. Trillo's paper X ,n4_=f  
    dz=L/M1;                       % space step, make sure nonlinear<0.05 $h`(toTyF  
    for m1 = 1:1:M1                                    % Start space evolution C93BK)$}  
       u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS {e\Pd!D?|  
       u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; gKeqf-UWKJ  
       ca1 = fftshift(fft(u1));                        % Take Fourier transform 8] skAh  
       ca2 = fftshift(fft(u2)); , (dg]7  
       c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation v".q578 0B  
       c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   #no~g( !o  
       u2 = ifft(fftshift(c2));                        % Return to physical space 1 rKKph  
       u1 = ifft(fftshift(c1)); eQu%TZ(x-$  
    if rem(m1,J) == 0                                 % Save output every J steps. >J[Bf9)>  
        U1 = [U1 u1];                                  % put solutions in U array Se<]g$eK?5  
        U2=[U2 u2]; n8UQIa4&=  
        MN1=[MN1 m1]; n|2`y?  
        z1=dz*MN1';                                    % output location m^0r9y,  
      end s0uI;WMg  
    end wI><kdz  
    hg=abs(U1').*abs(U1');                             % for data write to excel 2+zE|I.  
    ha=[z1 hg];                                        % for data write to excel ma9q?H#X  
    t1=[0 t']; Yv k Qh{  
    hh=[t1' ha'];                                      % for data write to excel file ;iR( Ir  
    %dlmwrite('aa',hh,'\t');                           % save data in the excel format =M'M/vKD  
    figure(1) rqW[B/a{  
    waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn HM57b>6  
    figure(2) A]ZCQ49  
    waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn oNQ;9&Z,^2  
    W&CQ87b  
    非线性超快脉冲耦合的数值方法的Matlab程序 59mNb:<  
    oJa6)+b(3  
    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。   bwo-9B  
    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 x2x) y08  
    w}No ^.I*4  
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    Wt5x*p-!C  
    %  This Matlab script file solves the nonlinear Schrodinger equations g?` g+:nug  
    %  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of W9n0Jv  
    %  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear ]T|9>o!  
    %  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 QR4rQu  
    uw!  
    C=1;                           h07Z.q ;  
    M1=120,                       % integer for amplitude e9e%8hL  
    M3=5000;                      % integer for length of coupler MJNY#v3  
    N = 512;                      % Number of Fourier modes (Time domain sampling points) Fx,08  
    dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. io :g ]g  
    T =40;                        % length of time:T*T0. Rs_0xh  
    dt = T/N;                     % time step a h<1&UG,  
    n = [-N/2:1:N/2-1]';          % Index uo0g51%9  
    t = n.*dt;   [ []'U'  
    ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. 'F%4[3a$\n  
    w=2*pi*n./T; ?xEQ'(UBQ  
    g1=-i*ww./2; {Hncm  
    g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; 06DT2  
    g3=-i*ww./2; r_C|gfIP  
    P1=0; [-o`^;  
    P2=0; HR)Dz~Obw  
    P3=1; pRI<L'  
    P=0; mr:;Wwd  
    for m1=1:M1                 RtVy^~=G  
    p=0.032*m1;                %input amplitude ~3byAL  
    s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 O@JgVdgf  
    s1=s10; ,XT#V\qne  
    s20=0.*s10;                %input in waveguide 2 )E;+C2G  
    s30=0.*s10;                %input in waveguide 3 ~RcI+jR)  
    s2=s20; 1d/-SxhZ  
    s3=s30; ] jbQou@  
    p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   [h>|6%sW  
    %energy in waveguide 1 W>C!V  
    p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   \#4??@+Xf  
    %energy in waveguide 2 FTM(y CN  
    p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   is=sV:j:  
    %energy in waveguide 3 &qw7BuF  
    for m3 = 1:1:M3                                    % Start space evolution %Q]u_0P*  
       s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS ").MU[q%Y  
       s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; *r!f! eA:  
       s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; l;i,V;@ t  
       sca1 = fftshift(fft(s1));                       % Take Fourier transform _&S?uz m  
       sca2 = fftshift(fft(s2)); TDI8L\rr  
       sca3 = fftshift(fft(s3)); >55c{|"@L  
       sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   a<X8l^Ln  
       sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); DLMG<4Cd~  
       sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); }~P%S(zB  
       s3 = ifft(fftshift(sc3)); kp3(/`xP  
       s2 = ifft(fftshift(sc2));                       % Return to physical space |8I #`  
       s1 = ifft(fftshift(sc1)); OJd!g/V  
    end (;utiupW  
       p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); Y" 9 o  
       p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); KTn,}7vZ  
       p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); w:Ui_-4*>  
       P1=[P1 p1/p10]; 1-Fg_G}|6  
       P2=[P2 p2/p10]; \)'nxFKqV  
       P3=[P3 p3/p10]; !_GY\@}  
       P=[P p*p]; )6|7L)Dk  
    end jvx9b([<sG  
    figure(1) ~~:w^(s9  
    plot(P,P1, P,P2, P,P3); $ tf;\R  
    4 -)'a} O  
    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~!~