[分享]求解光孤子或超短脉冲耦合方程的Matlab程序 [复制链接]

计算脉冲在非线性耦合器中演化的Matlab 程序 L/i'6(="  
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%  This Matlab script file solves the coupled nonlinear Schrodinger equations of Db|f"3rq?  
%  soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of Nx 42k|8  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
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%   pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 vNSUrf,r  
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%fid=fopen('e21.dat','w'); Rw?w7?I  
N = 128;                       % Number of Fourier modes (Time domain sampling points) 5i[O\@]5  
M1 =3000;              % Total number of space steps LKM018H>  
J =100;                % Steps between output of space |{#St-!-7  
T =10;                  % length of time windows:T*T0 @Tu`0=8  
T0=0.1;                 % input pulse width E=I'$*C\D  
MN1=0;                 % initial value for the space output location bBi>BP=  
dt = T/N;                      % time step D_l$"35?  
n = [-N/2:1:N/2-1]';           % Index LeCc`x,5  
t = n.*dt;   dcf,a<K\  
u10=1.*sech(1*t);              % input to waveguide1 amplitude: power=u10*u10 "Hw%@]#  
u20=u10.*0.0;                  % input to waveguide 2 "yu{b]AU  
u1=u10; u2=u20;                 Qw0k-t0=4  
U1 = u1;   Va?]:Q  
U2 = u2;                       % Compute initial condition; save it in U HZ9>4G3  
ww = 4*n.*n*pi*pi/T/T;         % Square of frequency. Note i^2=-1. P.Ntjz/B  
w=2*pi*n./T; aT,WXW*  
g=-i*ww./2;                    % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T I'5[8  
L=4;                           % length of evoluation to compare with S. Trillo's paper Ae2N"%Ej  
dz=L/M1;                       % space step, make sure nonlinear<0.05 =F\Xt "  
for m1 = 1:1:M1                                    % Start space evolution EID-ROMO  
   u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1;          % 1st sSolve nonlinear part of NLS y3efie {J  
   u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2; lV'?X%  
   ca1 = fftshift(fft(u1));                        % Take Fourier transform EB3/o7)L  
   ca2 = fftshift(fft(u2)); #6M |T+=  
   c2=exp(g.*dz).*(ca2+i*1*ca1.*dz);               % approximation n*[ZS[I  
   c1=exp(g.*dz).*(ca1+i*1*ca2.*dz);               % frequency domain phase shift   ;mpYcpI  
   u2 = ifft(fftshift(c2));                        % Return to physical space n/v.U,f&l@  
   u1 = ifft(fftshift(c1)); Yi9Y`~J  
if rem(m1,J) == 0                                 % Save output every J steps. dk7x<$h-h0  
    U1 = [U1 u1];                                  % put solutions in U array ep8UWxB5  
    U2=[U2 u2]; hJSvx  
    MN1=[MN1 m1]; Uh0g !zzp  
    z1=dz*MN1';                                    % output location iQO4IT   
  end LVUA"'6V  
end ]y#'U  
hg=abs(U1').*abs(U1');                             % for data write to excel Tgpu9V6  
ha=[z1 hg];                                        % for data write to excel 8=D,`wog  
t1=[0 t']; (PPC?6s  
hh=[t1' ha'];                                      % for data write to excel file &$XTe2  
%dlmwrite('aa',hh,'\t');                           % save data in the excel format X+Sqw5rH  
figure(1) 2D:/.9= 8v  
waterfall(t',z1',abs(U1').*abs(U1'))               % t' is 1xn, z' is 1xm, and U1' is mxn V?OTP&+J%  
figure(2) _)j\ b  
waterfall(t',z1',abs(U2').*abs(U2'))               % t' is 1xn, z' is 1xm, and U1' is mxn MsIR~  
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非线性超快脉冲耦合的数值方法的Matlab程序 mX>N1zAz  
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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。   3/gR}\=  
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 reR@@O  
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%  This Matlab script file solves the nonlinear Schrodinger equations /[?}LrDO  
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of !n;3jAl&$  
%  Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear +tk`$g  
%  pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004 @q!T,({kx  
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C=1;                           qUfoEpW2=6  
M1=120,                       % integer for amplitude p"P+8"`  
M3=5000;                      % integer for length of coupler [Q:mq=<Z%  
N = 512;                      % Number of Fourier modes (Time domain sampling points) -"zW"v)\  
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05. ;%0kzIvP  
T =40;                        % length of time:T*T0. ;39b.v\^  
dt = T/N;                     % time step #6a!OQj  
n = [-N/2:1:N/2-1]';          % Index -0xo6'mD  
t = n.*dt;   ^/2HH  
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1. T 9`AL  
w=2*pi*n./T; z4 =OR@ h  
g1=-i*ww./2; zf8SpQ2~  
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0; [4xZy5V  
g3=-i*ww./2; ts<\n-f  
P1=0; HT/!+#W.  
P2=0; @_t=0Rc  
P3=1; 0e&&k  
P=0; ];CIo> b_(  
for m1=1:M1                 oAifM1*0  
p=0.032*m1;                %input amplitude 'C}ku>B_r  
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1 R<fF ^^  
s1=s10; dfAw\7v/  
s20=0.*s10;                %input in waveguide 2 $S' TW3  
s30=0.*s10;                %input in waveguide 3 '+Jy//5?  
s2=s20; W;8A{3q%N0  
s3=s30; ^>%.l'1/(  
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));   )a0l:jEOc  
%energy in waveguide 1 XzI
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p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));   kIa16m  
%energy in waveguide 2 pq
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p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));   7C
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%energy in waveguide 3 fn/?I\  
for m3 = 1:1:M3                                    % Start space evolution /$clk=  
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS p*<I_QM!  
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2; Z796;qk  
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3; EKO'S+~  
   sca1 = fftshift(fft(s1));                       % Take Fourier transform j=U"t\{  
   sca2 = fftshift(fft(s2)); 4S*ifl  
   sca3 = fftshift(fft(s3)); &u^]YE{  
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift   |%5pzYe  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz); /tG as  
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz); ?7pn%_S  
   s3 = ifft(fftshift(sc3)); p2(ha3PW  
   s2 = ifft(fftshift(sc2));                       % Return to physical space gFuK/]gzI  
   s1 = ifft(fftshift(sc1)); =\u,4  
end $Tv~ *|a  
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1)))); J<H]vs  
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1)))); 8&HBR #  
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1)))); &\ca ? #  
   P1=[P1 p1/p10]; prt(xr4@  
   P2=[P2 p2/p10]; vN v'%;L  
   P3=[P3 p3/p10]; FO(QsR=\s  
   P=[P p*p]; "5dke^yk0  
end Uc_}="  
figure(1) Z  #  
plot(P,P1, P,P2, P,P3); 2%fzRXhu%  
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转自：http://blog.163.com/opto_wang/

谢谢哈~！~