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。  
 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

 

%  This Matlab script file solves the nonlinear Schrodinger equations
%  for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
%  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

C=1;                          
M1=120,                       % integer for amplitude
M3=5000;                      % integer for length of coupler
N = 512;                      % Number of Fourier modes (Time domain sampling points)
dz =3.14159/(sqrt(2.)*C)/M3;  % length of coupler is divided into M3 segments,  make sure nonlinearity<0.05.
T =40;                        % length of time:T*T0.
dt = T/N;                     % time step
n = [-N/2:1:N/2-1]';          % Index
t = n.*dt; 
ww = 4*n.*n*pi*pi/T/T;        % Square of frequency. Note i^2=-1.
w=2*pi*n./T;
g1=-i*ww./2;
g2=-i*ww./2;                  % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
g3=-i*ww./2;
P1=0;
P2=0;
P3=1;
P=0;
for m1=1:M1               
p=0.032*m1;                %input amplitude
s10=p.*sech(p.*t);         %input soliton pulse in waveguide 1
s1=s10;
s20=0.*s10;                %input in waveguide 2
s30=0.*s10;                %input in waveguide 3
s2=s20;
s3=s30;
p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1)))); 
%energy in waveguide 1
p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1)))); 
%energy in waveguide 2
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1)))); 
%energy in waveguide 3
for m3 = 1:1:M3                                    % Start space evolution
   s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1;          % 1st step, Solve nonlinear part of NLS
   s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
   s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
   sca1 = fftshift(fft(s1));                       % Take Fourier transform
   sca2 = fftshift(fft(s2));
   sca3 = fftshift(fft(s3));
   sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz);           % 2nd step, frequency domain phase shift  
   sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
   sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
   s3 = ifft(fftshift(sc3));
   s2 = ifft(fftshift(sc2));                       % Return to physical space
   s1 = ifft(fftshift(sc1));
 end
   p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
   p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
   p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
   P1=[P1 p1/p10];
   P2=[P2 p2/p10];
   P3=[P3 p3/p10];
   P=[P p*p];
end
figure(1)
plot(P,P1, P,P2, P,P3);