计算脉冲在非线性耦合器中演化的Matlab 程序 $ftxid8 W3gHz T?{ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
watTV \b % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
88KQ) NU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
gsY Q"/S9 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ye-[l7 M#k$[w}= %fid=fopen('e21.dat','w');
'#a;n N = 128; % Number of Fourier modes (Time domain sampling points)
&NX 7 M1 =3000; % Total number of space steps
39~te%;C7 J =100; % Steps between output of space
u7S C_3R T =10; % length of time windows:T*T0
eD|"?@cE T0=0.1; % input pulse width
M5:j)o W MN1=0; % initial value for the space output location
vN Hvuw K dt = T/N; % time step
biG :Xn n = [-N/2:1:N/2-1]'; % Index
A,EuUp
t = n.*dt;
o@L2c3?c5 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
>8|V[-H u20=u10.*0.0; % input to waveguide 2
cB)tf S4) u1=u10; u2=u20;
M8R/a[ -A U1 = u1;
O^n\lik U2 = u2; % Compute initial condition; save it in U
}.1}yz^y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
z.|[g$F w=2*pi*n./T;
cTQ ._|M g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
R*?!xD J L=4; % length of evoluation to compare with S. Trillo's paper
@ RZbo@{~ dz=L/M1; % space step, make sure nonlinear<0.05
j;I( w [@P for m1 = 1:1:M1 % Start space evolution
#^tnRfS" u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`>GXJ~:D[" u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
@~}~;}0x ca1 = fftshift(fft(u1)); % Take Fourier transform
>a bp se ca2 = fftshift(fft(u2));
.X5 A7 m c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
FX!Qd&kl1 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
BOD!0CR5 u2 = ifft(fftshift(c2)); % Return to physical space
{55f{5y3
c u1 = ifft(fftshift(c1));
m%nRHT0KAf if rem(m1,J) == 0 % Save output every J steps.
x*p'm[Tdtm U1 = [U1 u1]; % put solutions in U array
b2H -D!YO^ U2=[U2 u2];
MEu{'[C MN1=[MN1 m1];
>2v< ;. z1=dz*MN1'; % output location
d@tf+_Ih end
Y$#6%`*#>n end
Tb!F O"o hg=abs(U1').*abs(U1'); % for data write to excel
$b[Ha{9(v ha=[z1 hg]; % for data write to excel
uPC(|U% t1=[0 t'];
5j v*C]z hh=[t1' ha']; % for data write to excel file
Fk g%_v$ %dlmwrite('aa',hh,'\t'); % save data in the excel format
9fWR8iV figure(1)
RXo 6y(^ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
uqD|j:~ =k figure(2)
QQ=Kj%R waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
1,7
}ah_ $wyPGok 非线性超快脉冲耦合的数值方法的Matlab程序 ^%m{yf# 4|4 *rhwp 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
^M\X/u q$E 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
3.9/mztS NZO86y/ RY3=UeoF A ]1dR\p % This Matlab script file solves the nonlinear Schrodinger equations
S..8,5mBH % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Uw| -d[ ! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
#M<YNuE#" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$ i nKI KE~.f( C=1;
~'|^|*}~Dj M1=120, % integer for amplitude
vY"I M3=5000; % integer for length of coupler
VrWQ] L N = 512; % Number of Fourier modes (Time domain sampling points)
'blMwD{0&\ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
DL d~ T =40; % length of time:T*T0.
_~ 'MQ`P dt = T/N; % time step
8hYl73# n = [-N/2:1:N/2-1]'; % Index
%zo
6A1Q; t = n.*dt;
@
'c(q=K; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
C+>mehDC_G w=2*pi*n./T;
Z78i7k } g1=-i*ww./2;
&gr
T@ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
(N/-blto g3=-i*ww./2;
/q8B | (U P1=0;
C,%Dp0 P2=0;
7IQa Xcl P3=1;
<F AbImE} P=0;
j&U7xv for m1=1:M1
ROvY,-? p=0.032*m1; %input amplitude
]1eZ<le`6 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-x:7K\=$SX s1=s10;
neE
Zw#(Z s20=0.*s10; %input in waveguide 2
^6Zx-Mf\ s30=0.*s10; %input in waveguide 3
DC8\v+K s2=s20;
b4EUr SL s3=s30;
Ujqnl>l p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=T#hd7O`V %energy in waveguide 1
? * r p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
SL`; `// %energy in waveguide 2
2Nx:Y +[
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
-m[ tYp,q %energy in waveguide 3
kw} E0uY for m3 = 1:1:M3 % Start space evolution
G(wstHT;/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
=[[I<[BZq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Z op/ MeI s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Z15 =vsV sca1 = fftshift(fft(s1)); % Take Fourier transform
&y7=tEV sca2 = fftshift(fft(s2));
!I\ eIV>0b sca3 = fftshift(fft(s3));
Pa#Jwo sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
:4x6dYNU sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
F_i"v5# sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
G$)tp ^%] s3 = ifft(fftshift(sc3));
ZoYllk s2 = ifft(fftshift(sc2)); % Return to physical space
Jr %F#/ s1 = ifft(fftshift(sc1));
h?h)i> end
@P>>:002/ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
C3N1t p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
st~ l|| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
kGC*\?<LmR P1=[P1 p1/p10];
m5a'Vs P2=[P2 p2/p10];
L]X x-S P3=[P3 p3/p10];
ZsCwNZR P=[P p*p];
IP-M)_I end
-e?n4YO*\ figure(1)
[6
"5 plot(P,P1, P,P2, P,P3);
N}) vrB;1 @HnahD 转自：
http://blog.163.com/opto_wang/
