计算脉冲在非线性耦合器中演化的Matlab 程序 F5y&"Y_ cua ( w % This Matlab script file solves the coupled nonlinear Schrodinger equations of
- ykD/ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
\&l@rMD3s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
G +&p q % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Vg(M ^2L Q_Wg4n5 %fid=fopen('e21.dat','w');
V%B~ q`4 N = 128; % Number of Fourier modes (Time domain sampling points)
h\2iArw8 M1 =3000; % Total number of space steps
[FZq'E"87 J =100; % Steps between output of space
4 hxa|f T =10; % length of time windows:T*T0
^H -a@QM T0=0.1; % input pulse width
}kF?9w MN1=0; % initial value for the space output location
+4Fw13ADE dt = T/N; % time step
EywBT n = [-N/2:1:N/2-1]'; % Index
J0imWluhQ t = n.*dt;
>?#zPweA u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
K)
Ums-b u20=u10.*0.0; % input to waveguide 2
B>4/[
YHr; u1=u10; u2=u20;
7X)4ec9H\ U1 = u1;
=ym<yI< U2 = u2; % Compute initial condition; save it in U
!zsrORF{ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
F B:nkUR` w=2*pi*n./T;
U^eos;:s8 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
=\ k:] L=4; % length of evoluation to compare with S. Trillo's paper
s7 sTY dz=L/M1; % space step, make sure nonlinear<0.05
{5fL!`6w for m1 = 1:1:M1 % Start space evolution
:>/6:c?atG u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
D &@Iuo u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
mlPvF%Ba ca1 = fftshift(fft(u1)); % Take Fourier transform
zkiwFEHA= ca2 = fftshift(fft(u2));
Abi(1nXdQ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
>_\[C?8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
"LSzF_mK u2 = ifft(fftshift(c2)); % Return to physical space
#WJ*)$A@& u1 = ifft(fftshift(c1));
EqGpo_ if rem(m1,J) == 0 % Save output every J steps.
0yv p>{;p U1 = [U1 u1]; % put solutions in U array
\ @[Q3.VX U2=[U2 u2];
.lq83;
k MN1=[MN1 m1];
S;y 4Z:! z1=dz*MN1'; % output location
$ 4}G end
|fIyq}{7 end
m;A[ 2 6X hg=abs(U1').*abs(U1'); % for data write to excel
rLE+t(x(0 ha=[z1 hg]; % for data write to excel
GwfC l{l t1=[0 t'];
?z <-Ww hh=[t1' ha']; % for data write to excel file
rL&Mq}7QK %dlmwrite('aa',hh,'\t'); % save data in the excel format
ktS^^!,l % figure(1)
9UVT]acq waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
V#5$J Xp figure(2)
$ :\`E 56\ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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J P -nhG 非线性超快脉冲耦合的数值方法的Matlab程序 Dx`- h# Nd+1r|e' 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。
&r~s3S{pQ 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
RKE"}|i +S x(xi%?G X:I2wJDs\ PEm2w#X%L % This Matlab script file solves the nonlinear Schrodinger equations
3!o sQ1 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
~%C F3?e6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Yb4ku7} % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
dgIH`<U$ y4LUC;[n C=1;
1_#;+S M1=120, % integer for amplitude
q 5L^>" M3=5000; % integer for length of coupler
f $6N N = 512; % Number of Fourier modes (Time domain sampling points)
cJv/)hRaz dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
P tLWFO T =40; % length of time:T*T0.
fISK3t/=C dt = T/N; % time step
G}^= (,jl n = [-N/2:1:N/2-1]'; % Index
HZZZ [km t = n.*dt;
\/?J)k3H. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
5 7t . Ud w=2*pi*n./T;
*U]&a^N g1=-i*ww./2;
Nh_\{
&r g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
fK +
5 g3=-i*ww./2;
oI[rxr P1=0;
,of E*Wt P2=0;
ZJQFn P3=1;
<+-n
lK4 P=0;
,z>-_HOnw for m1=1:M1
)\ceanS p=0.032*m1; %input amplitude
DKu$u ]Z s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
IsE3-X| s1=s10;
"C\yM{JZ s20=0.*s10; %input in waveguide 2
{_\cd.AuT s30=0.*s10; %input in waveguide 3
FZ ?eX`, s2=s20;
q(: L8nKT] s3=s30;
GT)7VF rL p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Z#-N$%^F %energy in waveguide 1
c S7\,/4S p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
(lVMy\ %energy in waveguide 2
77yYdil^W+ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
bTm hz %energy in waveguide 3
)!\6 " { for m3 = 1:1:M3 % Start space evolution
VOM@x% 6#c s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?z#*eoPr s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
"q+Z* s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
Vjv6d&Q sca1 = fftshift(fft(s1)); % Take Fourier transform
q%e'WM G~n sca2 = fftshift(fft(s2));
_^#eO`4" sca3 = fftshift(fft(s3));
3&7? eO7* sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
oJr+RO sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
$ %MgIy sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
1h?ve,$ s3 = ifft(fftshift(sc3));
o]Ne|PEpO s2 = ifft(fftshift(sc2)); % Return to physical space
|cY,@X,X6 s1 = ifft(fftshift(sc1));
Se'SDJl= end
GI/NouaNfm p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
(k #xF"yI p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
5rB>)p05[ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
c{I]!y^! P1=[P1 p1/p10];
#eOHe4Vt P2=[P2 p2/p10];
{ qi # P3=[P3 p3/p10];
GZu12\0nZ P=[P p*p];
O5-GrR^yt end
5(J?C-Pk figure(1)
Ovk=s,a)K
plot(P,P1, P,P2, P,P3);
I V# 8W sV,Yz3E<u$ 转自：
http://blog.163.com/opto_wang/
