计算脉冲在非线性耦合器中演化的Matlab 程序 ?Q sQnQ 8hXl%{6d3 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
4F)- "ck % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
hq%?=2'9? % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
t'?.8}?)I& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
kr+D,h01 ,3?Q(=j %fid=fopen('e21.dat','w');
T3~k>"W N = 128; % Number of Fourier modes (Time domain sampling points)
t|a2;aq_ M1 =3000; % Total number of space steps
W6f/T3 J =100; % Steps between output of space
~KHV Y)@P T =10; % length of time windows:T*T0
R(('/J C T0=0.1; % input pulse width
Uhe=h&e2k@ MN1=0; % initial value for the space output location
N8k00*p65 dt = T/N; % time step
AB=daie n = [-N/2:1:N/2-1]'; % Index
mlixIW2 t = n.*dt;
A$<.a'&T! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
9zZr^{lUl u20=u10.*0.0; % input to waveguide 2
0":ib0= u1=u10; u2=u20;
}&/o'w2wY U1 = u1;
e]`[yf U2 = u2; % Compute initial condition; save it in U
<<@bl@9' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
yXz*5W_0D w=2*pi*n./T;
p qfUW+> g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Ewu O&q
L=4; % length of evoluation to compare with S. Trillo's paper
~kShq% dz=L/M1; % space step, make sure nonlinear<0.05
kB3H="3 [[ for m1 = 1:1:M1 % Start space evolution
$8;R[SU6Y u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
F=`AY^u0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
aAJU`=uq ca1 = fftshift(fft(u1)); % Take Fourier transform
oz AS[B6 ca2 = fftshift(fft(u2));
cJN7bA { c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
T@G? t0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
W=vG$ u2 = ifft(fftshift(c2)); % Return to physical space
&f"-d u1 = ifft(fftshift(c1));
xGu r if rem(m1,J) == 0 % Save output every J steps.
0TCBQ~ " U1 = [U1 u1]; % put solutions in U array
K#EvFs`s; U2=[U2 u2];
9
TvV= MN1=[MN1 m1];
eb.O#Y z1=dz*MN1'; % output location
aEM %R<e end
A9f)tqbc end
+g` 'J$ hg=abs(U1').*abs(U1'); % for data write to excel
I Y2)?"A ha=[z1 hg]; % for data write to excel
kgnm Guka t1=[0 t'];
q;QbUO hh=[t1' ha']; % for data write to excel file
U@gn;@\ %dlmwrite('aa',hh,'\t'); % save data in the excel format
E5 )b figure(1)
H$@`,{M629 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
(&}i` }v_ figure(2)
|<#{"'/= waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
<\Eh1[F ,RJtm%w 非线性超快脉冲耦合的数值方法的Matlab程序 MNC*Gl j= R<[qGt|L 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
:|_'fNd+! Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\Kl+ 5% L cV 5CaaL ~p1j`r; ^.#jF# u~ % This Matlab script file solves the nonlinear Schrodinger equations
vV[eWd.o6M % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
g6Q !8 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
{k>Ca % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
qR(\5 } h!&prYx C=1;
"]z-: \ V M1=120, % integer for amplitude
8S%52W| M3=5000; % integer for length of coupler
F{EnOr`,m= N = 512; % Number of Fourier modes (Time domain sampling points)
3|1i lP dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
SF&BbjBE0 T =40; % length of time:T*T0.
|p><'Q% * dt = T/N; % time step
6b+b/>G0 n = [-N/2:1:N/2-1]'; % Index
]Bm/eRy" t = n.*dt;
^~G8?]w ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"i U}]e0 w=2*pi*n./T;
jgbLN/_{ g1=-i*ww./2;
_{ r=.W+ w g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
lz"OC<D}( g3=-i*ww./2;
6xWe=QGE P1=0;
Fe]B &n P2=0;
Ys@}3 \Mc P3=1;
MKy[hT: P=0;
c.,2GwW for m1=1:M1
Rniq(FA x p=0.032*m1; %input amplitude
#tZ4N7 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
>)spqu] s1=s10;
jJuW-(/4[ s20=0.*s10; %input in waveguide 2
g{8,Wx,, s30=0.*s10; %input in waveguide 3
D&}3$ 7> s2=s20;
O>^C4c! s3=s30;
sB^<6W!`( p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
e
' 2F# %energy in waveguide 1
0BH_'ZW p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Z$0 uH* h %energy in waveguide 2
#bl6sa{E p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
?R K]FP"A %energy in waveguide 3
Au4yBm
u for m3 = 1:1:M3 % Start space evolution
J]&y$?C s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
G`\ f s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
+RnkJ* l s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
%,D<O,N sca1 = fftshift(fft(s1)); % Take Fourier transform
0JlZs] sca2 = fftshift(fft(s2));
cfcim.jB sca3 = fftshift(fft(s3));
t%'Z<DmG+ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Q\ cjPc0y sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
JMH8MH* sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
-PS#Z0> s3 = ifft(fftshift(sc3));
g>dA$h% s2 = ifft(fftshift(sc2)); % Return to physical space
#a`a$A s1 = ifft(fftshift(sc1));
\>C YC | end
f}1&HI8r p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
q|Q k2M p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
]`&Yqg p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[P 06lIO P1=[P1 p1/p10];
|1b_3?e P2=[P2 p2/p10];
2 I&o6 9x? P3=[P3 p3/p10];
Xtp"QY
p P=[P p*p];
'ow.=1N- end
.h9l7
nZt figure(1)
#|*F1K plot(P,P1, P,P2, P,P3);
_cc#Qlw 7 7.Z@ Wr? 转自：
http://blog.163.com/opto_wang/
