计算脉冲在非线性耦合器中演化的Matlab 程序 R+=wSG ] /*GCuc| % This Matlab script file solves the coupled nonlinear Schrodinger equations of
IP)%y%ycw % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
S&D8Rao 5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
o]GZq.. % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
FMWM : ;0uiO . %fid=fopen('e21.dat','w');
~]n=TEJ> N = 128; % Number of Fourier modes (Time domain sampling points)
=Tfm~+7nE M1 =3000; % Total number of space steps
aB`jFp- J =100; % Steps between output of space
1S yG T =10; % length of time windows:T*T0
hZ "Sqm] T0=0.1; % input pulse width
m3& b)O7 MN1=0; % initial value for the space output location
ocZ^rqo2w dt = T/N; % time step
\]dvwN3x n = [-N/2:1:N/2-1]'; % Index
M 5`hMfg t = n.*dt;
3~Ap1 _9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
.Sv/0&O u20=u10.*0.0; % input to waveguide 2
l 3 jlKB u1=u10; u2=u20;
Q5sJ|]Bc U1 = u1;
y'non 0P. U2 = u2; % Compute initial condition; save it in U
g0-rQA ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
b"B:DDw0 0 w=2*pi*n./T;
& VG g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
#u +~ ^M L=4; % length of evoluation to compare with S. Trillo's paper
QFgKEUNgl dz=L/M1; % space step, make sure nonlinear<0.05
#]Jg> for m1 = 1:1:M1 % Start space evolution
. lNf.x#u u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
P'*Fd3B#A= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}X qC'z ca1 = fftshift(fft(u1)); % Take Fourier transform
v I,T1%llu ca2 = fftshift(fft(u2));
@Qp#Tg<' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
aP"!}* c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Wv ~&Qh} u2 = ifft(fftshift(c2)); % Return to physical space
%3 6@1l-N u1 = ifft(fftshift(c1));
8xkLfN|N=
if rem(m1,J) == 0 % Save output every J steps.
,lFp4 C U1 = [U1 u1]; % put solutions in U array
s#(%u t U2=[U2 u2];
T8yMaC MN1=[MN1 m1];
!fjB oK+ z1=dz*MN1'; % output location
4=N(@mS end
,zxv>8Nt end
@ rF|WT hg=abs(U1').*abs(U1'); % for data write to excel
6 2K#rR S ha=[z1 hg]; % for data write to excel
oArJ%Y> t1=[0 t'];
x0) WrDb hh=[t1' ha']; % for data write to excel file
> 2X-98, %dlmwrite('aa',hh,'\t'); % save data in the excel format
l k yK figure(1)
9}H]4"f7 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
cH+ ~|3 figure(2)
P]armg% waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
ru4M=D aK 7 }} 非线性超快脉冲耦合的数值方法的Matlab程序 \xQu*M:! _rmKvSD% 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。
{Byh:-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
T )',}= :+ "H h% yqB!0)
< c5: X$k\ % This Matlab script file solves the nonlinear Schrodinger equations
Cl{Ar8d} % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
8(L6I%k* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
N,3iSH=cN[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
l[rK)PM -Zp BYX5e_ C=1;
,i8%qm8 M1=120, % integer for amplitude
n=|% H'U M3=5000; % integer for length of coupler
!e*T.
1Kz N = 512; % Number of Fourier modes (Time domain sampling points)
R z[3cN)?q dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
5L_`Fw\l T =40; % length of time:T*T0.
n 8
K6m ( dt = T/N; % time step
1l Cr? n = [-N/2:1:N/2-1]'; % Index
`*D" =5G+ t = n.*dt;
=G" ney2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\-f/\P/ w w=2*pi*n./T;
U3Z-1G~* r g1=-i*ww./2;
mrr~ #Bb> g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
/ :6|)AW.{ g3=-i*ww./2;
\O\q1
s~ P1=0;
0G0( g,3p P2=0;
p@[ fZj P3=1;
"F6gV;{Bt P=0;
KSHq0A6/q% for m1=1:M1
c*\;!dbP p=0.032*m1; %input amplitude
1:>F{g s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
"?<h,Hvi s1=s10;
d325C w? s20=0.*s10; %input in waveguide 2
x":o*(rSQ s30=0.*s10; %input in waveguide 3
?_cOU@n s2=s20;
i'4.w?O Z s3=s30;
&;=/^~EG p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
6U.|0mG[ %energy in waveguide 1
QR _h#N2h p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
u05Yy&(f %energy in waveguide 2
/,UnT(/k( p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
-e sQyLx %energy in waveguide 3
7D4tuXUq2 for m3 = 1:1:M3 % Start space evolution
Ak8Y?#"wz s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
! Dj2/][ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
#<ST.f@* s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
,wXmJ)/WZ sca1 = fftshift(fft(s1)); % Take Fourier transform
VpSpj/\m)' sca2 = fftshift(fft(s2));
_SJ:|I sca3 = fftshift(fft(s3));
w6WPfy(/2 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
=:]v~Ehq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
R&a$w8 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
T ~(Sc'8 s3 = ifft(fftshift(sc3));
X 8R`C0
s2 = ifft(fftshift(sc2)); % Return to physical space
Lj9RF<39g s1 = ifft(fftshift(sc1));
&i.sSqSI5 end
!8| }-eFY p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Q2uV/M1? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
RtzS e$O p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[ ~ 2imS P1=[P1 p1/p10];
^gZ,A]
P2=[P2 p2/p10];
M
+r!63T P3=[P3 p3/p10];
: -d_ P=[P p*p];
rp{|{>'`.q end
`fTM/" figure(1)
kS:# |yY8% plot(P,P1, P,P2, P,P3);
m! ueqV" -TH MTRFz 转自：
http://blog.163.com/opto_wang/
