计算脉冲在非线性耦合器中演化的Matlab 程序 gHc0n 0ZV F aO=<jYi % This Matlab script file solves the coupled nonlinear Schrodinger equations of
D/pc)3Ofe % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
8d.5D & % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Wi ]Mp7b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$8#zPJR& zTb!$8D"g %fid=fopen('e21.dat','w');
gd3~R+Kd N = 128; % Number of Fourier modes (Time domain sampling points)
S;[g 0j M1 =3000; % Total number of space steps
F/ ;uN5{o J =100; % Steps between output of space
{2?o: T =10; % length of time windows:T*T0
_:F0>=$ T0=0.1; % input pulse width
afY~Y?PJ< MN1=0; % initial value for the space output location
. zf#S0y%( dt = T/N; % time step
g}nlb.b]{m n = [-N/2:1:N/2-1]'; % Index
j]i:~9xKW t = n.*dt;
}Jkz0 JY~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
_hlLM ,p u20=u10.*0.0; % input to waveguide 2
o#Q0J17i? u1=u10; u2=u20;
L2:v#c()#) U1 = u1;
3n-~+2l U2 = u2; % Compute initial condition; save it in U
tM3eB= .* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
N3 qtq9{ w=2*pi*n./T;
dbF?#s~u g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
P}B{FIpNG L=4; % length of evoluation to compare with S. Trillo's paper
??Zh$^No: dz=L/M1; % space step, make sure nonlinear<0.05
+$R4'{9q for m1 = 1:1:M1 % Start space evolution
6rlafISvO u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
p%A
s6.
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
B;. ]<k'3 ca1 = fftshift(fft(u1)); % Take Fourier transform
W9>q 1 ca2 = fftshift(fft(u2));
wRu+:<o^. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
QV/ o; c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
B
^>} M u2 = ifft(fftshift(c2)); % Return to physical space
QfjgBJo% u1 = ifft(fftshift(c1));
)! 2$yD if rem(m1,J) == 0 % Save output every J steps.
Z%_"-ENT U1 = [U1 u1]; % put solutions in U array
r}ZL{uWMW U2=[U2 u2];
!#P|2>>u MN1=[MN1 m1];
PScq-*^ z1=dz*MN1'; % output location
\d~sU, L;] end
kGbtZ} W end
kc#<Gr& Z& hg=abs(U1').*abs(U1'); % for data write to excel
Yg_;Eu0'? ha=[z1 hg]; % for data write to excel
wWV`k t1=[0 t'];
QRb iO hh=[t1' ha']; % for data write to excel file
c\.Hs9T > %dlmwrite('aa',hh,'\t'); % save data in the excel format
*3 .+19Q figure(1)
=ZdP0l+V=k waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
\ci'Cbn\o figure(2)
D{1k{/cF waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
D=*3Xd Y]
Q=kI 非线性超快脉冲耦合的数值方法的Matlab程序 {=n-S2 % m]t`;lr< 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
U zZzt$Kw 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
bs{i@ 1$ ]; c JIa y" 4Nw]kU CMk0(sztU_ % This Matlab script file solves the nonlinear Schrodinger equations
Th&-n%r9K % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
.{ , PC % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Bn> "lDf, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Lo"w,p`n@ 0< i]ph C=1;
$#q:\yQsPC M1=120, % integer for amplitude
,S . <qmf M3=5000; % integer for length of coupler
@lvvI< U N = 512; % Number of Fourier modes (Time domain sampling points)
$Pw@EC ] dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
9C;Hm>WEpP T =40; % length of time:T*T0.
x3cno# dt = T/N; % time step
s^:8bFn9$ n = [-N/2:1:N/2-1]'; % Index
dg#w/}}m t = n.*dt;
!brXQj8D 7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P,.<3W"4i w=2*pi*n./T;
>^mNIfdE^= g1=-i*ww./2;
t;?M#I\,{ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
<_X`D4g]XO g3=-i*ww./2;
ySC;;k' P1=0;
d4'*K1m P2=0;
34k}7 k~n P3=1;
xqV>m P=0;
uCX+Lw+As for m1=1:M1
\^=Wp '5R p=0.032*m1; %input amplitude
=*K~U# uoC s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
j SLC L' s1=s10;
"M e)' s20=0.*s10; %input in waveguide 2
[]opPQ
1 s30=0.*s10; %input in waveguide 3
C)w11$.YQ9 s2=s20;
O3H~|R+^
s3=s30;
cE}y~2cH p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Mlr]-G u5Z %energy in waveguide 1
@y 3u'Y,B p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
:-Gf GL>] %energy in waveguide 2
QL_~E;U p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
y^utM H %energy in waveguide 3
ssdpwn' for m3 = 1:1:M3 % Start space evolution
)C
\ %R s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
R4xoc;b s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
\?n4d#=$o s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2L=+z1%I sca1 = fftshift(fft(s1)); % Take Fourier transform
4}mp~AXy;z sca2 = fftshift(fft(s2));
9wR-0E
) sca3 = fftshift(fft(s3));
3_%lN4sz sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
U%E 6"Hg sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
8&q|*/2 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
(wxdT6RVm\ s3 = ifft(fftshift(sc3));
j,7NLb9M s2 = ifft(fftshift(sc2)); % Return to physical space
?`& l Y s1 = ifft(fftshift(sc1));
{Pi+VuLE end
sY @S
p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
jlh yn0 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
CYIp 3D'k p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
eh`s fH P1=[P1 p1/p10];
z^tws*u],5 P2=[P2 p2/p10];
qs$%/ P3=[P3 p3/p10];
hqEn D P=[P p*p];
l)JNNcej end
)(&Z&2~A figure(1)
/jBjqE ;_ plot(P,P1, P,P2, P,P3);
#Y)Gos ym>>5 (bni 转自：
http://blog.163.com/opto_wang/
