计算脉冲在非线性耦合器中演化的Matlab 程序 o^gqpQv L{osh0 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
*"4
OXyV % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
nz+DPk[" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}9{6{ TD % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
O+c@B}[! spgY &OI; %fid=fopen('e21.dat','w');
NNS n]LP N = 128; % Number of Fourier modes (Time domain sampling points)
|VTm5.23 M1 =3000; % Total number of space steps
C$Ldz=d J =100; % Steps between output of space
fXO"Mr1 T =10; % length of time windows:T*T0
X8F _Mb* T0=0.1; % input pulse width
Fj -mo>" MN1=0; % initial value for the space output location
QD q 2< dt = T/N; % time step
rA k*~OK n = [-N/2:1:N/2-1]'; % Index
^D"}OQoh t = n.*dt;
&QLCij5: u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
[\eUCt F u20=u10.*0.0; % input to waveguide 2
Spt[b.4m F u1=u10; u2=u20;
wbVM'E/& U1 = u1;
J7_'@zU U2 = u2; % Compute initial condition; save it in U
if
r!ha+8! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
CQQ X7Y\ w=2*pi*n./T;
8K7zh.E g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
qFt%{~a
S L=4; % length of evoluation to compare with S. Trillo's paper
hP,SvN#!2 dz=L/M1; % space step, make sure nonlinear<0.05
% ;09J for m1 = 1:1:M1 % Start space evolution
H+\rCefba u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
@\b* a]CV u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
\s nbU'lfP ca1 = fftshift(fft(u1)); % Take Fourier transform
8&f}GdZh ca2 = fftshift(fft(u2));
yUqvF6+26 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
pu,/GBG_ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
'9]%#^[Q u2 = ifft(fftshift(c2)); % Return to physical space
No! P? u1 = ifft(fftshift(c1));
*!Vic#D% if rem(m1,J) == 0 % Save output every J steps.
A: 0 U1 = [U1 u1]; % put solutions in U array
iMYvC w/t6 U2=[U2 u2];
e*: [#LJ]C MN1=[MN1 m1];
e#)}.
z1=dz*MN1'; % output location
]Y}faW(&Y end
&(IL` % end
O=G2bdY{, hg=abs(U1').*abs(U1'); % for data write to excel
t-3wjS1v ha=[z1 hg]; % for data write to excel
7f~DD8 R t1=[0 t'];
-|:7<$2#I hh=[t1' ha']; % for data write to excel file
(+q?xwl!N %dlmwrite('aa',hh,'\t'); % save data in the excel format
w' #VN|;;! figure(1)
&7XB $ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*.~hn5Y|? figure(2)
JIjqGxR waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
lD _
u `9kjYSd#E 非线性超快脉冲耦合的数值方法的Matlab程序 &B/cy<;y, DbH{;
Fb 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。
f @Hp,- 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
gjk=`lU > rB7ms/@E EAqTXB@XU
QS mE:Y % This Matlab script file solves the nonlinear Schrodinger equations
vx5;}[Bhm % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
kS8srT
/H % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
GL.&
g{$#+ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%]nLCoQh Cx}
Yp- C=1;
U]@t\T3W M1=120, % integer for amplitude
)jn|+M M3=5000; % integer for length of coupler
l)Q,*i N = 512; % Number of Fourier modes (Time domain sampling points)
8n,i5>!d dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
cs8bRXjHa T =40; % length of time:T*T0.
t9zPJQlT} dt = T/N; % time step
VQ$=F8ivG n = [-N/2:1:N/2-1]'; % Index
eN,s#/i p] t = n.*dt;
acRPKTs
H ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
? k<wI)JR w=2*pi*n./T;
N_= 7 g1=-i*ww./2;
);@@>~ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
!3-mPG<
] g3=-i*ww./2;
9 %,_G. P1=0;
#z6RzZu P2=0;
N?p9h{DG P3=1;
o`DBzC P=0;
BT2[@qH|qF for m1=1:M1
i('z~ p=0.032*m1; %input amplitude
~bWqoJ;Q s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
n saf6y&E s1=s10;
w-H gC s20=0.*s10; %input in waveguide 2
4O[5, s30=0.*s10; %input in waveguide 3
uY5f mM9 s2=s20;
*J 7>6N:- s3=s30;
"k"q)5c p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
i6h:%n]Io %energy in waveguide 1
!Z<GUbl t p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
#:"\6s %energy in waveguide 2
Rl=NVo p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
t 8U)za %energy in waveguide 3
eOZA2 for m3 = 1:1:M3 % Start space evolution
|/]bpG 'z s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
RIC'JL WQ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
%_@8f|# ,M s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
1;?b-FEq: sca1 = fftshift(fft(s1)); % Take Fourier transform
Mzt T/31S sca2 = fftshift(fft(s2));
z ,P:i$ sca3 = fftshift(fft(s3));
&julw;E sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
X`.4byqdK sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
L_<&oq sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
"@$o'rfT s3 = ifft(fftshift(sc3));
c42p>}P[ s2 = ifft(fftshift(sc2)); % Return to physical space
W a2V Z s1 = ifft(fftshift(sc1));
ceH7Rq:4W end
%U V_
3 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
oMkB!s p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
1 mFc]1W p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z=?ainnKx P1=[P1 p1/p10];
qV/"30, K P2=[P2 p2/p10];
AZI%KM[ P3=[P3 p3/p10];
~.VWrHC P=[P p*p];
6:330"9 end
f|m.v
+7k figure(1)
ZT"?W $ plot(P,P1, P,P2, P,P3);
[\ @!~F{ RgRyo
转自：
http://blog.163.com/opto_wang/
