计算脉冲在非线性耦合器中演化的Matlab 程序 Ul '~opf s$f+/H s % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Aivu %}_| % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
cxtLy& C % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
fl} rz % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u3Zzu \{ g0^~J2sDd %fid=fopen('e21.dat','w');
* \=2KIF' N = 128; % Number of Fourier modes (Time domain sampling points)
wm ); aWP M1 =3000; % Total number of space steps
u~' m7 J =100; % Steps between output of space
d%}crM-KTL T =10; % length of time windows:T*T0
DePV, . T0=0.1; % input pulse width
F, ' ^se4& MN1=0; % initial value for the space output location
1Pud,!\%q dt = T/N; % time step
LVPt*S= / n = [-N/2:1:N/2-1]'; % Index
^t m++ t = n.*dt;
l(h;e&9x u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
L
LYHr u20=u10.*0.0; % input to waveguide 2
iYO
wB'z u1=u10; u2=u20;
3R)cbwL U1 = u1;
a<O CO0irJ U2 = u2; % Compute initial condition; save it in U
N oX_? ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
@D. R0uM w=2*pi*n./T;
v YRt2({}Z g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Z]mM L=4; % length of evoluation to compare with S. Trillo's paper
pRQ fx^ On dz=L/M1; % space step, make sure nonlinear<0.05
JVJ1Ay/be for m1 = 1:1:M1 % Start space evolution
|@ o]X?^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
6MLN>)t u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
>>oASo ca1 = fftshift(fft(u1)); % Take Fourier transform
v$gMLu= ca2 = fftshift(fft(u2));
TE aD-mY 3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
es.\e.HK c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
"TBQNWZ u2 = ifft(fftshift(c2)); % Return to physical space
l }2%?d u1 = ifft(fftshift(c1));
]wkSAi5z* if rem(m1,J) == 0 % Save output every J steps.
9B!im\]O U1 = [U1 u1]; % put solutions in U array
>wg9YZ~8 U2=[U2 u2];
^D W# MN1=[MN1 m1];
<|KK v5[ z1=dz*MN1'; % output location
&;6|nl9; end
r 85Xa'hh end
G 1#Bb5q: hg=abs(U1').*abs(U1'); % for data write to excel
%=NM_5a}] ha=[z1 hg]; % for data write to excel
|xsV(jK8 t1=[0 t'];
)Dk0V!%N hh=[t1' ha']; % for data write to excel file
Z ,|1G6f@ %dlmwrite('aa',hh,'\t'); % save data in the excel format
PBxK>a figure(1)
3PvZ_!G waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
H y.3ccZ0 figure(2)
jm#d7@~4 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
l6&v}M .R$+#_ 非线性超快脉冲耦合的数值方法的Matlab程序 APHtJ oS AhbT/ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
0p:ClM 2O
Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*f0.= ? c:h.J4mv 6m I_Q2 Y2=Brtc[@ % This Matlab script file solves the nonlinear Schrodinger equations
m' Ek p % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
9% 3 r-U= % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
}Ke}rM< % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[}9XHhY1O= 0TuO Y%+ C=1;
N#pl mPrZ M1=120, % integer for amplitude
b2}QoJ@` M3=5000; % integer for length of coupler
}l] 3m=) N = 512; % Number of Fourier modes (Time domain sampling points)
TzevC$m;z dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Ry8WNVO}R T =40; % length of time:T*T0.
PNx VW dt = T/N; % time step
yNLa3mW n = [-N/2:1:N/2-1]'; % Index
8aZey_Hw;+ t = n.*dt;
MUCJ/GF* ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Z5*(W;; w=2*pi*n./T;
7? Qt2 tr g1=-i*ww./2;
U>L=.\\| g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
48 ~m=mI g3=-i*ww./2;
A 5.'h< P1=0;
ZHiICh|et% P2=0;
282+1X P3=1;
+]S;U&vQ P=0;
-h G 9 for m1=1:M1
HjUw[Yz+6 p=0.032*m1; %input amplitude
j;AzkReb s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
<PfPh~ s1=s10;
nIT ^' s20=0.*s10; %input in waveguide 2
FQ9csUjpB s30=0.*s10; %input in waveguide 3
t'=~"?T/o s2=s20;
8)-t91hkL s3=s30;
(1elF) p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
t5X^(@q4N %energy in waveguide 1
^+- L;XkeY p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
J++sTQ(!? %energy in waveguide 2
q*RaX
4V p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
1(:=j Ofk %energy in waveguide 3
DETajf/<F for m3 = 1:1:M3 % Start space evolution
j6R{ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
St7D.| s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
k9_VhR |! s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
(!>g8=`" sca1 = fftshift(fft(s1)); % Take Fourier transform
eX
l%Qs#Y sca2 = fftshift(fft(s2));
f<> YYeY sca3 = fftshift(fft(s3));
{ Jw<<<G sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
d'AviW> sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
g]iy -,e sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
:WfB!4%! s3 = ifft(fftshift(sc3));
UwL"%0 u s2 = ifft(fftshift(sc2)); % Return to physical space
LHHDt<+B s1 = ifft(fftshift(sc1));
E? m#S end
3ciVjH>i p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
dnX`F5z d p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2p3u6\y p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
se n{f^U P1=[P1 p1/p10];
wh7a| P2=[P2 p2/p10];
t ls6rto P3=[P3 p3/p10];
S^Wq a:; P=[P p*p];
Ji}IV end
bF Y)o Z figure(1)
[q >i plot(P,P1, P,P2, P,P3);
<R~~yW:H AXU!-er$ 转自：
http://blog.163.com/opto_wang/
