计算脉冲在非线性耦合器中演化的Matlab 程序 <d*;d3gm AlPk o($E* % This Matlab script file solves the coupled nonlinear Schrodinger equations of
HV0! G -h % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
d;:H#F+ ( % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
hKx*V"7/#\ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x{'3eJ^ 8 WF#3'"I %fid=fopen('e21.dat','w');
8)KA {gN} N = 128; % Number of Fourier modes (Time domain sampling points)
m% $GiNs} M1 =3000; % Total number of space steps
%KjvV<f-a J =100; % Steps between output of space
8,VX%CS#q T =10; % length of time windows:T*T0
iwiHw T0=0.1; % input pulse width
N "',
MN1=0; % initial value for the space output location
5Yxs_t4 dt = T/N; % time step
owR`Z`^h) n = [-N/2:1:N/2-1]'; % Index
.
W7Z pV t = n.*dt;
lhk=yVG3 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
@Yzdq\FI u20=u10.*0.0; % input to waveguide 2
d x., u1=u10; u2=u20;
6_rgj {L U1 = u1;
*- S/{
.& U2 = u2; % Compute initial condition; save it in U
Gl!fT1zh0 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
,V`zW<8 w=2*pi*n./T;
0 aWy!d g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
II,snRD L=4; % length of evoluation to compare with S. Trillo's paper
'!V5 #J dz=L/M1; % space step, make sure nonlinear<0.05
@gc|Z]CV for m1 = 1:1:M1 % Start space evolution
2bnF#-( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
$T#yxx u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
O>vbAIu ca1 = fftshift(fft(u1)); % Take Fourier transform
XT "- ca2 = fftshift(fft(u2));
:6T 8\W c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
3oo Tn-`{ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Le ?yzf u2 = ifft(fftshift(c2)); % Return to physical space
g %e"K nU u1 = ifft(fftshift(c1));
Qnr7Qnb if rem(m1,J) == 0 % Save output every J steps.
NA/hs/ ' U1 = [U1 u1]; % put solutions in U array
RJ63"F $ U2=[U2 u2];
gK%^}xU+
MN1=[MN1 m1];
n[f<]4< z1=dz*MN1'; % output location
12olVTuw end
_=g;K+%fb end
Q >QES-.l hg=abs(U1').*abs(U1'); % for data write to excel
:~PzTUz ha=[z1 hg]; % for data write to excel
Vi:<W0: t1=[0 t'];
v:xfGA nP hh=[t1' ha']; % for data write to excel file
j34L*? %dlmwrite('aa',hh,'\t'); % save data in the excel format
.29y3}[PO figure(1)
Z\ 1wEGP7{ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
T+knd'2V6 figure(2)
}i\U,mH0_& waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
:enmMB#% S!J wF&EW 非线性超快脉冲耦合的数值方法的Matlab程序 n7$2 1*, -ge :y2R_w 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
L2WH-XP= Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+<TnE+>j ^6?) EM# I5$]{: L|9 U%qE=u - % This Matlab script file solves the nonlinear Schrodinger equations
[m+):q^ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
?*K{1Ghf % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^ALR.N+< % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
,bU 8S \8 z{uRq A G C=1;
caC-JcDXy M1=120, % integer for amplitude
EZw<)Q M3=5000; % integer for length of coupler
pf%B N = 512; % Number of Fourier modes (Time domain sampling points)
w 1q` dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
fEgwQ-] T =40; % length of time:T*T0.
3mCf>qj73 dt = T/N; % time step
q2U8]V U) n = [-N/2:1:N/2-1]'; % Index
= VFPZ t = n.*dt;
,T<q"d7-# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
mAZfo5 3 w=2*pi*n./T;
D>>?8a g1=-i*ww./2;
GyP.;$NHa[ g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
R4 x!b`:i g3=-i*ww./2;
Xqx mvN P1=0;
tpQ?E<O P2=0;
{OBV+}# P3=1;
$T-Pl57 P=0;
\])-Bp , for m1=1:M1
lBN1OL[N p=0.032*m1; %input amplitude
wx]r { s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
W5c?f, s1=s10;
$sa5aUg } s20=0.*s10; %input in waveguide 2
a|5^4 J \% s30=0.*s10; %input in waveguide 3
u .~` /O s2=s20;
J }M_Ka s3=s30;
2]i>kV/,0 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
L?:fyNA3[ %energy in waveguide 1
QswbIP/>:' p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
eX0ASI9 %energy in waveguide 2
z c4l{+3 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
3~5 %6 ` %energy in waveguide 3
|OarE 2 for m3 = 1:1:M3 % Start space evolution
K H&o`U(} s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
x } X1
O) s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Q}(D^rGP3 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
C#3K.0a sca1 = fftshift(fft(s1)); % Take Fourier transform
1:Dm, d; sca2 = fftshift(fft(s2));
PS\n0 sca3 = fftshift(fft(s3));
Ce~
a(J|" sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
898=9`7e sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
"eOFp\vPr sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
A av |N3 s3 = ifft(fftshift(sc3));
FsTl@zN s2 = ifft(fftshift(sc2)); % Return to physical space
g71|t7Q s1 = ifft(fftshift(sc1));
|on$ )vm end
FKpyD p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
2nsW )bd p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
)&$p?kF p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
YI!@ ,t P1=[P1 p1/p10];
66j L2XU< P2=[P2 p2/p10];
PYPDK*Ie P3=[P3 p3/p10];
Fmo^ ?~b P=[P p*p];
`k.Nphx~% end
DI,8y"!5 figure(1)
Z7: TPY$b plot(P,P1, P,P2, P,P3);
?loP1 8S
b ){S/h<4m 转自：
http://blog.163.com/opto_wang/
