计算脉冲在非线性耦合器中演化的Matlab 程序 CB {% ~ 1OJD!juL$ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
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5 )D % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
:Fz;nG-G % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
v!n\A}^: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
7pMQ1- ( w DswK "T %fid=fopen('e21.dat','w');
d0ThhO N = 128; % Number of Fourier modes (Time domain sampling points)
++n"`
]o, M1 =3000; % Total number of space steps
W iql c J =100; % Steps between output of space
1t haQ" T =10; % length of time windows:T*T0
20750 G T0=0.1; % input pulse width
,S 5tkTa MN1=0; % initial value for the space output location
f_a.BTtNO dt = T/N; % time step
,3l=44* n = [-N/2:1:N/2-1]'; % Index
~SgW+sDF u t = n.*dt;
eYZ{m o7 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
FjF:Eh u20=u10.*0.0; % input to waveguide 2
gD E',)3Q, u1=u10; u2=u20;
Rp$t;=SMD U1 = u1;
qplz != U2 = u2; % Compute initial condition; save it in U
NfvvwG;M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
" 9 ,z"k w=2*pi*n./T;
y^ 7;I- g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
M\O6~UFq! L=4; % length of evoluation to compare with S. Trillo's paper
,RIGV[u dz=L/M1; % space step, make sure nonlinear<0.05
$0>>Z for m1 = 1:1:M1 % Start space evolution
u&/[sq x u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\?uaHX`1 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
m8'B7|s ca1 = fftshift(fft(u1)); % Take Fourier transform
37GJ}%Qs ca2 = fftshift(fft(u2));
8Q&.S)hrN c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
zK`f X c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Gh }k9-L u2 = ifft(fftshift(c2)); % Return to physical space
0!X;C!v; u1 = ifft(fftshift(c1));
pwo5Ij,~q if rem(m1,J) == 0 % Save output every J steps.
zy\ p, U1 = [U1 u1]; % put solutions in U array
;d$PQi U2=[U2 u2];
9 l) .L L MN1=[MN1 m1];
*#+e_)d z1=dz*MN1'; % output location
(qd $wv^ h end
?w'a^+H end
4/ YEkD hg=abs(U1').*abs(U1'); % for data write to excel
W:D' k^u ha=[z1 hg]; % for data write to excel
@V{s'V t1=[0 t'];
AZ'
"M{wiI hh=[t1' ha']; % for data write to excel file
cpz'upVOZ %dlmwrite('aa',hh,'\t'); % save data in the excel format
`L p3snS figure(1)
T \%{zz_( waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
%qA@)u53 figure(2)
JTbg8b waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
&"GHD{ix ^Q!qJav 非线性超快脉冲耦合的数值方法的Matlab程序 Kq!E<|y M cx%[hM09 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
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32Ww Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
AQkH3p/W 0tbximmDb me] O iC-WQkQY % This Matlab script file solves the nonlinear Schrodinger equations
K..L8# SC % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
DVCO(
fz % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Md a~@)7$ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5Pmmt&#/Z XE8~R5 C=1;
r,}U-S.w M1=120, % integer for amplitude
qh}M!p2 M3=5000; % integer for length of coupler
v%Rc wVt| N = 512; % Number of Fourier modes (Time domain sampling points)
W\09h Z6 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Mf0!-bu T =40; % length of time:T*T0.
K07SbL7g!p dt = T/N; % time step
}`k >6B n = [-N/2:1:N/2-1]'; % Index
gQy {OU t = n.*dt;
mq~ rD)T ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
(ov=D7>t0 w=2*pi*n./T;
o6 f ^DG3* g1=-i*ww./2;
\+OP!` g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
d"zbY\` g3=-i*ww./2;
N<wy"N{iS P1=0;
$47cKit|k: P2=0;
x17cMfCH% P3=1;
`>:ozN#)\ P=0;
BNU]NcA#*, for m1=1:M1
B" N8NVn p=0.032*m1; %input amplitude
\ZdV|23 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
6itp
Mck s1=s10;
`jY*0{ s20=0.*s10; %input in waveguide 2
M$O}roOa s30=0.*s10; %input in waveguide 3
_%WJ7~> s2=s20;
4>]^1J7Wz s3=s30;
;)ff Gg> p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
;u;Y f Or %energy in waveguide 1
|a@$KF$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
s=`1 wkh0 %energy in waveguide 2
gE8=#%1< p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
:nki6Rkowt %energy in waveguide 3
cy=,Dr9O for m3 = 1:1:M3 % Start space evolution
_2{i}L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
zRyZrt,%& s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
2YvhzL[um s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
#5HJW[9 sca1 = fftshift(fft(s1)); % Take Fourier transform
$I(2}u?1+d sca2 = fftshift(fft(s2));
9:0JWW^so sca3 = fftshift(fft(s3));
<qH>[ \ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
d!)
&@k sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
uiq)?XUKv sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
k,0R pE s3 = ifft(fftshift(sc3));
xM85^B' s2 = ifft(fftshift(sc2)); % Return to physical space
7NG^X"N{Ul s1 = ifft(fftshift(sc1));
^T\JFzV end
* LJN 2; p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
)W9 $ _<Z p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
& i|x2;
v p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
~ ar8e P1=[P1 p1/p10];
L+Q"z*W P2=[P2 p2/p10];
jYKs| J)[ P3=[P3 p3/p10];
btb-MSkO P=[P p*p];
y I \ end
k^I4z^O=-; figure(1)
xy `aR< L plot(P,P1, P,P2, P,P3);
(1\!6 j6Acd~y\2 转自：
http://blog.163.com/opto_wang/
