计算脉冲在非线性耦合器中演化的Matlab 程序 ANq3r( r!y3VmJ'm % This Matlab script file solves the coupled nonlinear Schrodinger equations of
dd:vQOF; % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
D /b F % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
PHx No) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
OI^sd_gkZ qw6i|JM% %fid=fopen('e21.dat','w');
x|GkXD3 N = 128; % Number of Fourier modes (Time domain sampling points)
57[tUO M1 =3000; % Total number of space steps
fHiS'R J =100; % Steps between output of space
,j e T =10; % length of time windows:T*T0
L W!>_~g- T0=0.1; % input pulse width
1w'W)x MN1=0; % initial value for the space output location
(qDPGd*1 dt = T/N; % time step
]\(Ho
n = [-N/2:1:N/2-1]'; % Index
0 t2n7Y?N t = n.*dt;
KuZZKh u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
^"] ] rZ) u20=u10.*0.0; % input to waveguide 2
BD?u|Fd,i: u1=u10; u2=u20;
;C, t `( U1 = u1;
BI+x6S>d U2 = u2; % Compute initial condition; save it in U
n<e1 =L ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
a7n`(}?Y w=2*pi*n./T;
2"IDz01ne g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
W?<<al* L=4; % length of evoluation to compare with S. Trillo's paper
Y@ X>ejk" dz=L/M1; % space step, make sure nonlinear<0.05
dheobD for m1 = 1:1:M1 % Start space evolution
B ,U|V u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
q0 L\{ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
/B)`p F.n ca1 = fftshift(fft(u1)); % Take Fourier transform
?.^n,[2 ca2 = fftshift(fft(u2));
N^4CA@'{ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
O' h f8w c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
xq& r|el u2 = ifft(fftshift(c2)); % Return to physical space
Q#z U0K* ^ u1 = ifft(fftshift(c1));
A f Y ]i if rem(m1,J) == 0 % Save output every J steps.
?10L *PD@ U1 = [U1 u1]; % put solutions in U array
1xjWD30 U2=[U2 u2];
mv> -XJ+ MN1=[MN1 m1];
.~X&BY>qP z1=dz*MN1'; % output location
6k`O end
^j7> Ul, end
*R3^:Y& hg=abs(U1').*abs(U1'); % for data write to excel
jwmPy)X|s\ ha=[z1 hg]; % for data write to excel
^J'O8G$ t1=[0 t'];
ca <OG;R^ hh=[t1' ha']; % for data write to excel file
Q[)3r
,D %dlmwrite('aa',hh,'\t'); % save data in the excel format
H utQx figure(1)
Og7^7)) waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
#=N6[:, figure(2)
=
Oz pI waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
QY c/f"9 @cc}[Uw4B 非线性超快脉冲耦合的数值方法的Matlab程序 9Y+7o%6e Qt>Bvu Q 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。
Hi nJ }MF 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
]z8Th5a?o `6<Qb= yVWt%o/
i,,mt_/, % This Matlab script file solves the nonlinear Schrodinger equations
UJ><B" % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
|k#EYf#Y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
B]I*ymc# % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
SB,#y >Zv? AnoA5H C=1;
Kx02 2rgDU M1=120, % integer for amplitude
;?C`Jag x M3=5000; % integer for length of coupler
.>1vN+ N = 512; % Number of Fourier modes (Time domain sampling points)
^ O<@I dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
kQ"Ax? b T =40; % length of time:T*T0.
k i|OowP dt = T/N; % time step
rJ(A O' = n = [-N/2:1:N/2-1]'; % Index
B.L _EIw t = n.*dt;
+wfZFJ:1l ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[9yd29pQ] w=2*pi*n./T;
hPuF:iiQ4 g1=-i*ww./2;
']N\y6=fn9 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
|Xmzq X% g3=-i*ww./2;
f9t+x+ Z P1=0;
i
^,
$/ P2=0;
[8>#b_> P3=1;
r,q.RWuII P=0;
a:s$[+'Y for m1=1:M1
5 %+epzy p=0.032*m1; %input amplitude
!-t"}^) s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
f8-~&N/_R s1=s10;
DABV}@ K" s20=0.*s10; %input in waveguide 2
n[\L6} s30=0.*s10; %input in waveguide 3
Nz:p(X! s2=s20;
!QC ErE;r s3=s30;
#Q BW%L p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Q.Y6 %energy in waveguide 1
,{_56j^d, p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
SNf~%B?`L %energy in waveguide 2
<pM6fI6BD p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
m~4ik1 wq %energy in waveguide 3
VVfTFi< for m3 = 1:1:M3 % Start space evolution
tMXNi\Bj s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
O&sU Pv s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
@2` nBtk s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
%vbov}R sca1 = fftshift(fft(s1)); % Take Fourier transform
jI~$iDdOfs sca2 = fftshift(fft(s2));
.g 94|P sca3 = fftshift(fft(s3));
goND S5 } sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
>8&fFq sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
n8JM
0 U- sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
9 *XT|B s3 = ifft(fftshift(sc3));
IFW7MF9V s2 = ifft(fftshift(sc2)); % Return to physical space
k%iwt]i% s1 = ifft(fftshift(sc1));
?xuWha@: end
dh1 N/[ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
~du U& \ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
5Q: %f p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
@'y 8* _ P1=[P1 p1/p10];
( B%[NC 6 P2=[P2 p2/p10];
) )t]5Ys%; P3=[P3 p3/p10];
M !X^2 P=[P p*p];
OGO\u# end
?Ss ~!38 figure(1)
,$ U~<Zd plot(P,P1, P,P2, P,P3);
40z1Qkmaey C=2DxdZG 转自：
http://blog.163.com/opto_wang/
