计算脉冲在非线性耦合器中演化的Matlab 程序 pi|=3W `Sx1?@8( % This Matlab script file solves the coupled nonlinear Schrodinger equations of
J))U YJ O % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
[.Rdq]w6 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
L9 $`zc % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*Y':raP \
z3>kvk %fid=fopen('e21.dat','w');
8w$q4fg0 N = 128; % Number of Fourier modes (Time domain sampling points)
J# DN 2y < M1 =3000; % Total number of space steps
&J\<"3 J =100; % Steps between output of space
4 KX\'K T =10; % length of time windows:T*T0
(zX75QSKV T0=0.1; % input pulse width
% M*2 j%6 MN1=0; % initial value for the space output location
b%QcB[k[WB dt = T/N; % time step
Ya &\ b 6 n = [-N/2:1:N/2-1]'; % Index
@~QI3) =s t = n.*dt;
bo-L|R&O u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
h0&Oy52
u20=u10.*0.0; % input to waveguide 2
r>ag( ^J\ u1=u10; u2=u20;
]]NTvr U1 = u1;
l4 > c U2 = u2; % Compute initial condition; save it in U
m% cwhH_B ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
S}P rgw/ w=2*pi*n./T;
hb<cyn Y g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
r+!29 L=4; % length of evoluation to compare with S. Trillo's paper
W6s-epsRmT dz=L/M1; % space step, make sure nonlinear<0.05
!C@+CZXLx for m1 = 1:1:M1 % Start space evolution
$-p9cyk u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\4KV9wm u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
VfFbZds8f ca1 = fftshift(fft(u1)); % Take Fourier transform
1+#E|YWJ ca2 = fftshift(fft(u2));
qg2Vmj<H c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
v?YxF} c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
+!K*FU=). u2 = ifft(fftshift(c2)); % Return to physical space
20]p< u1 = ifft(fftshift(c1));
f@ILC=c< if rem(m1,J) == 0 % Save output every J steps.
YrsE
88QqI U1 = [U1 u1]; % put solutions in U array
Kk).KgR U2=[U2 u2];
"r~/E|Da< MN1=[MN1 m1];
^ X-6j[". z1=dz*MN1'; % output location
@R Jr
~y0 end
\hWac%# end
NX5 $x/uz hg=abs(U1').*abs(U1'); % for data write to excel
p^1~o/ ha=[z1 hg]; % for data write to excel
2; K2|G7 t1=[0 t'];
@*roW{?! hh=[t1' ha']; % for data write to excel file
1ozb
tn %dlmwrite('aa',hh,'\t'); % save data in the excel format
1H?I?IT30 figure(1)
M0T z('~s waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
NwVhJd o figure(2)
6 ZAZJn| waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
";;!c. !^ - ykD/ 非线性超快脉冲耦合的数值方法的Matlab程序 4y.qtiIP>$ S0tkqA4 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。
Vg(M ^2L 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
Q_Wg4n5 1ASoH,D/ [C\B2iU7_M (*_lLM@Cd % This Matlab script file solves the nonlinear Schrodinger equations
tAPf#7{|
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
cbYQ';{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
.%!^L#g % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
pfs]pDjS : CDPu(,^ C=1;
6Jq3l_ M1=120, % integer for amplitude
~6K.5t7 M3=5000; % integer for length of coupler
M?AKJE j5 N = 512; % Number of Fourier modes (Time domain sampling points)
1IlOU|4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
eL<jA9cJ9 T =40; % length of time:T*T0.
!b=W> 5h dt = T/N; % time step
X:lStO#5 n = [-N/2:1:N/2-1]'; % Index
da i+" t = n.*dt;
NT EN ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
7xFZJ# w=2*pi*n./T;
Cg|\UKfy$ g1=-i*ww./2;
[$F*R@,& g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
a`[9<AM1# g3=-i*ww./2;
\._|_+HiW P1=0;
g m%cAme P2=0;
%P{3c~?DH P3=1;
M ziOpra j P=0;
t 4VeXp6 for m1=1:M1
7<Qmpcp = p=0.032*m1; %input amplitude
xI.0m s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
&8Z .m,s] s1=s10;
B*E y&DAV s20=0.*s10; %input in waveguide 2
B[ q"o I` s30=0.*s10; %input in waveguide 3
J7qTE8 W= s2=s20;
\ @[Q3.VX s3=s30;
.lq83;
k p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
S;y 4Z:! %energy in waveguide 1
$ 4}G p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
|fIyq}{7 %energy in waveguide 2
m;A[ 2 6X p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
hsT &c| %energy in waveguide 3
A2;6Vz=z for m3 = 1:1:M3 % Start space evolution
-SfU.XlZl s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
b dLi _k s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
c&x1aF "B s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
d S'J @e=# sca1 = fftshift(fft(s1)); % Take Fourier transform
Nu OxEyC sca2 = fftshift(fft(s2));
U8 2mO+} sca3 = fftshift(fft(s3));
)0]U"Nf ho sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
#vhN$H :&q sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
N'-[>w7vK2 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
znPh7{|< s3 = ifft(fftshift(sc3));
u>G9r#~`k s2 = ifft(fftshift(sc2)); % Return to physical space
=Xg/[J% s1 = ifft(fftshift(sc1));
h5pfmN\-5 end
@g4o8nH} p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
"wuO[c&%/ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
l^Ofl ZC~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
D,R',(3 P1=[P1 p1/p10];
+iFt ) P2=[P2 p2/p10];
n >R(e> P3=[P3 p3/p10];
: e nR8MS P=[P p*p];
E1tCY.N{ end
."=%]l 0 figure(1)
h6OQeZ. plot(P,P1, P,P2, P,P3);
{=?(v`88 EFljUT?& 转自：
http://blog.163.com/opto_wang/
