计算脉冲在非线性耦合器中演化的Matlab 程序 $"MGu^0;1 &}\{qFD; % This Matlab script file solves the coupled nonlinear Schrodinger equations of
}nSu7)3$B % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
[&(~1C|C % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S>jOVWB % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
PzustC|
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%fid=fopen('e21.dat','w');
{ _Y'%Ggh N = 128; % Number of Fourier modes (Time domain sampling points)
cg9*+] rc M1 =3000; % Total number of space steps
^)h &s* J =100; % Steps between output of space
KEf1GU6s T =10; % length of time windows:T*T0
xc 7Rrh]} T0=0.1; % input pulse width
[Mj5o<k;I MN1=0; % initial value for the space output location
;Eh"]V,e dt = T/N; % time step
FtlJ3fB@ n = [-N/2:1:N/2-1]'; % Index
U8@P/Z9 t = n.*dt;
Bj\Us$cZ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
"~Zdv}^xS u20=u10.*0.0; % input to waveguide 2
AoK;6je`K^ u1=u10; u2=u20;
`YO & U1 = u1;
@q{. U2 = u2; % Compute initial condition; save it in U
O3pd5&^g ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
(!Xb8rV0_ w=2*pi*n./T;
>ul&x!?@ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
J/PK #< L=4; % length of evoluation to compare with S. Trillo's paper
XinKG< 3! dz=L/M1; % space step, make sure nonlinear<0.05
dTte4lh for m1 = 1:1:M1 % Start space evolution
ft0tRv(s: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
jc@=
b:r= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
nP|ah~
q ca1 = fftshift(fft(u1)); % Take Fourier transform
1[- `*Ph ca2 = fftshift(fft(u2));
,wy;7T>ODd c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
j HObWUX c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
@X=sfyg k u2 = ifft(fftshift(c2)); % Return to physical space
g4;|u K; u1 = ifft(fftshift(c1));
$-<yX<. if rem(m1,J) == 0 % Save output every J steps.
ZT`"
{ #L U1 = [U1 u1]; % put solutions in U array
*z_`$Y U2=[U2 u2];
=F dFLrx~l MN1=[MN1 m1];
e-.( O8 z1=dz*MN1'; % output location
h]IoH0 / end
kV3LFPf>0 end
A;f)`i0l, hg=abs(U1').*abs(U1'); % for data write to excel
S& ;)F|-q ha=[z1 hg]; % for data write to excel
$#wi2Ve=6b t1=[0 t'];
= \K/ulZo hh=[t1' ha']; % for data write to excel file
Z&h :3; %dlmwrite('aa',hh,'\t'); % save data in the excel format
::3 [ H$ figure(1)
4`7~~:W!M5 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
`V.tqZF figure(2)
~bis!(}p- waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
"j.Q*Hazg )0 Vj\> 非线性超快脉冲耦合的数值方法的Matlab程序 -x?|[ +% %:dd#';g 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。
TT){15T;" 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
^{NN- ]eTp?q%0 r\y\]AmF $lJ !f % This Matlab script file solves the nonlinear Schrodinger equations
e"Z,!Q^-L % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
-vt6n1A&b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[T,Df& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
9>_ VU"T `eGp.[ffT C=1;
?pA_/ wwp M1=120, % integer for amplitude
# X6=`Xe# M3=5000; % integer for length of coupler
j}8^gz] N = 512; % Number of Fourier modes (Time domain sampling points)
7'`nTF-@v dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
[u-=<hnoa T =40; % length of time:T*T0.
E#kH>q@K`$ dt = T/N; % time step
.&K?@T4l n = [-N/2:1:N/2-1]'; % Index
_sHeB7K t = n.*dt;
c|4_nT
2 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
](IOn:MuDE w=2*pi*n./T;
*6v5JH&K g1=-i*ww./2;
F-$NoE L g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
p%OVl[^jp g3=-i*ww./2;
%,d+ jBM P1=0;
ubsx NCqD P2=0;
6\)u\m`7-l P3=1;
UG6\OgkL+ P=0;
0+A#k7c6p for m1=1:M1
LI"N^K' z p=0.032*m1; %input amplitude
eE{
2{C s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
q z!^<
M s1=s10;
26j-1c!NGd s20=0.*s10; %input in waveguide 2
~Oi.bP<, s30=0.*s10; %input in waveguide 3
!Z; Nv s2=s20;
1+tPd7U s3=s30;
/ ]nrxT p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
Mv 7tK
l %energy in waveguide 1
0s.4]Zg>5 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
(k%r_O 6 %energy in waveguide 2
fY|vq
amA; p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
MOIVt) ZY %energy in waveguide 3
4&~*;an7 for m3 = 1:1:M3 % Start space evolution
86o'3G9@ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
8JO(P0aT s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
d-]!aFj|U s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
4 @9cO)m sca1 = fftshift(fft(s1)); % Take Fourier transform
<*p sca2 = fftshift(fft(s2));
[bN_0T.YI sca3 = fftshift(fft(s3));
eBe5H
=I@ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
RLDu5 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
vNU[ K%U sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
&2W`dEv]? s3 = ifft(fftshift(sc3));
U,aMv[Z B s2 = ifft(fftshift(sc2)); % Return to physical space
ulk yP s1 = ifft(fftshift(sc1));
_Aw-{HE' end
"VA bU s p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<XnxAA p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
ZXWm? 9uw p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
1oG'm P1=[P1 p1/p10];
r;fcBepO P2=[P2 p2/p10];
N&u(9Fxn P3=[P3 p3/p10];
'EkjySZ]F{ P=[P p*p];
C 7Hgzc|U end
Vb~;"WABo figure(1)
PS??wlp7 plot(P,P1, P,P2, P,P3);
) KY U[ 77G4E ,] 转自：
http://blog.163.com/opto_wang/
