计算脉冲在非线性耦合器中演化的Matlab 程序 SA}]ZK P Ii ;~ xc % This Matlab script file solves the coupled nonlinear Schrodinger equations of
}mX;0qO % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Bm^vKzp % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Mq6"7L % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@!K)(B;A0b )82x)c<e %fid=fopen('e21.dat','w');
dGZVWEaPfx N = 128; % Number of Fourier modes (Time domain sampling points)
PF4Cs3m/ M1 =3000; % Total number of space steps
Ff.gR x J =100; % Steps between output of space
U|iSJ% K T =10; % length of time windows:T*T0
#K
]k T0=0.1; % input pulse width
{GZHD^Ce MN1=0; % initial value for the space output location
8_W<BXW dt = T/N; % time step
Z!tt(y\ n = [-N/2:1:N/2-1]'; % Index
V5M_ N;h t = n.*dt;
'%)7%O,2 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
0gx bo u20=u10.*0.0; % input to waveguide 2
tTC[^Dji u1=u10; u2=u20;
tZ4W]od U1 = u1;
o^gqpQv U2 = u2; % Compute initial condition; save it in U
1) M3*h3 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:h?Zg(l w=2*pi*n./T;
,p0R 4gi g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ck-w Md L=4; % length of evoluation to compare with S. Trillo's paper
.LdLm991,Y dz=L/M1; % space step, make sure nonlinear<0.05
YQ2ie>C8 for m1 = 1:1:M1 % Start space evolution
]yA|
m3^2 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
NaLec|6<t u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
)7:2v1Xr] ca1 = fftshift(fft(u1)); % Take Fourier transform
N#Y4nllJ ca2 = fftshift(fft(u2));
Xv6z>z. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
oO!@s` c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
\O`B@!d a~ u2 = ifft(fftshift(c2)); % Return to physical space
ll73}v u1 = ifft(fftshift(c1));
i3N _wv{ if rem(m1,J) == 0 % Save output every J steps.
h yFq>XFo U1 = [U1 u1]; % put solutions in U array
F5:4 B]ZF U2=[U2 u2];
J*qepq`_ MN1=[MN1 m1];
7G!SlC
X}W z1=dz*MN1'; % output location
g,mcxX O end
zN*/ G6>A end
mI "`. hg=abs(U1').*abs(U1'); % for data write to excel
NC|&7qQ ha=[z1 hg]; % for data write to excel
,??xW{* | t1=[0 t'];
{WT"\Xj>B? hh=[t1' ha']; % for data write to excel file
8K7zh.E %dlmwrite('aa',hh,'\t'); % save data in the excel format
@4_W}1W figure(1)
NZmmO )p4 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
DBb mM*r figure(2)
"\]kK @, waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
K4snp u hC M"ZP s 非线性超快脉冲耦合的数值方法的Matlab程序 f!eC|:D pu,/GBG_ 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。
WUMx:a0! 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
JaiYVx( 4f'WF5S/}8 }mk9-7 'P39^rb % This Matlab script file solves the nonlinear Schrodinger equations
)k- 7mwkZ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
n!A')]y" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
,b KA]#(2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
C<eeAWP3v 0q>f x C=1;
m>jX4D7KZ M1=120, % integer for amplitude
}ZlJ M3=5000; % integer for length of coupler
^7vh ize N = 512; % Number of Fourier modes (Time domain sampling points)
#c./<<P5} dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
\bZbz/ +D T =40; % length of time:T*T0.
>d n[oS, dt = T/N; % time step
0&$e:O'v n = [-N/2:1:N/2-1]'; % Index
LPvyfD;Zy t = n.*dt;
cg}46)^<QH ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]nEN3RJ w=2*pi*n./T;
`3*>tq g1=-i*ww./2;
&W)k s g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
0[x?Q[~S_0 g3=-i*ww./2;
TJ
;4QL P1=0;
)|q,RA n P2=0;
gjk=`lU P3=1;
> rB7ms/@E P=0;
WB"$NYB for m1=1:M1
K &Ht37T p=0.032*m1; %input amplitude
Xb&r|pR s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Z[slN5]([ s1=s10;
-P!vCf^{
t s20=0.*s10; %input in waveguide 2
72@8 M s30=0.*s10; %input in waveguide 3
^kch]?
s2=s20;
_Oh;._PS s3=s30;
cJGA5m/{I p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
v'2EYTVNJD %energy in waveguide 1
bv)E>%Yy p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
Z"mpE+U* %energy in waveguide 2
L/ c$p`- p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
(uD( ,3/Cw %energy in waveguide 3
- $.$6"] for m3 = 1:1:M3 % Start space evolution
7"Zr:|$U s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Fx/9T2%= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
6jO*rseC s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
N_= 7 sca1 = fftshift(fft(s1)); % Take Fourier transform
,D
[ sca2 = fftshift(fft(s2));
4&R\6!*s sca3 = fftshift(fft(s3));
0v,DQJ?w8 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
jcYI"f"~ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
{o*z iZh sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
.1t$(]CyC s3 = ifft(fftshift(sc3));
Go^W\y
s2 = ifft(fftshift(sc2)); % Return to physical space
aGr(djD s1 = ifft(fftshift(sc1));
6<(HT#=# end
P(VQ D>G p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
qWy{{ A+ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~lzV=c$t p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
k(3 s^B P1=[P1 p1/p10];
bsR^H5O@ P2=[P2 p2/p10];
2Qc&6-;` P3=[P3 p3/p10];
'i%Azzv P=[P p*p];
i6h:%n]Io end
!Z<GUbl t figure(1)
#:"\6s plot(P,P1, P,P2, P,P3);
Rl=NVo %&V<kH"7Q{ 转自：
http://blog.163.com/opto_wang/
