计算脉冲在非线性耦合器中演化的Matlab 程序 if@,vc oKiD8': % This Matlab script file solves the coupled nonlinear Schrodinger equations of
W p4K6x % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.e $%[ )D % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
mJ$Ht yr % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@dV9Dpu V6+Zh>'S %fid=fopen('e21.dat','w');
\HG$V>2 N = 128; % Number of Fourier modes (Time domain sampling points)
:c<*%*e M1 =3000; % Total number of space steps
!a[$)c J =100; % Steps between output of space
6Ahr _{ T =10; % length of time windows:T*T0
,s? dAy5 T0=0.1; % input pulse width
+2y&B,L_Wh MN1=0; % initial value for the space output location
p`p ?li dt = T/N; % time step
NL-_#N$ n = [-N/2:1:N/2-1]'; % Index
8^T2^gs t = n.*dt;
gvo?([j-m u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
-fPT}v u20=u10.*0.0; % input to waveguide 2
ai^t=
s u1=u10; u2=u20;
H:Lt$ U1 = u1;
$_bZA;EMQ U2 = u2; % Compute initial condition; save it in U
:<UtHf<=k ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$WClpvVj w=2*pi*n./T;
>[P%Ty); g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
`EVg'?pl L=4; % length of evoluation to compare with S. Trillo's paper
*;X-\6 dz=L/M1; % space step, make sure nonlinear<0.05
LYNZP4(R for m1 = 1:1:M1 % Start space evolution
s7M}NA 0 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\!4|tBKVY u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
j%5a+(H,z; ca1 = fftshift(fft(u1)); % Take Fourier transform
mQ=sNZ-d ] ca2 = fftshift(fft(u2));
m9Il\PoTq c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
ol# yjrv c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
]|y}\7Aa u2 = ifft(fftshift(c2)); % Return to physical space
-%=RFgU4 u1 = ifft(fftshift(c1));
e?1KbJ?. if rem(m1,J) == 0 % Save output every J steps.
OA5f } + U1 = [U1 u1]; % put solutions in U array
~4+8p9f U2=[U2 u2];
D&f!( n MN1=[MN1 m1];
S ;h&5.p z1=dz*MN1'; % output location
p2^)2v end
g@(4ujOT end
`fMpV8vv hg=abs(U1').*abs(U1'); % for data write to excel
94YA2_f ; ha=[z1 hg]; % for data write to excel
& L'6KEahR t1=[0 t'];
!"%S#nrL$ hh=[t1' ha']; % for data write to excel file
)r pD2H %dlmwrite('aa',hh,'\t'); % save data in the excel format
?cJA ^W figure(1)
kw#X]`c3 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
qzHU)Ns(_ figure(2)
,@479ZvvR3 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
u ]SZ{[ e n5\}KZh 非线性超快脉冲耦合的数值方法的Matlab程序 u`+ 'lBE, d^y86 pq. 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。
JeL~]F 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
=t HD 4I 3wo'jOb j Vs(x
wE8]'o % This Matlab script file solves the nonlinear Schrodinger equations
B/ rzh? b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
G4O3h Y.` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
g kn)V~ij % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
n@_)fFD% xlk5Gob* C=1;
]An_5J
M1=120, % integer for amplitude
}q]jj s M3=5000; % integer for length of coupler
9LHa&"" N = 512; % Number of Fourier modes (Time domain sampling points)
ZLuPz # dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
gz #+ T =40; % length of time:T*T0.
) u-ns5 dt = T/N; % time step
# 'wL\3 n = [-N/2:1:N/2-1]'; % Index
*iYMX[$ t = n.*dt;
!L/tLHk+ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
4NJVW+:2 w=2*pi*n./T;
88#N~j~P g1=-i*ww./2;
OFp#<o,p g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
i"< ZVw g3=-i*ww./2;
- G FwFkWm P1=0;
q{[1fE"[K4 P2=0;
g(1"GKg3K P3=1;
y%JF8R ;n P=0;
_E&U?>g+ for m1=1:M1
YT][\x p=0.032*m1; %input amplitude
r <v _CFJ s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
b13nE . s1=s10;
!#C)99L"F s20=0.*s10; %input in waveguide 2
k~& o s30=0.*s10; %input in waveguide 3
oH= 4m~'V s2=s20;
5R)[Ou. s3=s30;
G%Y*q(VrEu p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
raSF3b/0 %energy in waveguide 1
p?}&)Un p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
)G mb? !/^ %energy in waveguide 2
X"wF Qa p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
a!&bc8J7 %energy in waveguide 3
80 dSQ"y for m3 = 1:1:M3 % Start space evolution
z"9aAytd s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
=%xIjxYl s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
nM=2"`@$ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
V, E9Uds sca1 = fftshift(fft(s1)); % Take Fourier transform
h a N"/C^ sca2 = fftshift(fft(s2));
]!q
}|bP sca3 = fftshift(fft(s3));
Q:kwQg:~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
0= 2H9v sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
g~eJ
YS, sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
pz.Y=V\t s3 = ifft(fftshift(sc3));
w' .'Yu6 s2 = ifft(fftshift(sc2)); % Return to physical space
hjw4Xz ju s1 = ifft(fftshift(sc1));
gfV ]^v end
\A` gK\/h p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$ V3n~.= p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
w 7Cne%J8 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
dvC0 <*V P1=[P1 p1/p10];
H^ESA s6 P2=[P2 p2/p10];
7? +5%7- P3=[P3 p3/p10];
5aa}FdUq P=[P p*p];
b$PT_!d end
/5&3WG&<u figure(1)
O 0Vn";Q 4 plot(P,P1, P,P2, P,P3);
7ZL ,p:f 4
`j,&= 转自：
http://blog.163.com/opto_wang/
