计算脉冲在非线性耦合器中演化的Matlab 程序 h{p=WWK 4^Q : % This Matlab script file solves the coupled nonlinear Schrodinger equations of
] =";IN:SU % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Kt|1&Gk % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
QC;^xG+W % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
KiO cu=F iN0nw]_* %fid=fopen('e21.dat','w');
.0O2Qqdg N = 128; % Number of Fourier modes (Time domain sampling points)
F[[TWf/ M1 =3000; % Total number of space steps
yz*6W
z D J =100; % Steps between output of space
! 0C^TCuG T =10; % length of time windows:T*T0
D{d>5P?W T0=0.1; % input pulse width
XW s"jt MN1=0; % initial value for the space output location
J6G(_(d dt = T/N; % time step
F^LZeF[#t n = [-N/2:1:N/2-1]'; % Index
P(73!DT+ t = n.*dt;
8o 0%@5M u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
*9c!^ $V u20=u10.*0.0; % input to waveguide 2
}HYjA4o\A u1=u10; u2=u20;
% v7[[U{T U1 = u1;
tl '9IGlc U2 = u2; % Compute initial condition; save it in U
/E5 5Pec ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
>Ll$p 0W w=2*pi*n./T;
ZMLg;-T.&4 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
i?:_ :"^x L=4; % length of evoluation to compare with S. Trillo's paper
s)2fG\1 dz=L/M1; % space step, make sure nonlinear<0.05
mL`5 u f for m1 = 1:1:M1 % Start space evolution
0,rTdjH7 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
m[@Vf9 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
1YJ C{bO ca1 = fftshift(fft(u1)); % Take Fourier transform
z2hc.29t ca2 = fftshift(fft(u2));
Xy &uZ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
pzgSg[ | c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
n`
TSu$ u2 = ifft(fftshift(c2)); % Return to physical space
]
0m&(9 u1 = ifft(fftshift(c1));
"0k8IVwp if rem(m1,J) == 0 % Save output every J steps.
a~!G%})'a U1 = [U1 u1]; % put solutions in U array
-,{-bi U2=[U2 u2];
^ Dt# $Z MN1=[MN1 m1];
qTo-pA G` z1=dz*MN1'; % output location
N**g]T
0` end
pO kLb
# end
R$Tp8G >j hg=abs(U1').*abs(U1'); % for data write to excel
3y~r72J ha=[z1 hg]; % for data write to excel
P?]aWJ t1=[0 t'];
\7
NpT }dj hh=[t1' ha']; % for data write to excel file
-TOI c% %dlmwrite('aa',hh,'\t'); % save data in the excel format
"y<?Q}1 figure(1)
\ y{Tn@7 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
g@Qgxsyk> figure(2)
V$rlA' +1v waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
)& <=.q iTg; 7~1pY 非线性超快脉冲耦合的数值方法的Matlab程序 ~ E^, =4 N#_GJSG_| 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。
2JS`Wqy 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
awUx=%ERtA *8tI*Pus KyO8A2'U I;?X f % This Matlab script file solves the nonlinear Schrodinger equations
h<\_XJJ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
zn @N'R/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xN@Pz)y o % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
o!r8{L X*7\ lf2 C=1;
Ep4Hqx $ M1=120, % integer for amplitude
C}*cx$. M3=5000; % integer for length of coupler
b]JI@=s? N = 512; % Number of Fourier modes (Time domain sampling points)
W Qc> dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
D*Q. G8( T =40; % length of time:T*T0.
e% >b+ Sv dt = T/N; % time step
CCGV~e+ n = [-N/2:1:N/2-1]'; % Index
F("#^$ t = n.*dt;
@&hnL9D8lL ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
] k8/#@19 w=2*pi*n./T;
|uH %6&\ g1=-i*ww./2;
5]1h8PW!Y g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
`: G % g3=-i*ww./2;
l"zUv P1=0;
X}6#II P2=0;
B,(H eg P3=1;
.~gl19#:T P=0;
<d7V<&@o= for m1=1:M1
2sp g?] p=0.032*m1; %input amplitude
Sm2>'C s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Fequm + s1=s10;
do
^RF<G s20=0.*s10; %input in waveguide 2
p=QYc)3F s30=0.*s10; %input in waveguide 3
Ih[+K#t+E s2=s20;
}p9F#gr s3=s30;
OlQ,Ce p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
#DkD!dW(l %energy in waveguide 1
^SfS~G Q p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
1 Ee>S\9t %energy in waveguide 2
cDXsi#Raj p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
@oG )LT %energy in waveguide 3
m!OMrZ%)} for m3 = 1:1:M3 % Start space evolution
<39!G7ny s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
1[;@AE2Y s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
oT|m1aGE s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
bO/*2oau sca1 = fftshift(fft(s1)); % Take Fourier transform
WnAd5#G sca2 = fftshift(fft(s2));
- n6jG}01b sca3 = fftshift(fft(s3));
p&K\]l} sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
L6i|:D32p sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
[&P `ak sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
>LF&E M] s3 = ifft(fftshift(sc3));
!)Rr]
~ s2 = ifft(fftshift(sc2)); % Return to physical space
cub <G! K s1 = ifft(fftshift(sc1));
xkA2g[ end
O:.,+,BH p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
v&MU=Tcqi p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
K.SeK3( p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
! ]Mc4!E P1=[P1 p1/p10];
emA!Ew(g P2=[P2 p2/p10];
B">yKB:D}t P3=[P3 p3/p10];
czBi Dk4 P=[P p*p];
8Xm@r#Oy 5 end
I&1!v8 figure(1)
*[kx F*^ plot(P,P1, P,P2, P,P3);
(=T$_-Dj`} xNN@ 1P[* 转自：
http://blog.163.com/opto_wang/
