计算脉冲在非线性耦合器中演化的Matlab 程序 og MLv} riZFcVsB % This Matlab script file solves the coupled nonlinear Schrodinger equations of
'15j$q % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
p]`pUw{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]? -56c, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
vi4 1` Y::fcMJr;Q %fid=fopen('e21.dat','w');
>tr?5 iKxc N = 128; % Number of Fourier modes (Time domain sampling points)
dVVeH\o M1 =3000; % Total number of space steps
7oF`Os+U J =100; % Steps between output of space
nX5*pTfjL3 T =10; % length of time windows:T*T0
,M7sOp6} T0=0.1; % input pulse width
#1hT#YN MN1=0; % initial value for the space output location
10}oaL S dt = T/N; % time step
KwPJ0
]('_ n = [-N/2:1:N/2-1]'; % Index
rZu_"bcJ t = n.*dt;
k }ps-w6: u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
?*}76u u20=u10.*0.0; % input to waveguide 2
V== ' 7n u1=u10; u2=u20;
(m) %5*: U1 = u1;
<tf4j3lwH U2 = u2; % Compute initial condition; save it in U
&-<"HW ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
L)8 +/+ w=2*pi*n./T;
E=~H,~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
s%GiM L=4; % length of evoluation to compare with S. Trillo's paper
><LIOFqsS dz=L/M1; % space step, make sure nonlinear<0.05
.~v~~VL1NS for m1 = 1:1:M1 % Start space evolution
+Jt"JJ>% k u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
lx$Y-Tb^F u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
/T#<g: ca1 = fftshift(fft(u1)); % Take Fourier transform
;T#t)oV ca2 = fftshift(fft(u2));
hNDhee`%6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
C$ *`c6R c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
8S]Mf*~S' u2 = ifft(fftshift(c2)); % Return to physical space
] |u}P2 u1 = ifft(fftshift(c1));
&@dMk4BH< if rem(m1,J) == 0 % Save output every J steps.
CS r{MF`]e U1 = [U1 u1]; % put solutions in U array
cnLC> _hY U2=[U2 u2];
v^@L?{" }8 MN1=[MN1 m1];
1"/V?ArfL z1=dz*MN1'; % output location
<$?: | end
h4?+/jk 7 end
Z6D4VZVF hg=abs(U1').*abs(U1'); % for data write to excel
T:)>Tcv}: ha=[z1 hg]; % for data write to excel
u:HKmP; t1=[0 t'];
7IK<9i4O hh=[t1' ha']; % for data write to excel file
{)b`fq %dlmwrite('aa',hh,'\t'); % save data in the excel format
Jk{>*jYk` figure(1)
~%#?;hJ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
!-N!8 0 figure(2)
|o!<@/iH= waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
EHzZ9zH\ Y\+^\`Tqu 非线性超快脉冲耦合的数值方法的Matlab程序 ~%<PEl| lg8~`96 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
2CmeO&(Qf* Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;L y4Z*!2 bzJKoxU uFok'3!g7% MO _9Yi % This Matlab script file solves the nonlinear Schrodinger equations
AP@xZ%;K % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
@%#(H se % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
,7j`5iq[m % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
50I6:=@\\ 8U;!1!+
7) C=1;
aLsGden| M1=120, % integer for amplitude
Qb(CH M3=5000; % integer for length of coupler
spl*[ d N = 512; % Number of Fourier modes (Time domain sampling points)
s &.Z;X dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
R=e`QMq T =40; % length of time:T*T0.
htF&VeIte dt = T/N; % time step
xDQ$Ui. n = [-N/2:1:N/2-1]'; % Index
y.O? c &! t = n.*dt;
\]9;c6( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
92SB'T> w=2*pi*n./T;
VqbiZOZ@ g1=-i*ww./2;
wZC 'BLD g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
s]I],>}RU g3=-i*ww./2;
PN'8"8`{ P1=0;
} 2\"(_ P2=0;
<5X@r#Lz P3=1;
`2@-'/$\I| P=0;
mD=?C for m1=1:M1
C$tSsw?A p=0.032*m1; %input amplitude
hV,3xrm?P s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
^#=L?e s1=s10;
7q\c\qL s20=0.*s10; %input in waveguide 2
p0tv@8C> s30=0.*s10; %input in waveguide 3
.H>Rqikj s2=s20;
K&X'^|en s3=s30;
@"~\ [z5 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
]Yj>~k:K %energy in waveguide 1
{ c J6Lq& p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
%b*%'#iK %energy in waveguide 2
E$ 1^}RGT) p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
gRFC n6Q %energy in waveguide 3
Ym6ec|9; for m3 = 1:1:M3 % Start space evolution
$bo^UYZ6 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
gO/(/e>P s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
x$Dv&4 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
2tbqmWw/s sca1 = fftshift(fft(s1)); % Take Fourier transform
H,I }R sca2 = fftshift(fft(s2));
cpy"1=K~M sca3 = fftshift(fft(s3));
kDz.{Ih sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
W +e N%w5 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
~"wD4Ue sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
4ku /3/ 6 s3 = ifft(fftshift(sc3));
e"2QV vB s2 = ifft(fftshift(sc2)); % Return to physical space
OP&[5X+Y s1 = ifft(fftshift(sc1));
68!]q(!6F end
7 dz E"m p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
VsmL#@E p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
U;nC)'~YW9 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
{L=[1 P1=[P1 p1/p10];
x3P@AC$\ P2=[P2 p2/p10];
t,+S~Cj| P3=[P3 p3/p10];
nZT@d;]U9 P=[P p*p];
q)~qd$yMS end
&-* nr/xT figure(1)
O`u! P\ plot(P,P1, P,P2, P,P3);
nx4aGS" F: toWmm(7v 转自：
http://blog.163.com/opto_wang/
