计算脉冲在非线性耦合器中演化的Matlab 程序 J+8T Ie 5I@2U vV8 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
0t}&32 lL& % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Yc1v e % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
nK |WzUtp % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
l050n9#9p ,(CIcDJ2U_ %fid=fopen('e21.dat','w');
fmq9u(!R N = 128; % Number of Fourier modes (Time domain sampling points)
. xdSUe M1 =3000; % Total number of space steps
$v+t ~b J =100; % Steps between output of space
: w 4Sba3 T =10; % length of time windows:T*T0
mGqT_
T0=0.1; % input pulse width
a;e~D
9%1 MN1=0; % initial value for the space output location
OO+QH 2j dt = T/N; % time step
~!W{C_*N n = [-N/2:1:N/2-1]'; % Index
j]5bs *G t = n.*dt;
) %& ~CW+ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
u@-x3%W u20=u10.*0.0; % input to waveguide 2
)F)
(Hg u1=u10; u2=u20;
4> W ov U1 = u1;
`>cB R,)r U2 = u2; % Compute initial condition; save it in U
/__@a&9t ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
DJf!{:b) w=2*pi*n./T;
];1M g g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
:;]iUjiC8 L=4; % length of evoluation to compare with S. Trillo's paper
=%V(n{7= dz=L/M1; % space step, make sure nonlinear<0.05
NJr aol for m1 = 1:1:M1 % Start space evolution
0 ?
QTi( u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
F"Y .'m y8 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
.d>TU bR; ca1 = fftshift(fft(u1)); % Take Fourier transform
L) ]|\| ca2 = fftshift(fft(u2));
6vQCghI c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
h|j $Jy c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
I
;Sm<P7* u2 = ifft(fftshift(c2)); % Return to physical space
nuip u1 = ifft(fftshift(c1));
P6ztP$M( if rem(m1,J) == 0 % Save output every J steps.
iFy_ D U1 = [U1 u1]; % put solutions in U array
]hL `HP U2=[U2 u2];
89 [5a MN1=[MN1 m1];
yy%'9E ldc z1=dz*MN1'; % output location
sox0:9Oqnf end
M &g1'zv?/ end
0qj:v"~Q hg=abs(U1').*abs(U1'); % for data write to excel
T!*lTzNHm ha=[z1 hg]; % for data write to excel
`i,l)X] t1=[0 t'];
r{T}pc>^ hh=[t1' ha']; % for data write to excel file
/RzL,~] %dlmwrite('aa',hh,'\t'); % save data in the excel format
[Cx'a7KWL figure(1)
yIL6Sb waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
jLRh/pbz4 figure(2)
fvDt_g9 oI waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Hq*\,`b& TUQ+?[ 非线性超快脉冲耦合的数值方法的Matlab程序 "Vg1'd }f dC7YVs_,# 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。
1webk;IM 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
\Y0o~JD `H.~ # $ O#g'4 S `EUu fTYi % This Matlab script file solves the nonlinear Schrodinger equations
ueyz@{On~ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
+y$%S4>0tp % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Nj<}t/ e % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
J .r^"K\ a9ko3L C=1;
:4f>S) m M1=120, % integer for amplitude
y\Z$8'E5W M3=5000; % integer for length of coupler
?~vVS Y N = 512; % Number of Fourier modes (Time domain sampling points)
Nm.H
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
iz&$q ]P8 T =40; % length of time:T*T0.
xV_,R'l dt = T/N; % time step
D+Ke)-/ n = [-N/2:1:N/2-1]'; % Index
L|wD2iw t = n.*dt;
UbD1h_ b ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rff=ud>Jf w=2*pi*n./T;
a5/6DK> g1=-i*ww./2;
Li jisE g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
#E?T E g3=-i*ww./2;
)AxgKBW P1=0;
!\
IgTt, P2=0;
Df\~ ZWs! P3=1;
WU wH W P=0;
"0Wi-52=V for m1=1:M1
eDh]uKg p=0.032*m1; %input amplitude
~$GRgOn s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Tq\S-K}4! s1=s10;
-VqZw&" s20=0.*s10; %input in waveguide 2
kK27h fsw s30=0.*s10; %input in waveguide 3
g>m)|o' s2=s20;
cmLGMlF T s3=s30;
)U?Tmh p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
\(ygdZ{R %energy in waveguide 1
,cgFdOM. p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
t<)Cbple\ %energy in waveguide 2
,N[N;Uoj p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
77FI&*q %energy in waveguide 3
#JmVq-) for m3 = 1:1:M3 % Start space evolution
KT 3W>/#E s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
>Mu I-^ 3 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
i++a^f s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
laR cEXj sca1 = fftshift(fft(s1)); % Take Fourier transform
7# ~v<M6 sca2 = fftshift(fft(s2));
F/ZB%;O9 sca3 = fftshift(fft(s3));
B6N/nCvHK sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
:~I^ni sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
U9 <AL. sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Zj+S "`P s3 = ifft(fftshift(sc3));
:y/1Jf'2f s2 = ifft(fftshift(sc2)); % Return to physical space
|WiE`&?xP s1 = ifft(fftshift(sc1));
DzfgPY_Py end
pyvH [ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
1V\tKDM p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~4 ~c+^PF p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
I~^t\iujs P1=[P1 p1/p10];
jGg,)~)Y P2=[P2 p2/p10];
}Y}f7 3-| P3=[P3 p3/p10];
#?OJ9pyG' P=[P p*p];
InO;DA\ end
$?_/`S13 figure(1)
/|<Pn!}J plot(P,P1, P,P2, P,P3);
CIxa" MW Qm-I=Rh+ 转自：
http://blog.163.com/opto_wang/
