计算脉冲在非线性耦合器中演化的Matlab 程序 H!*ypJ Oj-\ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
l%}q&_ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
F] M-r{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=rymd3/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
x8aOXN#w} ?OW!D? %fid=fopen('e21.dat','w');
]Ea-MeH N = 128; % Number of Fourier modes (Time domain sampling points)
CUJq [ M1 =3000; % Total number of space steps
XQ~Xls%]
J =100; % Steps between output of space
A+^okT37r T =10; % length of time windows:T*T0
M|c_P)7ym T0=0.1; % input pulse width
NzAh3k MN1=0; % initial value for the space output location
o2dO\$' dt = T/N; % time step
k.C&6*l!5; n = [-N/2:1:N/2-1]'; % Index
nA0%M1a t = n.*dt;
%%ouf06.| u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
xO_ >%F^? u20=u10.*0.0; % input to waveguide 2
='jT
5Mg u1=u10; u2=u20;
&|Wqzdo?# U1 = u1;
%}(` ? U2 = u2; % Compute initial condition; save it in U
$y6 <2w%b ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hDi~{rbmc w=2*pi*n./T;
/a*){JQ5 j g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
,c"J[$i$ L=4; % length of evoluation to compare with S. Trillo's paper
inh:b .,B dz=L/M1; % space step, make sure nonlinear<0.05
s! 2[zJ19p for m1 = 1:1:M1 % Start space evolution
I;Mm +5A u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
|&"aZ!Kn u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
\dCGu~bT ca1 = fftshift(fft(u1)); % Take Fourier transform
vyDxX ca2 = fftshift(fft(u2));
k eC'/\e c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
{@ CQ
( c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
MrzD
ah9UG u2 = ifft(fftshift(c2)); % Return to physical space
Tr _gc~ u1 = ifft(fftshift(c1));
e_e\Ie/pDc if rem(m1,J) == 0 % Save output every J steps.
M~\dvJ$cH U1 = [U1 u1]; % put solutions in U array
#w.0 C c U2=[U2 u2];
7LU^Xm8 MN1=[MN1 m1];
KANR=G z1=dz*MN1'; % output location
A:ts_* end
pMT7 /y- end
~-Kx^3(# hg=abs(U1').*abs(U1'); % for data write to excel
FB wG3x ha=[z1 hg]; % for data write to excel
lIS`_H} t1=[0 t'];
3F]Dh^IR9 hh=[t1' ha']; % for data write to excel file
8!|vp7/ %dlmwrite('aa',hh,'\t'); % save data in the excel format
IQU1 JVk Z figure(1)
v4hrS\M waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
r'Wf4p^Xd figure(2)
ke8g tbm waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
( 0/M?YQ F Pw<' rN8'' 非线性超快脉冲耦合的数值方法的Matlab程序 Dx1(}D ~\(c;J*Ir 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。
7YD+zd: 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
o) XrC nE u:& 4 qK7:[\T|?T %d];h % This Matlab script file solves the nonlinear Schrodinger equations
Z@1kx3Wx$ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
UB5H8&Rf! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
joskKik^ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
f$QkzWvr <&Xl b0 C=1;
n[0u&m8 M1=120, % integer for amplitude
xgMh@@e M3=5000; % integer for length of coupler
rmzzbLTu N = 512; % Number of Fourier modes (Time domain sampling points)
`$Rgn3 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
:0:Tl/)) T =40; % length of time:T*T0.
,2$<Pt; dt = T/N; % time step
'UhHcMh: n = [-N/2:1:N/2-1]'; % Index
QNOdt 2NN t = n.*dt;
.x%w# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
l S,Jo/T@ w=2*pi*n./T;
'y; Kj g1=-i*ww./2;
N<i5X.X g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
@\w}p E g3=-i*ww./2;
pDlrK&;\z P1=0;
h"+7c c@ P2=0;
y:98}gW`n P3=1;
uCr& ` P=0;
rs?Dn6:;B for m1=1:M1
> \[]z^J p=0.032*m1; %input amplitude
.2c/ V s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
s R1_L/ . s1=s10;
]uox ^HC s20=0.*s10; %input in waveguide 2
vcdVck@ s30=0.*s10; %input in waveguide 3
KxK,en4)+ s2=s20;
qZ^
PC- s3=s30;
=(
|%%,3 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
H9)n<r %energy in waveguide 1
Is4,QnY_[ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
j5/pVXO %energy in waveguide 2
#epbc K p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
':pDlUA %energy in waveguide 3
,Tr&`2w for m3 = 1:1:M3 % Start space evolution
#4mRMsW5" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Xd %qebK s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
]S4" JcM s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
3[u-
LYW sca1 = fftshift(fft(s1)); % Take Fourier transform
sMGo1pG( sca2 = fftshift(fft(s2));
7 2JwG7qh sca3 = fftshift(fft(s3));
^}Vc||S sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
+"-l~`+<es sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
FzX ;~CA sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
IOZw[9](+ s3 = ifft(fftshift(sc3));
G^t)^iI"' s2 = ifft(fftshift(sc2)); % Return to physical space
T" {~mQ* s1 = ifft(fftshift(sc1));
Ck
)W= end
aC[G_ACwc p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
3XlQ 4 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Qw2`@P8W p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
ISC>]` P1=[P1 p1/p10];
|1!fuB A P2=[P2 p2/p10];
UDr 1t n P3=[P3 p3/p10];
9JP:wE~y P=[P p*p];
0a89<yX end
pRV.\*:c figure(1)
bK%F_v3' plot(P,P1, P,P2, P,P3);
dh`s^D6Q> w>j5oz } 转自：
http://blog.163.com/opto_wang/
