计算脉冲在非线性耦合器中演化的Matlab 程序 ][Ne ;F6 R* m=V{iu` % This Matlab script file solves the coupled nonlinear Schrodinger equations of
zT;F4_p3G- % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
`/WX!4eR, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
NWK+.{s>m % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'`.bmiM 6 w"-& %fid=fopen('e21.dat','w');
)_$F/ug N = 128; % Number of Fourier modes (Time domain sampling points)
lLq9)+HGN M1 =3000; % Total number of space steps
:nk $? 5ib J =100; % Steps between output of space
l Je =z T =10; % length of time windows:T*T0
==$>M
d T0=0.1; % input pulse width
0taopDi ;d MN1=0; % initial value for the space output location
pq<302uBQ dt = T/N; % time step
~Q q0 n = [-N/2:1:N/2-1]'; % Index
+mc0:e{W F t = n.*dt;
(`z`ni u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
lIs<&-0 u20=u10.*0.0; % input to waveguide 2
$:v!* 0/ u1=u10; u2=u20;
7 (}gs?&w U1 = u1;
4d\1W?i- U2 = u2; % Compute initial condition; save it in U
9d4Agj
M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Xbm\"g \ w=2*pi*n./T;
%XIPPEHU g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
+YS0yTWeX L=4; % length of evoluation to compare with S. Trillo's paper
<, r(^Ntz dz=L/M1; % space step, make sure nonlinear<0.05
~,1 99K#' for m1 = 1:1:M1 % Start space evolution
<{
Z$!]i1 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
r-Nv<oH; u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
uif1)y`Q$C ca1 = fftshift(fft(u1)); % Take Fourier transform
=#tQh g,_ ca2 = fftshift(fft(u2));
s>i`=[qFc c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Uc j
eB c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
D_n(T ') u2 = ifft(fftshift(c2)); % Return to physical space
]`p*ZTr)\ u1 = ifft(fftshift(c1));
Us5P?} if rem(m1,J) == 0 % Save output every J steps.
AD_aI
%7 U1 = [U1 u1]; % put solutions in U array
:cx }I U2=[U2 u2];
fu}ZOPu MN1=[MN1 m1];
d&z^u.SY z1=dz*MN1'; % output location
g\Ck!KJ/y end
3%"r%:fQB/ end
^xB=d S~ hg=abs(U1').*abs(U1'); % for data write to excel
^#^\ @jLm ha=[z1 hg]; % for data write to excel
F;I % 9-R t1=[0 t'];
' a}<|Et. hh=[t1' ha']; % for data write to excel file
r `t|}m %dlmwrite('aa',hh,'\t'); % save data in the excel format
vMDX figure(1)
jB"?iC. waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
6*!R' figure(2)
m^6& !`CD waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
!|SVRaS Bu :h_sV D 非线性超快脉冲耦合的数值方法的Matlab程序 s ]D&): ncF|wz 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
9_~[ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
O@[jNs)]. -d|Q|zF^x X4- _l$j d[cqs9=\ % This Matlab script file solves the nonlinear Schrodinger equations
%f v;C % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
O.ce"5Y^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
C(RZ09,.S % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@raw8w\Zj+ st|;] q9? C=1;
>EMsBX M1=120, % integer for amplitude
- AJ$-y M3=5000; % integer for length of coupler
@|N'V"*MT N = 512; % Number of Fourier modes (Time domain sampling points)
R:Pw@ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Y? 1
3_~
K T =40; % length of time:T*T0.
2HxT+|~d6 dt = T/N; % time step
|zJxR_) n = [-N/2:1:N/2-1]'; % Index
1;e"3x" t = n.*dt;
fV 6$ YCf ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
s 8/sH]; w=2*pi*n./T;
f{} zqCK g1=-i*ww./2;
{iz,iv/U g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
u]D>O$_ s g3=-i*ww./2;
\R m 2c8Z2 P1=0;
v#HaZT]u P2=0;
J ejDF*Q P3=1;
] bPj%sb*@ P=0;
3)? v for m1=1:M1
5BztOYn, p=0.032*m1; %input amplitude
mnZS](> s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
\[nvdvJv s1=s10;
}I1A4=d s20=0.*s10; %input in waveguide 2
Lq-Di|6q s30=0.*s10; %input in waveguide 3
c
h_1 - s2=s20;
QG|KZ 8uO s3=s30;
13:yaRo p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
,b &-o?.{ %energy in waveguide 1
+IRr&J*P p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
=LFrV9 %energy in waveguide 2
e:h(, p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
I6k S1 %energy in waveguide 3
'1$#onx for m3 = 1:1:M3 % Start space evolution
-<R" s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
j K!Y- s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
c `hj^t s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
r35'U#VMk? sca1 = fftshift(fft(s1)); % Take Fourier transform
zW,Nv>Ac5 sca2 = fftshift(fft(s2));
(Wj2%*N T sca3 = fftshift(fft(s3));
N@o Ng}D&: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
8Wa&&YTB sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
3?}W0dZ$d sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{3jV ,S s3 = ifft(fftshift(sc3));
#Cwzk{p( s2 = ifft(fftshift(sc2)); % Return to physical space
RR%[]M#_T s1 = ifft(fftshift(sc1));
&TpzJcd" end
h-^7cHI} p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
B\/"$" p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
d %"?^e p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
\:ELO[(#|{ P1=[P1 p1/p10];
FY^#%0~ P2=[P2 p2/p10];
+cDz`)N,, P3=[P3 p3/p10];
S.!0~KR: U P=[P p*p];
C*S% aR end
Ws+Zmpk% figure(1)
K*ZH<@o4 plot(P,P1, P,P2, P,P3);
BUuU#e5 w&M)ws;$ 转自：
http://blog.163.com/opto_wang/
