计算脉冲在非线性耦合器中演化的Matlab 程序 %wu,c e]* 8F)9.s,* % This Matlab script file solves the coupled nonlinear Schrodinger equations of
nHfAx/9! % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
s-&i!d % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ygQAA!&'] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
u V'C_H MC B2 %fid=fopen('e21.dat','w');
kZ:~m1dd N = 128; % Number of Fourier modes (Time domain sampling points)
6OQ\f,h @ M1 =3000; % Total number of space steps
@}+B%R J =100; % Steps between output of space
1OqVNp%K T =10; % length of time windows:T*T0
Kl(u~/=6 T0=0.1; % input pulse width
chE}`I? MN1=0; % initial value for the space output location
s <$*A;t dt = T/N; % time step
:N
xksL^ n = [-N/2:1:N/2-1]'; % Index
(~b0-3s t = n.*dt;
gKPqU @$* u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
uIJ
zz4 u20=u10.*0.0; % input to waveguide 2
" 68=dC u1=u10; u2=u20;
3zM>2)T- U1 = u1;
!+Sd%2o U2 = u2; % Compute initial condition; save it in U
$uK[[k~=S ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
??P3gA w=2*pi*n./T;
g$# JdN g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
9w\C
vO&R L=4; % length of evoluation to compare with S. Trillo's paper
3+M+5 dz=L/M1; % space step, make sure nonlinear<0.05
n!NA}Oa for m1 = 1:1:M1 % Start space evolution
z KG]7 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
KDDx[]1Q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-#AO4xpI ca1 = fftshift(fft(u1)); % Take Fourier transform
kh>i#9Ie ca2 = fftshift(fft(u2));
' 1 \UFz c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
cavz Xz c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
a -5 #8 u2 = ifft(fftshift(c2)); % Return to physical space
l~*d0E-$ u1 = ifft(fftshift(c1));
AAc2u^spx if rem(m1,J) == 0 % Save output every J steps.
|X~vsM0 U1 = [U1 u1]; % put solutions in U array
<<1_rRL] U2=[U2 u2];
f{D~ZC.* MN1=[MN1 m1];
!/e8x;_ z1=dz*MN1'; % output location
k~ $}&O end
u$x'P <b end
1 |3vwgRhs hg=abs(U1').*abs(U1'); % for data write to excel
TiI3<.a! ha=[z1 hg]; % for data write to excel
]#$r TWMl' t1=[0 t'];
#}'sknvM} hh=[t1' ha']; % for data write to excel file
~$ 4!C'0 %dlmwrite('aa',hh,'\t'); % save data in the excel format
n(Ry~Xu _ figure(1)
b yj7c ( waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
:HN\A4=kc( figure(2)
~T'$gl waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
uF-Rl##
> xEe3,tb'e 非线性超快脉冲耦合的数值方法的Matlab程序 %TQ5#{Y lMX Ld91 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。
Y2y =
P 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
TJ(vq] |& _We4% BH?fFe&J:` OV $ |!n % This Matlab script file solves the nonlinear Schrodinger equations
T7 XbbU % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
a[V 4EX1E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
J`A )WsKkb % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'Z^KpW &uu69)u C=1;
'\B!1B>T M1=120, % integer for amplitude
aaesgF M3=5000; % integer for length of coupler
#TY[\$ BHs N = 512; % Number of Fourier modes (Time domain sampling points)
n0'"/zyc dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
s!K9-qZl< T =40; % length of time:T*T0.
~^"s.Lsb dt = T/N; % time step
T Z@S?r>^ n = [-N/2:1:N/2-1]'; % Index
^9*Jz{e t = n.*dt;
.?-]+ -J?` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
u]QG^1.qYe w=2*pi*n./T;
mF] 8 g1=-i*ww./2;
5!^?H"#c g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
v@]\
P<E g3=-i*ww./2;
Ezw< P1=0;
Q! }LtR$ P2=0;
^Jn=a9Q6Z P3=1;
EN2/3~syO- P=0;
5B+I\f& for m1=1:M1
e5.sqft p=0.032*m1; %input amplitude
&GLe4zEh s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?O#,|\v?] s1=s10;
H}&4#CQ'! s20=0.*s10; %input in waveguide 2
RB/;qdq R s30=0.*s10; %input in waveguide 3
a6.0 $' s2=s20;
'9q:gFO s3=s30;
{, CvWL p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
6I$:mHEhd %energy in waveguide 1
GxcW^{; p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
? $rH yI %energy in waveguide 2
m^ [VM &% p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"+KAYsVtU %energy in waveguide 3
5QJ FNE for m3 = 1:1:M3 % Start space evolution
#_[W*-|L s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
!mRDzr7 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
)1S"D~j- s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
q| 7$@H^* sca1 = fftshift(fft(s1)); % Take Fourier transform
&IgH]?t sca2 = fftshift(fft(s2));
Nc[V kJ] sca3 = fftshift(fft(s3));
SI@Yct]<g sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
n!t][d/g+ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
RI64QD sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Hs6}~d s3 = ifft(fftshift(sc3));
u NRT@@oCq s2 = ifft(fftshift(sc2)); % Return to physical space
>4eZ%</D5 s1 = ifft(fftshift(sc1));
nfzKUJ Y end
:\8&Th}Se p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
n aB`@ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
h O}nc$S p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
5 Dlx]_ P1=[P1 p1/p10];
Qp]-4%^Vz P2=[P2 p2/p10];
'2.11cM 3 P3=[P3 p3/p10];
2
VGGSLr P=[P p*p];
(qXl=e8 end
`SSUQ#@ figure(1)
`h|>;u plot(P,P1, P,P2, P,P3);
P _3U4J vAp?Zl? g 转自：
http://blog.163.com/opto_wang/
