计算脉冲在非线性耦合器中演化的Matlab 程序 [ByQ;s5tY vf<UBa;Xm % This Matlab script file solves the coupled nonlinear Schrodinger equations of
fD{II +T % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
lto qtB\s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
9x? B5Ap[ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[![ G7H%f H-(q#?: %fid=fopen('e21.dat','w');
77*qkKr N = 128; % Number of Fourier modes (Time domain sampling points)
rnO0-h-; M1 =3000; % Total number of space steps
x` 2| }AP( J =100; % Steps between output of space
X D) 8? T =10; % length of time windows:T*T0
|g<* Rk0
T0=0.1; % input pulse width
yxwW j>c MN1=0; % initial value for the space output location
pj!:[d dt = T/N; % time step
z1vw'VT> n = [-N/2:1:N/2-1]'; % Index
(bv,02 t = n.*dt;
NG" yPn u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
\gItZ}+c4} u20=u10.*0.0; % input to waveguide 2
R"3
M[^ u1=u10; u2=u20;
W`rMtzL5 U1 = u1;
VYaSB?`/ U2 = u2; % Compute initial condition; save it in U
b}@(m$W ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
WhFS2Jl0 w=2*pi*n./T;
H-I{-Fm g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|CIC$ 2u L=4; % length of evoluation to compare with S. Trillo's paper
s]H^wrg& dz=L/M1; % space step, make sure nonlinear<0.05
pjw aL^ for m1 = 1:1:M1 % Start space evolution
Y % Ieg.o u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\G>Zk gU u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
}"_j0ax ca1 = fftshift(fft(u1)); % Take Fourier transform
u[")*\ CP ca2 = fftshift(fft(u2));
=X-Tcj?3g c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
yfEb
c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
nWJ:=JQ i" u2 = ifft(fftshift(c2)); % Return to physical space
$*\L4<( u1 = ifft(fftshift(c1));
f<<r TE6 if rem(m1,J) == 0 % Save output every J steps.
gsPl _ U1 = [U1 u1]; % put solutions in U array
brSi< U2=[U2 u2];
=P`~t<ajB MN1=[MN1 m1];
T5|c$doQ z1=dz*MN1'; % output location
88lxHoPV end
S&(^<gwl end
k 1='c7s hg=abs(U1').*abs(U1'); % for data write to excel
}T.?c9l X ha=[z1 hg]; % for data write to excel
" xR[mJ@U t1=[0 t'];
J! TBREK hh=[t1' ha']; % for data write to excel file
sbo^"&%w %dlmwrite('aa',hh,'\t'); % save data in the excel format
j U[
O figure(1)
A6{b?aQ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
909md|9K3 figure(2)
QA;!caNp waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
~@4'HMQ }]+xFj9[> 非线性超快脉冲耦合的数值方法的Matlab程序 o' 'wCr% ;%!B[+ut" 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。
zhblLBpeE\ 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
;% Hf)F > cN~U3 *7$P] / i_ @ % This Matlab script file solves the nonlinear Schrodinger equations
bZ 443SG % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
6!q#x[A % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
iv&v 8;B % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
=f1B,%7G+5 \or G63T: C=1;
A],ooiq< M1=120, % integer for amplitude
LF*&(NC M3=5000; % integer for length of coupler
)ev< 7g9*q N = 512; % Number of Fourier modes (Time domain sampling points)
}
JiSmi6o dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
JC#> Td T =40; % length of time:T*T0.
e ]Fp= *# dt = T/N; % time step
Kw5Lhc1V n = [-N/2:1:N/2-1]'; % Index
&miexSNeF t = n.*dt;
EME.h&A\G` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Anm=*;*M` w=2*pi*n./T;
0N :XIGFa g1=-i*ww./2;
Wu1 {[a| g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
MJ{%4S{K,p g3=-i*ww./2;
a
W%5~3 P1=0;
5n lMrK P2=0;
[I;^^#'P P3=1;
I+( /TP P=0;
^W?Z for m1=1:M1
++-{]wB3=. p=0.032*m1; %input amplitude
q MYe{{r s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
HQP}w%8x s1=s10;
sTRJ:fR s20=0.*s10; %input in waveguide 2
{aY Y85j s30=0.*s10; %input in waveguide 3
]3iH[,KU3 s2=s20;
zDTv\3rZ4X s3=s30;
@A<PkpNL p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
.L6Zm U %energy in waveguide 1
%
ps$qB' p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
J% H;%ROx %energy in waveguide 2
[K / m
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
_~u2: yl ( %energy in waveguide 3
IiBD?} for m3 = 1:1:M3 % Start space evolution
}J:+{4Yn s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
4LH[4Yj?` s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
cD| Htt" s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
UBv@+\Y8m sca1 = fftshift(fft(s1)); % Take Fourier transform
?:{sH#ua sca2 = fftshift(fft(s2));
^ 5GW$ sca3 = fftshift(fft(s3));
+HT1 ct+dI sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
a| 7a_s4( sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ikD1N sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
b75 $?_+ s3 = ifft(fftshift(sc3));
DV)3 s2 = ifft(fftshift(sc2)); % Return to physical space
!TM*o+; s1 = ifft(fftshift(sc1));
q$( 5Vd : end
#|GSQJ$F)` p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<_Z:'~Zp p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
gD`>Twa&6 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
$d S@y+ P1=[P1 p1/p10];
B.r4$:+jb2 P2=[P2 p2/p10];
BVsD(
@lX P3=[P3 p3/p10];
l5xCz=dw P=[P p*p];
$$APgj"|< end
t VrY3)c figure(1)
@yd4$Mv8% plot(P,P1, P,P2, P,P3);
S"Lx% =@2FX&&E_ 转自：
http://blog.163.com/opto_wang/
