计算脉冲在非线性耦合器中演化的Matlab 程序 $g\&5sstE ~~qWI>. 4 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Sycw %k % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
GjT#%GBF % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!a- b6A a % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
elO<a]hX }DjYGMrTB %fid=fopen('e21.dat','w');
,.mBJ S E3 N = 128; % Number of Fourier modes (Time domain sampling points)
8l+H"M& | M1 =3000; % Total number of space steps
p,!$/Q+l J =100; % Steps between output of space
>fs 2kha T =10; % length of time windows:T*T0
B6M+mx"G T0=0.1; % input pulse width
1{PG>W MN1=0; % initial value for the space output location
gS9>N/b| dt = T/N; % time step
Z~u9VYi! n = [-N/2:1:N/2-1]'; % Index
q 31>uF t = n.*dt;
4 < S' u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
mY-hN| u20=u10.*0.0; % input to waveguide 2
`!4,jd u1=u10; u2=u20;
Akk
3 Qx U1 = u1;
"8<K'zeS8 U2 = u2; % Compute initial condition; save it in U
M"Y0jQ( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
UT ]?;o" w=2*pi*n./T;
K` 6z&* g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
F:g= i}7 L=4; % length of evoluation to compare with S. Trillo's paper
2xxB\J dz=L/M1; % space step, make sure nonlinear<0.05
0!GAk for m1 = 1:1:M1 % Start space evolution
nb , 2,H u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
`'4 )q}bB u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
N|Cs=-+ ca1 = fftshift(fft(u1)); % Take Fourier transform
W<,F28jI3v ca2 = fftshift(fft(u2));
w=_Jc8/. c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Lxe^v/LsT c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Oe !6){OG) u2 = ifft(fftshift(c2)); % Return to physical space
@!%n$>p/V u1 = ifft(fftshift(c1));
:1wr VU-?h if rem(m1,J) == 0 % Save output every J steps.
HEF?mD3h U1 = [U1 u1]; % put solutions in U array
#/-_1H U2=[U2 u2];
p3x?[ Ww MN1=[MN1 m1];
4Y ROB912 z1=dz*MN1'; % output location
?UZ?NY end
E5GJi end
p~jlx~1-] hg=abs(U1').*abs(U1'); % for data write to excel
`C72sA{M. ha=[z1 hg]; % for data write to excel
6[P-Ny{z t1=[0 t'];
` lpz-"EEV hh=[t1' ha']; % for data write to excel file
4ne5=YY * %dlmwrite('aa',hh,'\t'); % save data in the excel format
&Z^(y}jPr figure(1)
)}lRd#V waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
"MOpsb, figure(2)
"M
H6fF waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
zqySm) o] '- PC7"o 非线性超快脉冲耦合的数值方法的Matlab程序 7=}F{U -_A$DM!^=w 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。
lFG9=Wf 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
/R8p] > 0> %5'6Tj +Wn& ,?3^ % This Matlab script file solves the nonlinear Schrodinger equations
' 0aG
N<c % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Ty4S~ClO#' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_F(P*[[& % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
c-1 q2y #?O & C=1;
NTs7 KSgZ M1=120, % integer for amplitude
]7 GlO9 M3=5000; % integer for length of coupler
J
m{ N = 512; % Number of Fourier modes (Time domain sampling points)
Z=z %$l dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
nhT(P`6 T =40; % length of time:T*T0.
~Qj}ijWD dt = T/N; % time step
P
}7zE3V n = [-N/2:1:N/2-1]'; % Index
|CD"*[j] t = n.*dt;
UXr5aZ7y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#Z ,E><t w=2*pi*n./T;
iAn'a W\TF g1=-i*ww./2;
kyYLP"oB= g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
m]Y;c_DO: g3=-i*ww./2;
?;ukvD P1=0;
%/9;ZV P2=0;
v({N:ya P3=1;
#(;< -7M2 P=0;
cD}Sf> for m1=1:M1
'o4p#`R:8 p=0.032*m1; %input amplitude
}M>r E s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
WY s1=s10;
<E,%@ s20=0.*s10; %input in waveguide 2
?? qq: `s s30=0.*s10; %input in waveguide 3
jQs>`P-CM s2=s20;
X$?3U! s3=s30;
Zl/< w(f_ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
X* eW#|$\ %energy in waveguide 1
%ati7{2! p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
<v
0*]NiX %energy in waveguide 2
kQ>^->w p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
GRqT-/n" %energy in waveguide 3
pV[ '' for m3 = 1:1:M3 % Start space evolution
\f WW' s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
5r,r%{@K s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
vXj < s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
L5fuM]G` sca1 = fftshift(fft(s1)); % Take Fourier transform
IND ]j72 sca2 = fftshift(fft(s2));
1eS_
nLFw~ sca3 = fftshift(fft(s3));
?knYY>Kzh1 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
I~*
? d sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
?*"srE,#JX sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
W
!}{$ s3 = ifft(fftshift(sc3));
f2I6!_C!+ s2 = ifft(fftshift(sc2)); % Return to physical space
95W?{>
@ s1 = ifft(fftshift(sc1));
l1=JrpCan end
+/{L#e> p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
{D&9UZm p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
csZ c|kDI p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
-Sv"gL B P1=[P1 p1/p10];
X|LxV ] P2=[P2 p2/p10];
wBk@F5\< P3=[P3 p3/p10];
nR;D#"p% P=[P p*p];
ZAKeEm2A end
tAu4haa4; figure(1)
,,L2(N plot(P,P1, P,P2, P,P3);
cgu~ 7 Cqcb>\X 转自：
http://blog.163.com/opto_wang/
