计算脉冲在非线性耦合器中演化的Matlab 程序 y M`Q VO!; 4Mr)~f rc % This Matlab script file solves the coupled nonlinear Schrodinger equations of
s^lm
81; % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
"( NJ{J#A % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
032PR;] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
k>W}9^ cK Cz) /Bq %fid=fopen('e21.dat','w');
tFrNnbmlQ N = 128; % Number of Fourier modes (Time domain sampling points)
KpF/g[m M1 =3000; % Total number of space steps
!IAd.<, J =100; % Steps between output of space
1_MaaA;ow" T =10; % length of time windows:T*T0
r(i!". Z T0=0.1; % input pulse width
d:GAa MN1=0; % initial value for the space output location
wNtPh& dt = T/N; % time step
YL kdT% n = [-N/2:1:N/2-1]'; % Index
!`qw" i t = n.*dt;
K!A;C#b! u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{+ @M! u20=u10.*0.0; % input to waveguide 2
,Z aPY u1=u10; u2=u20;
;: 4PT~\* U1 = u1;
hY}.2 U2 = u2; % Compute initial condition; save it in U
%5-
ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
_]q%H ve w=2*pi*n./T;
F0 ^kUyF| g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
v#E RXIrf L=4; % length of evoluation to compare with S. Trillo's paper
c3X8Wi7m dz=L/M1; % space step, make sure nonlinear<0.05
VU ,tCTXz for m1 = 1:1:M1 % Start space evolution
FtmI\, u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
=qy{8MsjA u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
-h1FrDBt ca1 = fftshift(fft(u1)); % Take Fourier transform
Ua\<oD79] ca2 = fftshift(fft(u2));
c,FhI~>R c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
vI1UFD
D c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
L AcK% u2 = ifft(fftshift(c2)); % Return to physical space
g'nN#O u1 = ifft(fftshift(c1));
jdW#;
]7+y if rem(m1,J) == 0 % Save output every J steps.
8 B"my\ U1 = [U1 u1]; % put solutions in U array
03^?+[C U2=[U2 u2];
_ ;8+L\ MN1=[MN1 m1];
"Qfw)!# z1=dz*MN1'; % output location
; w+<yW}EL end
0{zA6Xu end
X0+M|8: hg=abs(U1').*abs(U1'); % for data write to excel
1EcXvT= ha=[z1 hg]; % for data write to excel
e,rCutA) t1=[0 t'];
[ (eO_I5ep hh=[t1' ha']; % for data write to excel file
]YqeI *BX %dlmwrite('aa',hh,'\t'); % save data in the excel format
A_xUP9g@? figure(1)
VSQxlAGk@ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
~vv\A5O[| figure(2)
HS[N]'dc waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
xGVL|/?8 N %" /mcO 非线性超快脉冲耦合的数值方法的Matlab程序 & GM&, }5{#f`Ca6 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。
~ @Au < 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
8"2X 8 C8 2 }HS`) / :"e,&
% =h/0k
y % This Matlab script file solves the nonlinear Schrodinger equations
+'fdAc:5', % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
'l`T(_zL\% % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=`y.L 5 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:.%Hu9=GL q" %;),@ C=1;
" J(7fL$! M1=120, % integer for amplitude
?iQA>P9B M3=5000; % integer for length of coupler
UB&)U\hn N = 512; % Number of Fourier modes (Time domain sampling points)
Y/aNrIK7 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
p/GYfa
dU T =40; % length of time:T*T0.
Ls~F4ar$/ dt = T/N; % time step
Gkq<?q({t n = [-N/2:1:N/2-1]'; % Index
]&kzIxh t = n.*dt;
Vg^@6z U ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
\JX.)&>
- w=2*pi*n./T;
ob 3Z
I g1=-i*ww./2;
kH10z~(e g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
b6E,u*)" g3=-i*ww./2;
I%q&4L7pj P1=0;
cr_Q,* P2=0;
g,seqh% P3=1;
eE'2B."F P=0;
? [K \X for m1=1:M1
sG~5O\,E p=0.032*m1; %input amplitude
]\Tcy [5 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
1]l m0bfs s1=s10;
Tfba3+V s20=0.*s10; %input in waveguide 2
&v# * s30=0.*s10; %input in waveguide 3
DMY?'Nts! s2=s20;
ua -cX3 E s3=s30;
MxXu&.| _ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
<Hq|<^_K %energy in waveguide 1
k_c8\::p# p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
i1#\S0jN %energy in waveguide 2
8yDu(. Q p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
I}a iy.l %energy in waveguide 3
=Qcz :ng for m3 = 1:1:M3 % Start space evolution
XdDy0e4{%< s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
T"2D<7frbo s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
p ^U:O&U( s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
PB :Lj sca1 = fftshift(fft(s1)); % Take Fourier transform
`<C /-Au sca2 = fftshift(fft(s2));
IaU sca3 = fftshift(fft(s3));
7xOrG],E sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
ci @U
a}T sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
@ qfVt sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
yBPaGZ{ f s3 = ifft(fftshift(sc3));
45hjN6
s2 = ifft(fftshift(sc2)); % Return to physical space
~ZSP K;D[ s1 = ifft(fftshift(sc1));
$Qv+*% c end
9W{=6D86e p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
)bqfj>%#c p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
mGXjSWs d p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
,4 -) e P1=[P1 p1/p10];
Qn77ZpL:LJ P2=[P2 p2/p10];
eoS8e$} P3=[P3 p3/p10];
5Z 7 <X2 P=[P p*p];
lglC1W-q end
8/;q~:v figure(1)
L//Z\xr| plot(P,P1, P,P2, P,P3);
7J]tc1-re TvE M{ 转自：
http://blog.163.com/opto_wang/
