计算脉冲在非线性耦合器中演化的Matlab 程序 9n[ovX 7n! b^]@8I[M % This Matlab script file solves the coupled nonlinear Schrodinger equations of
l T RQ/B % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Qcf5* ]V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
J 4OgV? % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
B)4>:j:{?W COf>H0^%Q %fid=fopen('e21.dat','w');
4w5mn6 MxR N = 128; % Number of Fourier modes (Time domain sampling points)
{Jj
vF M1 =3000; % Total number of space steps
coQ>CbHg J =100; % Steps between output of space
K-b'jP\ T =10; % length of time windows:T*T0
9! sR} T0=0.1; % input pulse width
rVo?I MN1=0; % initial value for the space output location
Fb{kql= dt = T/N; % time step
MKN],l
N n = [-N/2:1:N/2-1]'; % Index
=^LX,!2zp{ t = n.*dt;
eDPmUlC+- u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
) 2jBhT u20=u10.*0.0; % input to waveguide 2
{g(-C& u1=u10; u2=u20;
%VD>S U1 = u1;
oH|<(8efD U2 = u2; % Compute initial condition; save it in U
#c:b 8rw ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
oj1,DU w=2*pi*n./T;
cc ^ [ u+ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
)W& $FU4JK L=4; % length of evoluation to compare with S. Trillo's paper
q|+`ihut dz=L/M1; % space step, make sure nonlinear<0.05
4D-4BxN* for m1 = 1:1:M1 % Start space evolution
rpu{YC1C% u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
M '4$z^@Z u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
06#40- ca1 = fftshift(fft(u1)); % Take Fourier transform
^1^mu c[ ca2 = fftshift(fft(u2));
C`0; c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
6X@$xe847[ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
`Mxi2Y{vp u2 = ifft(fftshift(c2)); % Return to physical space
S!;:7?mq u1 = ifft(fftshift(c1));
eJ23 $VM+9 if rem(m1,J) == 0 % Save output every J steps.
q g+bh U1 = [U1 u1]; % put solutions in U array
<8Z m}-U U2=[U2 u2];
\Y{^Q7!>:8 MN1=[MN1 m1];
=7U_ jDME z1=dz*MN1'; % output location
D!oE LZ3 end
?{
0MF end
WI $MT6 hg=abs(U1').*abs(U1'); % for data write to excel
*=X$j~#X ha=[z1 hg]; % for data write to excel
xC ,;IS k, t1=[0 t'];
:nHa-N3 hh=[t1' ha']; % for data write to excel file
nd[{DF?)/ %dlmwrite('aa',hh,'\t'); % save data in the excel format
EhOy<f[4W figure(1)
eaxp(VX?oy waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
s@ ~Y!A figure(2)
O*ql!9} E{ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
_K?{DnTb VkNg Vjg 非线性超快脉冲耦合的数值方法的Matlab程序 I,@ f*o 1eZ759PoO 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。
u, R;=DNl 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
c9eLNVM h!L/ZeRaV 9y~5@/3 2R [Ie;Jd>gG % This Matlab script file solves the nonlinear Schrodinger equations
Z7X_U` Q % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
[JY 1| N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
; SS/bS| % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fgW>U*.ar .ZB(!v/2 C=1;
POtj6 ?a M1=120, % integer for amplitude
!4(X9}a M3=5000; % integer for length of coupler
/@<&{_sybp N = 512; % Number of Fourier modes (Time domain sampling points)
X RMYR97 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
&C.{7ZNt T =40; % length of time:T*T0.
/ >Z`? dt = T/N; % time step
z|o7k;raH n = [-N/2:1:N/2-1]'; % Index
5V U
5kiCt t = n.*dt;
Ltx eT . ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
$ X9`~Sv _ w=2*pi*n./T;
f+/A D g1=-i*ww./2;
;w/|5 ;{A; g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
3 :XF7T g3=-i*ww./2;
fR& ;E P1=0;
]}wo$7pO P2=0;
z)RJUmY3B P3=1;
<Oi65O_X P=0;
e-Xr^@M*Q for m1=1:M1
[=})^t?8 p=0.032*m1; %input amplitude
& .zG?e. s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
fq@r6\TI s1=s10;
,co~@a@9 s20=0.*s10; %input in waveguide 2
UC!?. s30=0.*s10; %input in waveguide 3
#^+C
k HX s2=s20;
a,GO S:?O5 s3=s30;
dOm@cs p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
R d?8LLz %energy in waveguide 1
m+t<<5I[- p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
[O"9OW'2!B %energy in waveguide 2
Md4hd#z p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
d-zNv bU" %energy in waveguide 3
:6
, `M, for m3 = 1:1:M3 % Start space evolution
;
S(KJV s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
*Vbf ;=Mb s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
J <"=c
z$ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
A)2eo<ij4 sca1 = fftshift(fft(s1)); % Take Fourier transform
, G q? sca2 = fftshift(fft(s2));
0^H"eQO sca3 = fftshift(fft(s3));
CNo'qlvF5N sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
(;9-8Y&_ d sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
LFzL{rny!U sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Yq 6e=?- s3 = ifft(fftshift(sc3));
b6`_;Z s2 = ifft(fftshift(sc2)); % Return to physical space
gQ < >S s1 = ifft(fftshift(sc1));
|6cz r end
;qA(!`h+ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
;;^OKrzWW p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
8=GgTpO5 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Io|3zE*< P1=[P1 p1/p10];
V<:)bG4;d P2=[P2 p2/p10];
9 BZyCz P3=[P3 p3/p10];
K1th>!JW' P=[P p*p];
/IO<TF(X end
I@$ cw3 figure(1)
#~_ZG% u plot(P,P1, P,P2, P,P3);
GOKca%DT= `X["Bgk$!T 转自：
http://blog.163.com/opto_wang/
