计算脉冲在非线性耦合器中演化的Matlab 程序 GTvb^+6 Ymvd= F % This Matlab script file solves the coupled nonlinear Schrodinger equations of
B!a nY} /U % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
?[">%^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
RwKN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
;_t on?bF eL !6}y}W %fid=fopen('e21.dat','w');
de=T7,G# N = 128; % Number of Fourier modes (Time domain sampling points)
jd*H$ BU^ M1 =3000; % Total number of space steps
\O~P
!` J =100; % Steps between output of space
(*tJCz`Sj T =10; % length of time windows:T*T0
>6 q@Tr T0=0.1; % input pulse width
2S/ 7f: MN1=0; % initial value for the space output location
H[C n@XE dt = T/N; % time step
w6 .HvH-@? n = [-N/2:1:N/2-1]'; % Index
q[ZYlF,Ho t = n.*dt;
VPbNLi u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
'fsOKx4Z u20=u10.*0.0; % input to waveguide 2
E~N r4vq u1=u10; u2=u20;
HC+R :Dz U1 = u1;
'l;|t"R12 U2 = u2; % Compute initial condition; save it in U
uy~j$ lrn ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
v/d cb% w=2*pi*n./T;
oJy/PR 3 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
<s >SnOD
L=4; % length of evoluation to compare with S. Trillo's paper
CqV
\:50g dz=L/M1; % space step, make sure nonlinear<0.05
2 ]wh1) for m1 = 1:1:M1 % Start space evolution
{ `> x"Y5 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
%94"e7Hy u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
G1|:b-C ca1 = fftshift(fft(u1)); % Take Fourier transform
: 08UeEy ca2 = fftshift(fft(u2));
V
ALYA=w/ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
mx2 Jt1 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
}$ d er u2 = ifft(fftshift(c2)); % Return to physical space
dXhV]xK u1 = ifft(fftshift(c1));
(%1*<6ka if rem(m1,J) == 0 % Save output every J steps.
s~CA
@ U1 = [U1 u1]; % put solutions in U array
BlCKJp{m$ U2=[U2 u2];
HZNX1aQ|Q# MN1=[MN1 m1];
4Ki'r&L\ z1=dz*MN1'; % output location
t{9Ph]e end
QHK$ end
6822xk hg=abs(U1').*abs(U1'); % for data write to excel
:gXj( $ ha=[z1 hg]; % for data write to excel
2bmppDk t1=[0 t'];
l_WY];a hh=[t1' ha']; % for data write to excel file
.1;?#t]ZV %dlmwrite('aa',hh,'\t'); % save data in the excel format
81&!!qhfS figure(1)
= j - waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
_>.%X45xi figure(2)
n~Ix8|S h waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
&oBJY'1 Qk=
w ,` 非线性超快脉冲耦合的数值方法的Matlab程序 hwJ.M4 M6>l%[ 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。
i~4Kek6,I 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
-kO=pY P*O 4'M#m|V 7">.{
@S O`eNuQSv % This Matlab script file solves the nonlinear Schrodinger equations
1EN5 ZN, % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
| zf||ju % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
pR $c<p % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
zI(Pti
eUl[ gHP C=1;
^,3 >}PU M1=120, % integer for amplitude
IKt9=T x M3=5000; % integer for length of coupler
;iEq a"gO N = 512; % Number of Fourier modes (Time domain sampling points)
=o {`vv dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
"3K0 wR5 T =40; % length of time:T*T0.
F~ :5/-zs dt = T/N; % time step
&8N\
6K= n = [-N/2:1:N/2-1]'; % Index
:?,& u,8 t = n.*dt;
,F1$Of/'@\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`J C!u c w=2*pi*n./T;
WJ%b9 {< g1=-i*ww./2;
r=vE 0;7 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
z}5XLa^ g3=-i*ww./2;
Y\rKw!u_! P1=0;
T@L^RaPX P2=0;
Sdn]
f4 P3=1;
:=/D F P=0;
`f (!i mN for m1=1:M1
@{bf]Oc p=0.032*m1; %input amplitude
E^ rN) s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
R75sK(oS s1=s10;
4B |f}7%\ s20=0.*s10; %input in waveguide 2
XjV7Ew^7 s30=0.*s10; %input in waveguide 3
f ~53:;L/ s2=s20;
DP?gozm s3=s30;
v;OA hF r| p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
$wBUu %energy in waveguide 1
7':|f " p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
iaMZ37 %energy in waveguide 2
Q5Wb ) p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Q>|<R[.7 %energy in waveguide 3
x[_+U 4-/ for m3 = 1:1:M3 % Start space evolution
MQI6e". s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
J[^-k!9M s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
CkOd> Kn s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
\X(.%5xC sca1 = fftshift(fft(s1)); % Take Fourier transform
m$U2|5un& sca2 = fftshift(fft(s2));
p}h)WjC sca3 = fftshift(fft(s3));
RSp=If+4 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
oRC j]9I$ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
5y.kOe4vH sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
\KTX{qI"f s3 = ifft(fftshift(sc3));
VlK W WQj s2 = ifft(fftshift(sc2)); % Return to physical space
M]oaWQu s1 = ifft(fftshift(sc1));
?@tp1?) end
-ohqw+D p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
.(! $j-B p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
gg<lWeS/3 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Wu: evaZ:i P1=[P1 p1/p10];
5B a e HzI P2=[P2 p2/p10];
f-
_~rQ P3=[P3 p3/p10];
pJV<#<#Z P=[P p*p];
;XANIT V end
"wdC/ figure(1)
6z~6o 0s~ plot(P,P1, P,P2, P,P3);
9OX&;O+5 =ove#3 转自：
http://blog.163.com/opto_wang/
