计算脉冲在非线性耦合器中演化的Matlab 程序 8 >EWKI9 Sv#XIMw{, % This Matlab script file solves the coupled nonlinear Schrodinger equations of
IMFDM."s % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
bo>*fNqAIy % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
ou lVg]; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*%NT~C
q y2dCEmhY %fid=fopen('e21.dat','w');
2;`1h[, -^ N = 128; % Number of Fourier modes (Time domain sampling points)
_Ey9G M1 =3000; % Total number of space steps
_/$Bpr{R J =100; % Steps between output of space
n
ATuD T =10; % length of time windows:T*T0
^ 7cGq+t T0=0.1; % input pulse width
\ a<h/ 4#| MN1=0; % initial value for the space output location
Qj.#) R dt = T/N; % time step
@ V sG' n = [-N/2:1:N/2-1]'; % Index
.V/Rfq t = n.*dt;
A RuA<vQ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
L#?Ek- u20=u10.*0.0; % input to waveguide 2
X/!o\yyT u1=u10; u2=u20;
rQs)O<jl U1 = u1;
8I?Wt
W U2 = u2; % Compute initial condition; save it in U
6r0kr bN ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
K(rWNO w=2*pi*n./T;
6dt] `zv/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
HYZ5EV L=4; % length of evoluation to compare with S. Trillo's paper
CS5?Ti6 dz=L/M1; % space step, make sure nonlinear<0.05
".V$~n( for m1 = 1:1:M1 % Start space evolution
(O?.)jEW(. u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
z&)A,ryW0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
;(/ZO%h ca1 = fftshift(fft(u1)); % Take Fourier transform
W~; `WR;. ca2 = fftshift(fft(u2));
%QGC8T z c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
\;3~a9q% c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|Nn)m u2 = ifft(fftshift(c2)); % Return to physical space
py!|\00} u1 = ifft(fftshift(c1));
o3^l~iT if rem(m1,J) == 0 % Save output every J steps.
Pb4X\9^ U1 = [U1 u1]; % put solutions in U array
0B/,/KX U2=[U2 u2];
^7 U
G$A MN1=[MN1 m1];
m|n%$$S& z1=dz*MN1'; % output location
L|:`^M+^w end
2DtM20<> end
- >-KCd1b hg=abs(U1').*abs(U1'); % for data write to excel
Nq[uoaT ha=[z1 hg]; % for data write to excel
<tNBxa$gS t1=[0 t'];
!8d{q)JZ hh=[t1' ha']; % for data write to excel file
w^|*m/h|@u %dlmwrite('aa',hh,'\t'); % save data in the excel format
?k&Vy figure(1)
vn!3l1\+J waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
k 8[n+^ figure(2)
R6 .hA_ih waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
'&tG?gb& +H-6e P 非线性超快脉冲耦合的数值方法的Matlab程序 6+|do+0Icg 9igiZmM 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。
m)t;9J5 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
Y-_`23x` jh%Eq+#S Fn;SF4KOm V)HG (k % This Matlab script file solves the nonlinear Schrodinger equations
@ $ ;q ; % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
QUc= &5 % % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
]I dk:et % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
{_[N<U:QT& i Dp)FQ$ C=1;
x7&B$.>3 M1=120, % integer for amplitude
dO<ER Y M3=5000; % integer for length of coupler
HZC"nb}r4 N = 512; % Number of Fourier modes (Time domain sampling points)
3 *"WG O5 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
QvlObEhcS T =40; % length of time:T*T0.
ghG**3xr dt = T/N; % time step
rNWw?_H-H( n = [-N/2:1:N/2-1]'; % Index
zm5 ]J t = n.*dt;
.+3g*Dv{& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1 ~Y< //5E w=2*pi*n./T;
q s6]- g1=-i*ww./2;
:Uzm
g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
D rUO- g3=-i*ww./2;
&tLgG4pd P1=0;
d9f C<Tp P2=0;
y| i,| P3=1;
nLZTK&7} P=0;
_~l5u8{^ 6 for m1=1:M1
f;o5=)Y p=0.032*m1; %input amplitude
{l1. 2! s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
.Ni\\ s1=s10;
~F|+o}a `
s20=0.*s10; %input in waveguide 2
A@!qv#' s30=0.*s10; %input in waveguide 3
b.JuI s2=s20;
)
<[XtK s3=s30;
HSE!x_$ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
{0Yf]FQb-a %energy in waveguide 1
P6'1.R p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
T= y}y %energy in waveguide 2
8yR.uMI$/ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
`!;_ho %energy in waveguide 3
/ |;RV" for m3 = 1:1:M3 % Start space evolution
abmYA# s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
r"3=44St s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
FF`T \&u s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
VX0 %a@ur sca1 = fftshift(fft(s1)); % Take Fourier transform
z1 | T C sca2 = fftshift(fft(s2));
urs,34h sca3 = fftshift(fft(s3));
wY{-BuX v sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
F3[T.sf sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
TTX5EDCrC sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Q2 w_X8 s3 = ifft(fftshift(sc3));
KEo ,m s2 = ifft(fftshift(sc2)); % Return to physical space
E1 aHKjLQ s1 = ifft(fftshift(sc1));
y{B=-\ O] end
7?!d^$B p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
?DS@e@lx p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
"yy5F>0Wt p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
bivuqKA P1=[P1 p1/p10];
Drgv`z P2=[P2 p2/p10];
'A=^S e`= P3=[P3 p3/p10];
,GhS[VJjR P=[P p*p];
U awyDs end
9IdA%RM~mH figure(1)
CAig ]=2' plot(P,P1, P,P2, P,P3);
Fc)@,/R"v HTv2# 转自：
http://blog.163.com/opto_wang/
