计算脉冲在非线性耦合器中演化的Matlab 程序 Z?[;Japg *%'4.He7V % This Matlab script file solves the coupled nonlinear Schrodinger equations of
2 Ua_7 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
q^Lj)zmnK % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
h|dVVCsN % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
g8mVjM\B; a9"x_IVU %fid=fopen('e21.dat','w');
nTY`1w.; N = 128; % Number of Fourier modes (Time domain sampling points)
HGB96,o f9 M1 =3000; % Total number of space steps
}_0?S0<# J =100; % Steps between output of space
Ka2U@ fK" T =10; % length of time windows:T*T0
WW@/q`h T0=0.1; % input pulse width
X.xp'/d MN1=0; % initial value for the space output location
TF|GGY i dt = T/N; % time step
W+a>*#* n = [-N/2:1:N/2-1]'; % Index
9+9}^B5@A t = n.*dt;
I'BoP u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
BkA>':bUr u20=u10.*0.0; % input to waveguide 2
ag14omM- u1=u10; u2=u20;
J 7emoD [ U1 = u1;
}Q`Kg8L U2 = u2; % Compute initial condition; save it in U
LcE!e%3 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
;%]Q% 7 w=2*pi*n./T;
Pp:(PoH g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
XV)ej>A-V L=4; % length of evoluation to compare with S. Trillo's paper
sqei(OXy dz=L/M1; % space step, make sure nonlinear<0.05
@= 6} w_ for m1 = 1:1:M1 % Start space evolution
R8Lp8!F' u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
)#T (2 A u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
h -+vM9j ca1 = fftshift(fft(u1)); % Take Fourier transform
`BMg\2Ud* ca2 = fftshift(fft(u2));
k 5xzC& c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
HvK<>9 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
c%Y vj u2 = ifft(fftshift(c2)); % Return to physical space
mR[J Xh9s u1 = ifft(fftshift(c1));
o9 # if rem(m1,J) == 0 % Save output every J steps.
`HgT 5} U1 = [U1 u1]; % put solutions in U array
eek5Xm U2=[U2 u2];
% &4sHDP MN1=[MN1 m1];
8Y
sn8 z1=dz*MN1'; % output location
MT$OjH'Q` end
}a"T7y23 end
(# eB % hg=abs(U1').*abs(U1'); % for data write to excel
. CLi v ha=[z1 hg]; % for data write to excel
,/m<= `*N| t1=[0 t'];
+~ :1H.
hh=[t1' ha']; % for data write to excel file
r=s ,Ath %dlmwrite('aa',hh,'\t'); % save data in the excel format
hBLJKSv figure(1)
+0.$w waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
b3H~a2"d figure(2)
niFX8%<hP waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
IcoK22/ iwJBhu0@# 非线性超快脉冲耦合的数值方法的Matlab程序 E[Tz%x=P _w Cp.[3?t 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(s\ Q[ 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
7sC$hm] `w@fxv 6*S|$lo9B x{Gb4=?l % This Matlab script file solves the nonlinear Schrodinger equations
dU3UCD+2y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
zW!3>(L/ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
z62e4U][ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+Ys<V sn+i[ C=1;
jL I (Z M1=120, % integer for amplitude
lHV
bn7 M3=5000; % integer for length of coupler
pTST\0? N = 512; % Number of Fourier modes (Time domain sampling points)
{Lk~O)E dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
0 4x[@f` T =40; % length of time:T*T0.
*["9;_K D dt = T/N; % time step
.2C}8GGC' n = [-N/2:1:N/2-1]'; % Index
AJiEyAC!)5 t = n.*dt;
`]FA} wC ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
a"b9h{h@ w=2*pi*n./T;
S3MMyS8 g1=-i*ww./2;
"k)( , g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
xA`Q4"[I g3=-i*ww./2;
=mn)].Wg P1=0;
0X ~
P2=0;
!\}Dxt P3=1;
S s@\'K3e P=0;
I+!w9o2nZ for m1=1:M1
^IjKT p=0.032*m1; %input amplitude
o`+6E
q0w s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
d?oupW}uu s1=s10;
mK% !9F
V s20=0.*s10; %input in waveguide 2
hW~,Uqy s30=0.*s10; %input in waveguide 3
]\v'1m" s2=s20;
6ALf`: s3=s30;
`5r*4N< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
)xiic3F %energy in waveguide 1
0<>I\UN0b p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
W LP A51R %energy in waveguide 2
aG%KiJ7KEN p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
|[>`3p "& %energy in waveguide 3
6|V713\ for m3 = 1:1:M3 % Start space evolution
z[M LMf[c s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
K,&)\r kzD s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
N0O8to}V s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
B0?E$8a sca1 = fftshift(fft(s1)); % Take Fourier transform
jF<Y,(C\ sca2 = fftshift(fft(s2));
0F8y 8s sca3 = fftshift(fft(s3));
8v8?D8\=| sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
54_CewL1P] sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
#|v\UJ:Pf/ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
|qH -^b.F s3 = ifft(fftshift(sc3));
0vbn!<: s2 = ifft(fftshift(sc2)); % Return to physical space
azr|Fz/ s1 = ifft(fftshift(sc1));
lE78 Yl ] end
}y(1mzb p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
SpdQ<] p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
&$lz@Z p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
!e?=I P1=[P1 p1/p10];
gGxgU$`#c P2=[P2 p2/p10];
ZF_*h`B
P3=[P3 p3/p10];
sTP`xaY P=[P p*p];
w,SOvbAxX2 end
;2(8&. figure(1)
a9j
f7r1 plot(P,P1, P,P2, P,P3);
E
y1mlW M/x49qO# 转自：
http://blog.163.com/opto_wang/
