计算脉冲在非线性耦合器中演化的Matlab 程序 $AoN ,B> oSxHTbp? % This Matlab script file solves the coupled nonlinear Schrodinger equations of
fuQ? @F % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
++ x EMP) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
# *\PU % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
HdVGkv/ *K!V$8k=99 %fid=fopen('e21.dat','w');
,rQznE1e N = 128; % Number of Fourier modes (Time domain sampling points)
/+%1Kq.hP M1 =3000; % Total number of space steps
fY \QI
= J =100; % Steps between output of space
(ZDRjBth[ T =10; % length of time windows:T*T0
} nu hLt1 T0=0.1; % input pulse width
o <sX6a9e MN1=0; % initial value for the space output location
lv,<[Hw1 dt = T/N; % time step
>pr{)b p G n = [-N/2:1:N/2-1]'; % Index
an.)2*u t = n.*dt;
"#( ]{MY u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
U1dz:OG> u20=u10.*0.0; % input to waveguide 2
}56"4/ Z u1=u10; u2=u20;
H =EvT'g U1 = u1;
j&ddpS(s U2 = u2; % Compute initial condition; save it in U
haS`V ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/8lGP! z w=2*pi*n./T;
]x! vPIyq g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
amOBUD5Ld` L=4; % length of evoluation to compare with S. Trillo's paper
"h\{PoG dz=L/M1; % space step, make sure nonlinear<0.05
^BW V6 for m1 = 1:1:M1 % Start space evolution
zkB_$=sbn# u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Wk`G+VR+ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
P5kkaLzG ca1 = fftshift(fft(u1)); % Take Fourier transform
q
f-1} ca2 = fftshift(fft(u2));
3Cq17A 9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
J %URg=r c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
$} N'm u2 = ifft(fftshift(c2)); % Return to physical space
-_v[oqf$ u1 = ifft(fftshift(c1));
&H<-joZ)Z\ if rem(m1,J) == 0 % Save output every J steps.
p<tj6O U1 = [U1 u1]; % put solutions in U array
yin"+&<T U2=[U2 u2];
(yn !~El3 MN1=[MN1 m1];
Xfk&{zO-j z1=dz*MN1'; % output location
CZt)Q4 end
=]E;wWC end
mbU[fHyV hg=abs(U1').*abs(U1'); % for data write to excel
D O(FG-R ha=[z1 hg]; % for data write to excel
(WX,&`a<$ t1=[0 t'];
U SfOc hh=[t1' ha']; % for data write to excel file
E: L =>} %dlmwrite('aa',hh,'\t'); % save data in the excel format
t
:sKvJ figure(1)
Q];+?Pu. waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
/EA4-#uw figure(2)
D\bW' k]! waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
6(VCQ{ @?f3 (G h, 非线性超快脉冲耦合的数值方法的Matlab程序 ?&j[Rj0pH G/bWn@ 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。
Lr V)}1&5 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
9co1+y=i{ U_ y)p Cd A tzp\oO UXnd~DA % This Matlab script file solves the nonlinear Schrodinger equations
W EZ(4ah % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
\M'b % % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8(\Az5 % % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
!Yz~HO,u+ 1)X%n)2pr C=1;
pTX{j=n! M1=120, % integer for amplitude
s-J>(|
M3=5000; % integer for length of coupler
z<hy#BIjnd N = 512; % Number of Fourier modes (Time domain sampling points)
ZOi8)Y~ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Ul )2A T =40; % length of time:T*T0.
oOnk,U dt = T/N; % time step
ZjF$zVk n = [-N/2:1:N/2-1]'; % Index
t=d~\_Oa t = n.*dt;
]4@_KKP ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0bVtku K;G w=2*pi*n./T;
rc<^6Hq D g1=-i*ww./2;
:w_Zr5H] g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
s
'u6Ep/V g3=-i*ww./2;
j]6 Z*AxQ P1=0;
![18+Q\ P2=0;
k:nr!Y< P3=1;
e%afK@c P=0;
1>[3(o3t for m1=1:M1
m1heU3BUWU p=0.032*m1; %input amplitude
kS%FV;9>( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
G!C2[:[g s1=s10;
u`xmF/jhQ s20=0.*s10; %input in waveguide 2
!vHnMY~AG s30=0.*s10; %input in waveguide 3
yNoJrA s2=s20;
pn{Mj s3=s30;
Zm >Q-7r9 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
pLE|#58I %energy in waveguide 1
zQMsS p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
y+)][Wa0 %energy in waveguide 2
)O#]W vr p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Zz'(!h Uy %energy in waveguide 3
bN`oQ.Z 4 for m3 = 1:1:M3 % Start space evolution
RF U(wek s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
:A g]^ot s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
f<=
#WV s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
EW%%W 6O6 sca1 = fftshift(fft(s1)); % Take Fourier transform
`(vgBz`e[ sca2 = fftshift(fft(s2));
O[+S/6uy sca3 = fftshift(fft(s3));
lbZ,?wm sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
M}k )Ep9 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
DN2K4%cM%' sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
r :{2}nE s3 = ifft(fftshift(sc3));
2Vxr s2 = ifft(fftshift(sc2)); % Return to physical space
N)K};yMf s1 = ifft(fftshift(sc1));
<*3{Twa1T end
B.-5$4*s p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
:DXkAb2 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
gbL99MZ@~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
(YVl5}V P1=[P1 p1/p10];
\bw7 1( Q P2=[P2 p2/p10];
S7N3L." P3=[P3 p3/p10];
^>gRK*, P=[P p*p];
^3B{|cqf end
Fb O- K - figure(1)
{+r
pMUs# plot(P,P1, P,P2, P,P3);
LyH8T'C~ ,UopGlA
, 转自：
http://blog.163.com/opto_wang/
