计算脉冲在非线性耦合器中演化的Matlab 程序 RL@VSHXc R6kD=JY/! % This Matlab script file solves the coupled nonlinear Schrodinger equations of
V) ~.~2$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
( u\._Gwsx % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
_u5#v0Y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
'$ => C.Kh [V\Ut %fid=fopen('e21.dat','w');
T?tgd J N = 128; % Number of Fourier modes (Time domain sampling points)
p'*>vk M1 =3000; % Total number of space steps
C'.L20qW J =100; % Steps between output of space
t(NI-UXBp T =10; % length of time windows:T*T0
8pIP T0=0.1; % input pulse width
{ GK;63`1 MN1=0; % initial value for the space output location
M3c$=> dt = T/N; % time step
Q
Nh|Wz n = [-N/2:1:N/2-1]'; % Index
hI s4@0 t = n.*dt;
5
ZGNz1)?V u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
N `5,\TR2f u20=u10.*0.0; % input to waveguide 2
s%nUaWp~ u1=u10; u2=u20;
)U7t U1 = u1;
bpJ(XN}E U2 = u2; % Compute initial condition; save it in U
vNV/eB8#S ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
RKHyw 08 w=2*pi*n./T;
Z'`g J&6n g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
P q;U &, L=4; % length of evoluation to compare with S. Trillo's paper
\E72L5nJW dz=L/M1; % space step, make sure nonlinear<0.05
P;=n9hgHI for m1 = 1:1:M1 % Start space evolution
`scR*]f1+ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
4o
<Uy u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
v7BA[j Qr ca1 = fftshift(fft(u1)); % Take Fourier transform
_~IR6dKE ca2 = fftshift(fft(u2));
r3&G)g=u c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Vd,jlt.t c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
GK )? YM u2 = ifft(fftshift(c2)); % Return to physical space
ZRh~`yy u1 = ifft(fftshift(c1));
Ch&a/S} if rem(m1,J) == 0 % Save output every J steps.
9Y IM'q>`v U1 = [U1 u1]; % put solutions in U array
n BjqTud
U2=[U2 u2];
vM*-D{ MN1=[MN1 m1];
p
Dx1z|@z z1=dz*MN1'; % output location
0=@?ob7 end
`<`` 8 end
E4`N-3 hg=abs(U1').*abs(U1'); % for data write to excel
X@ +{5% ha=[z1 hg]; % for data write to excel
&S{RGXj_ t1=[0 t'];
J*yf2& lI5 hh=[t1' ha']; % for data write to excel file
Zd^rNHhA %dlmwrite('aa',hh,'\t'); % save data in the excel format
H[s(e5 6z figure(1)
ck ]Do!h waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
AK ,J 7 figure(2)
Xb:;</ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
GY6`JWk Uol|9F 非线性超快脉冲耦合的数值方法的Matlab程序 [-65PC4aN W98i[Q9A7 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。
<r .)hT"0 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
\rx3aJl / ;$#d}R 1tEgl\u\ Fsmycr!R % This Matlab script file solves the nonlinear Schrodinger equations
w k( VR % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
rHC>z7+z. % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
`slL %j^" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`YFtL 9Tg IB C=1;
zvYq@Mhr M1=120, % integer for amplitude
0LPig[ M3=5000; % integer for length of coupler
y6ECdVF N = 512; % Number of Fourier modes (Time domain sampling points)
)IP,; < dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
ciFmaM . T =40; % length of time:T*T0.
[;r)9mh7 dt = T/N; % time step
<;9 I@VYK n = [-N/2:1:N/2-1]'; % Index
'-r).X k t = n.*dt;
^nT/i
.#_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
!*s?B L w=2*pi*n./T;
~ZmN44?R g1=-i*ww./2;
:8L8q< U g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
}6p@lla,%] g3=-i*ww./2;
F |d\k Q P1=0;
i2@VB6]? P2=0;
#+:9T /*>0 P3=1;
= }lh_ P=0;
X\]L=>]C for m1=1:M1
\kp8S'qVo p=0.032*m1; %input amplitude
j | v%)A s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
t9,\Hdo s1=s10;
Ee)T1 ~;W s20=0.*s10; %input in waveguide 2
#^`4DhQ/
1 s30=0.*s10; %input in waveguide 3
o9| nJ; s2=s20;
J ][T"K s3=s30;
j|4<i9^} p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
?zeJ#i %energy in waveguide 1
%z /hf p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
y Wg@v + %energy in waveguide 2
$*SW8'],` p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
[=E %energy in waveguide 3
x*![fK for m3 = 1:1:M3 % Start space evolution
4~k\ j s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
qIVx9jNN s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
@XgKYm
s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
`Bo*{}E sca1 = fftshift(fft(s1)); % Take Fourier transform
r;B8i !gD sca2 = fftshift(fft(s2));
t|H^`Cv6 sca3 = fftshift(fft(s3));
Z8# (kmBdB sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
88VZR&v sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
hU(umL< sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
r;/ 4F/6" s3 = ifft(fftshift(sc3));
y[`l3;u:' s2 = ifft(fftshift(sc2)); % Return to physical space
#D< C )Q s1 = ifft(fftshift(sc1));
iW RH{mK end
`s"'r ! p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
o}$XH,-9& p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
qS403+Su1= p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
W0y '5` P1=[P1 p1/p10];
!2 LCLN\ P2=[P2 p2/p10];
NhfJ30~ P3=[P3 p3/p10];
K-e9>fmB# P=[P p*p];
M3 J#'%$ end
<A [E:*`* figure(1)
{HL3<2=o plot(P,P1, P,P2, P,P3);
VCu{&Sh* :j5n7s?&=y 转自：
http://blog.163.com/opto_wang/
