计算脉冲在非线性耦合器中演化的Matlab 程序 zg .' WQ \' z?P % This Matlab script file solves the coupled nonlinear Schrodinger equations of
YKJk)% ;+w % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
T@U_;v |rf % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
2Y(P hw2% % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
e=o<yf9>Q 6|V713\ %fid=fopen('e21.dat','w');
z[M LMf[c N = 128; % Number of Fourier modes (Time domain sampling points)
K,&)\r kzD M1 =3000; % Total number of space steps
9jDV]!N4 J =100; % Steps between output of space
L
Bb&av T =10; % length of time windows:T*T0
s_hf ,QH T0=0.1; % input pulse width
H~i+: X=I MN1=0; % initial value for the space output location
Op" \i dt = T/N; % time step
E
b-?wzh n = [-N/2:1:N/2-1]'; % Index
c+f~>AaI t = n.*dt;
xlp^XT6# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
8Focs p2
u20=u10.*0.0; % input to waveguide 2
izebQVQO* u1=u10; u2=u20;
W#P)v{K U1 = u1;
Ett%Y*D+J U2 = u2; % Compute initial condition; save it in U
T6=c9f?7 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
B[F x2r`0 w=2*pi*n./T;
zy(sekX ; g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
gGxgU$`#c L=4; % length of evoluation to compare with S. Trillo's paper
4'Z =T\: dz=L/M1; % space step, make sure nonlinear<0.05
|#D3~au
for m1 = 1:1:M1 % Start space evolution
+XLy Pj u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
\zR@FOl`q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
BKP XXR ca1 = fftshift(fft(u1)); % Take Fourier transform
btkD<1{g ca2 = fftshift(fft(u2));
\l?\%aqm c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
+;c)GNQ)6: c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
\sEq
r)\k u2 = ifft(fftshift(c2)); % Return to physical space
^ b{0 |: u1 = ifft(fftshift(c1));
e[$=5U~c if rem(m1,J) == 0 % Save output every J steps.
0.'$U}#b U1 = [U1 u1]; % put solutions in U array
<.HX_z3l U2=[U2 u2];
(TM1(<j MN1=[MN1 m1];
N\ChA]Ck z1=dz*MN1'; % output location
=H%c/Jty end
12U1DEd>- end
= Bcwd7+ hg=abs(U1').*abs(U1'); % for data write to excel
#f0J .) M ha=[z1 hg]; % for data write to excel
%D< =6suW t1=[0 t'];
5 < wIJ5t hh=[t1' ha']; % for data write to excel file
y2;uG2IS_g %dlmwrite('aa',hh,'\t'); % save data in the excel format
Qh<_/X? figure(1)
}d QW -U waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
%JeT,{ figure(2)
V|e9G,z~A waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
= +% QfuK .aV#W@iyK 非线性超快脉冲耦合的数值方法的Matlab程序 H:Y?(" k "#\\p~D/< 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。
[`Se h $ 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
_CN5,mLNRk pyhC%EZU )ZC 0/>R ]&w8"q % This Matlab script file solves the nonlinear Schrodinger equations
uDvZ]Q| . % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
- L%tiz`_ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*` &4< >=n % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Z`y%#B6x. J5e C=1;
EVZuwbO)| M1=120, % integer for amplitude
|(G^3+5Uwm M3=5000; % integer for length of coupler
L lOUK 2tZ N = 512; % Number of Fourier modes (Time domain sampling points)
*Wdn P.'Y dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
{_T?0L T =40; % length of time:T*T0.
)F*;7]f dt = T/N; % time step
, 7-@eZ n = [-N/2:1:N/2-1]'; % Index
D]X&Va t = n.*dt;
$L%gQkz_ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
P7np
-I* w=2*pi*n./T;
"I+71Ce g1=-i*ww./2;
}GI8p* ]o= g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
p?F%a;V3 g3=-i*ww./2;
uvC ![j^~ P1=0;
kEi WE| P2=0;
_]zm02| P3=1;
6/e+=W2 P=0;
;U$Fz~rJ for m1=1:M1
3"afrA p=0.032*m1; %input amplitude
U0>Uqk", s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Ot,eAiaX s1=s10;
o+Cd\D69S s20=0.*s10; %input in waveguide 2
Q #!|h:K s30=0.*s10; %input in waveguide 3
:+ Ti^FF`w s2=s20;
bit@Kv1<C s3=s30;
[C_Dv-d p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
9?W!E_ %energy in waveguide 1
L WwWxerZ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
0P)"_x_ %energy in waveguide 2
yvN; |R
p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
e+416
~X
v %energy in waveguide 3
F&pJ faig for m3 = 1:1:M3 % Start space evolution
Rf*cW&}% s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
h |m>JDxn s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
CjeAO 2 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
=VXxQ\{ sca1 = fftshift(fft(s1)); % Take Fourier transform
oY Y?`<N# sca2 = fftshift(fft(s2));
Y24 3mq- sca3 = fftshift(fft(s3));
[@K#BFA sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
1=NP=ZB sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Vm6
0aXm_ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
ZDffR: An s3 = ifft(fftshift(sc3));
D X|yL!4[ s2 = ifft(fftshift(sc2)); % Return to physical space
>2kjd s1 = ifft(fftshift(sc1));
R8"qD j end
b @9>1d$ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
[&_c.ti p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
ftr? @^ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
7Qoy~=E P1=[P1 p1/p10];
w&U>w@H^ P2=[P2 p2/p10];
uPZ<hG#K P3=[P3 p3/p10];
r* I u6 P=[P p*p];
q,ur[ & < end
< Wz+f+HC figure(1)
P gdv)i3 plot(P,P1, P,P2, P,P3);
|-vc/t2k>T H<YhO&D*u 转自：
http://blog.163.com/opto_wang/
