计算脉冲在非线性耦合器中演化的Matlab 程序 iII=;:p &dM.
d! % This Matlab script file solves the coupled nonlinear Schrodinger equations of
<0b)YJb4M % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Y$Z x, % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
.E`\MtA % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~Sj9GxTe ,}3
'I [ %fid=fopen('e21.dat','w');
hIy ~B[' N = 128; % Number of Fourier modes (Time domain sampling points)
n^Hm;BiE# M1 =3000; % Total number of space steps
hQYL`Dni J =100; % Steps between output of space
w65K[l;2 T =10; % length of time windows:T*T0
d,+Hd2o^X T0=0.1; % input pulse width
}>>1<P<8- MN1=0; % initial value for the space output location
T|nDTezr dt = T/N; % time step
U' H$`$Ov n = [-N/2:1:N/2-1]'; % Index
RRmz"j> t = n.*dt;
O _ `VV* u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
BXtCSfY $ u20=u10.*0.0; % input to waveguide 2
b*a#<K$T_ u1=u10; u2=u20;
IwQ"eUnK U1 = u1;
i3tg6 o4C U2 = u2; % Compute initial condition; save it in U
EK {Eo9l ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
]<ldWL w=2*pi*n./T;
24
[+pu g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
2BQ
j L=4; % length of evoluation to compare with S. Trillo's paper
zQcL| (N dz=L/M1; % space step, make sure nonlinear<0.05
Hx"ob_^'7 for m1 = 1:1:M1 % Start space evolution
7''??X u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
&XIt5<$~R u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
u(@$a 4z ca1 = fftshift(fft(u1)); % Take Fourier transform
k.uH~S _ ca2 = fftshift(fft(u2));
uG wm
r c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
n&$j0k c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Ro\8ZX UQa u2 = ifft(fftshift(c2)); % Return to physical space
o}
J&E{Tk u1 = ifft(fftshift(c1));
J l( &!?j if rem(m1,J) == 0 % Save output every J steps.
'~5LY!H(pT U1 = [U1 u1]; % put solutions in U array
T1 ut"Zu U2=[U2 u2];
6 eLR2 MN1=[MN1 m1];
fz|cnU z1=dz*MN1'; % output location
'*K :
lx end
YmL06<Mh end
s2h@~y hg=abs(U1').*abs(U1'); % for data write to excel
^yW L,$ ha=[z1 hg]; % for data write to excel
`g(Y*uCp t1=[0 t'];
EAT"pxP hh=[t1' ha']; % for data write to excel file
/a{la8Ni %dlmwrite('aa',hh,'\t'); % save data in the excel format
]^yFaTfS figure(1)
l{5IUuUi waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
s3z$e+A8 figure(2)
Kz~ps
5 waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
6Y^23W F p*< 0" 0 非线性超快脉冲耦合的数值方法的Matlab程序 H= <S 9M 8m-U){r!U^ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
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G [ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
m4**~xfC tI`Q /a5@ {+ ] [5<q .!Oo|m`V@ % This Matlab script file solves the nonlinear Schrodinger equations
51#_Vg % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
"i
nd$Z`c % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5&QJ7B,! % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
B-xGX$<z . k#U]M
C=1;
$|L
Sx M1=120, % integer for amplitude
*{YlN}vA M3=5000; % integer for length of coupler
m}C>ti`VD N = 512; % Number of Fourier modes (Time domain sampling points)
.8@$\Z RP dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
IoxgjUa T =40; % length of time:T*T0.
tR s [ YK dt = T/N; % time step
Bn^0^J- n = [-N/2:1:N/2-1]'; % Index
! +a. Ei t = n.*dt;
rNrxaRQ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
CnU*Jb w=2*pi*n./T;
.I7pA 5V{# g1=-i*ww./2;
2a-w%
(K g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
EMh7z7}Rr g3=-i*ww./2;
C;; Sih5 P1=0;
' KP@W9j P2=0;
6@Y_*4$| P3=1;
(] Z_UTT P=0;
~FZ&.<s
for m1=1:M1
tWJZoD 6}h p=0.032*m1; %input amplitude
n4s+>|\M s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
?ME6+Z\ s1=s10;
+O" !qAiK s20=0.*s10; %input in waveguide 2
Z
8S \@I s30=0.*s10; %input in waveguide 3
,-$LmECg s2=s20;
zvvhF N2s s3=s30;
q['Euy p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ot,jp|N>f~ %energy in waveguide 1
mi=Q{>rb p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
/ 'Ass(=6 %energy in waveguide 2
?5 +.`L 9H p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"fQ~uzg=" %energy in waveguide 3
_ 64A( U for m3 = 1:1:M3 % Start space evolution
xmNB29# s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
}QN1| mP2 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
%oF}HF. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
spGb!Y`mR sca1 = fftshift(fft(s1)); % Take Fourier transform
9`T)@Uj2n sca2 = fftshift(fft(s2));
XR8,Vt) = sca3 = fftshift(fft(s3));
]jtK I4 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Y4OPEo 5o sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
qt"G[9; sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
NiNM{[3o S s3 = ifft(fftshift(sc3));
=qoWCmg"& s2 = ifft(fftshift(sc2)); % Return to physical space
7G:s2432 s1 = ifft(fftshift(sc1));
zE336 end
:I"2V p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
h(<,fg1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
c CSs p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
>] qc-{>& P1=[P1 p1/p10];
!lREaSM P2=[P2 p2/p10];
GX)u|g P3=[P3 p3/p10];
jk"`Z< j~ P=[P p*p];
~t@cO.c end
!xz eM VI figure(1)
<vnHz?71c plot(P,P1, P,P2, P,P3);
V8 e> l[tH B p*K]3_ 转自：
http://blog.163.com/opto_wang/
