计算脉冲在非线性耦合器中演化的Matlab 程序 \p=W4W/ Jr*S2 z<* % This Matlab script file solves the coupled nonlinear Schrodinger equations of
M }KM] < % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
c<t3y7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
zi DlJ3]^ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
o\ :f9JL s poWdRM2 %fid=fopen('e21.dat','w');
GF/x;,Ae N = 128; % Number of Fourier modes (Time domain sampling points)
K E)D =P M1 =3000; % Total number of space steps
0q V*d J =100; % Steps between output of space
o- e,
T =10; % length of time windows:T*T0
TF iM[ T0=0.1; % input pulse width
>7v.`m6?H MN1=0; % initial value for the space output location
> Qbc(}w dt = T/N; % time step
tX`[6` n = [-N/2:1:N/2-1]'; % Index
XCi]()TZ_ t = n.*dt;
t5B|c<Hb\ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
BC0c c[x u20=u10.*0.0; % input to waveguide 2
E+m"yQp{ u1=u10; u2=u20;
=QKgsgLh U1 = u1;
re 1k] U2 = u2; % Compute initial condition; save it in U
hhgz =7Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GO
GXM4I w=2*pi*n./T;
cT Iw A:)D g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
A(@gv8e[H^ L=4; % length of evoluation to compare with S. Trillo's paper
<[B[ dz=L/M1; % space step, make sure nonlinear<0.05
w)y9!li for m1 = 1:1:M1 % Start space evolution
"6o}qeB l u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
8iH;GFNJ7' u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
[#*?uu+
jK ca1 = fftshift(fft(u1)); % Take Fourier transform
pN f9 ca2 = fftshift(fft(u2));
,5+X%~' c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
x_iy;\s1 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
JLV}Fw u2 = ifft(fftshift(c2)); % Return to physical space
MHT,rqG u1 = ifft(fftshift(c1));
2Q'XB if rem(m1,J) == 0 % Save output every J steps.
{ )GEgC U1 = [U1 u1]; % put solutions in U array
Y 1ilH-8 U2=[U2 u2];
~m09yc d< MN1=[MN1 m1];
zam0(^= z1=dz*MN1'; % output location
byj mH end
VOK$;s'9} end
4l!Yop0h hg=abs(U1').*abs(U1'); % for data write to excel
a:%5.!Vd ha=[z1 hg]; % for data write to excel
[W|7r
n,q t1=[0 t'];
{ $TB#=G hh=[t1' ha']; % for data write to excel file
{F9Qy0.*u %dlmwrite('aa',hh,'\t'); % save data in the excel format
A%8`zR figure(1)
OVo waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
wj5s5dH figure(2)
].T;x| waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
a.U:B
[v` |ij5c@~& 非线性超快脉冲耦合的数值方法的Matlab程序 f<U m2YGW BG? 2PO{ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
|b @A:8ss Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
y!c7y]9__2 @DC2ci
> 7<'i #E~ 1YD.jU^;HD % This Matlab script file solves the nonlinear Schrodinger equations
xjk|O;ak % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
86 /i~s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xr3PO?: % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
h)RM9813< E=~WQ13Q C=1;
jG ;(89QR/ M1=120, % integer for amplitude
N$ a-i M3=5000; % integer for length of coupler
_ ,1kcD u N = 512; % Number of Fourier modes (Time domain sampling points)
L , Fso./y dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
xdU
pp~}+. T =40; % length of time:T*T0.
U*U )l$! dt = T/N; % time step
)w?$~q n = [-N/2:1:N/2-1]'; % Index
|nZB/YZt t = n.*dt;
v6Wf7)d/1 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
1xV1#'@[Jd w=2*pi*n./T;
n.UM+2G g1=-i*ww./2;
ZO6bG$y64 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Kf<_A{s g3=-i*ww./2;
r9'H7J P1=0;
jy|xDQ P2=0;
`a-T95IFy P3=1;
G.ARu-2's P=0;
=0fx6V for m1=1:M1
8/$iCW p=0.032*m1; %input amplitude
Tka="eyIj3 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
oOSyO D s1=s10;
(lsod#wEMg s20=0.*s10; %input in waveguide 2
l8lR 5< s30=0.*s10; %input in waveguide 3
cDyC&} :f s2=s20;
V+5
n|L5 s3=s30;
gCI'YEx p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
O Wfj<#}t+ %energy in waveguide 1
Z'bMIdV p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
B&j+fi %energy in waveguide 2
k8>^dZub p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
1Nu`@)D0 %energy in waveguide 3
0DT2q M[, for m3 = 1:1:M3 % Start space evolution
emIbG kH s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
nW*Oo|p~= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
_u5U> w s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
x)mC^ sca1 = fftshift(fft(s1)); % Take Fourier transform
'E 8Qi'g sca2 = fftshift(fft(s2));
<q=B(J' sca3 = fftshift(fft(s3));
h!%`odl%
sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
d/QM sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
$oj<yH<i sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
tV4aUve s3 = ifft(fftshift(sc3));
e2ZUl` {g s2 = ifft(fftshift(sc2)); % Return to physical space
hrt-<7U s1 = ifft(fftshift(sc1));
FEswNB(]* end
nE%qm - p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Vo8"/]_h p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
_I5+o\;1 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
o-Arfc3Q P1=[P1 p1/p10];
x"De
9SB P2=[P2 p2/p10];
K%Ml2V
P3=[P3 p3/p10];
R;2 -/MT- P=[P p*p];
z KT<QM!` end
$ayD55W4 figure(1)
G<1mj!{Vp plot(P,P1, P,P2, P,P3);
f#b[KB^Z,2 IvH+94 [)
转自：
http://blog.163.com/opto_wang/
