计算脉冲在非线性耦合器中演化的Matlab 程序 P # Z +:T J n1 (- % This Matlab script file solves the coupled nonlinear Schrodinger equations of
R"JT+m % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
FS6ZPjG) % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
k'1i quc#u % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fq[,9lK Uv=hxV[7y %fid=fopen('e21.dat','w');
*W1:AGp z N = 128; % Number of Fourier modes (Time domain sampling points)
Hl*/s M1 =3000; % Total number of space steps
PZCOJK J =100; % Steps between output of space
!}&f2!?.W T =10; % length of time windows:T*T0
um
mkAeWb T0=0.1; % input pulse width
!
d " i MN1=0; % initial value for the space output location
,J e9]XT dt = T/N; % time step
ADlLodG n = [-N/2:1:N/2-1]'; % Index
jb!15Vlt" t = n.*dt;
{
daEKac5 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
>l0D,-O]m u20=u10.*0.0; % input to waveguide 2
w 8oIq* u1=u10; u2=u20;
3 *[YM7y U1 = u1;
<a$'tw-8 U2 = u2; % Compute initial condition; save it in U
*4{GI D ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G\o *j | w=2*pi*n./T;
t3FfPV!P" g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
A>Oi9%OY: L=4; % length of evoluation to compare with S. Trillo's paper
oxg h;v* dz=L/M1; % space step, make sure nonlinear<0.05
CB%O8d # for m1 = 1:1:M1 % Start space evolution
/-&a]PJ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
^-pHhh|g u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
+ |d[q? ca1 = fftshift(fft(u1)); % Take Fourier transform
W{*w<a_ ` ca2 = fftshift(fft(u2));
`]l*H3+hg c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
g{$F;qbkO c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
Q.])En >i u2 = ifft(fftshift(c2)); % Return to physical space
s*.&DN u1 = ifft(fftshift(c1));
Qo \;) if rem(m1,J) == 0 % Save output every J steps.
d"hW45L U1 = [U1 u1]; % put solutions in U array
m}>#s3KPA U2=[U2 u2];
r4FGz!U MN1=[MN1 m1];
H+2m z1=dz*MN1'; % output location
58 .b@@T end
^# gR"\F`d end
*^ -~J/ hg=abs(U1').*abs(U1'); % for data write to excel
uf&Ke
k, ha=[z1 hg]; % for data write to excel
Z{J{6j t1=[0 t'];
uS,XQy2 hh=[t1' ha']; % for data write to excel file
0!!z'm3
%dlmwrite('aa',hh,'\t'); % save data in the excel format
)M(-EDL>Qk figure(1)
B&k"B?9mL waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
j @+QwZL| figure(2)
BD ( waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
C@Fk Y)]x1I 非线性超快脉冲耦合的数值方法的Matlab程序 ley : =( [qGj*`@C 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。
;wvhe;! 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
jV!9IK;HA. u!WjG@ 5 U{}A\q #:n:3]t % This Matlab script file solves the nonlinear Schrodinger equations
EvEI5/ z % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
wnoL<p % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&> &UqWL % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
c O[Hr .q^+llM C=1;
(lBwkQNQGd M1=120, % integer for amplitude
8LM 91 M3=5000; % integer for length of coupler
n d)bRB N = 512; % Number of Fourier modes (Time domain sampling points)
BYBf`F)4 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
:CJ]^ v T =40; % length of time:T*T0.
Y
&"rf
dt = T/N; % time step
_R ?:?{r, n = [-N/2:1:N/2-1]'; % Index
]NrA2i? t = n.*dt;
J$X{4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
`96PY !$u w=2*pi*n./T;
ggn:DE " g1=-i*ww./2;
bW9a_m yE g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
>
R5<D'cEN g3=-i*ww./2;
_: 0 P1=0;
`78:TU~5S P2=0;
#nOS7Q#uW P3=1;
R8U ?s/* P=0;
fxKhe[; for m1=1:M1
^YLk&A)X p=0.032*m1; %input amplitude
wZ_k ]{J s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
-U"h3Ye^ s1=s10;
zJ2dPp~u s20=0.*s10; %input in waveguide 2
Rt^~db s30=0.*s10; %input in waveguide 3
!C$bO hc s2=s20;
^t{2k[@ s3=s30;
]a}K% D)H p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
hkhk,bhI %energy in waveguide 1
2MapB* p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
`X06JTqf: %energy in waveguide 2
mrgieb% p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
1>BY:xZr %energy in waveguide 3
J XKqQxZ[X for m3 = 1:1:M3 % Start space evolution
(`
N@4w= s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
L 93&.d@m9 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
L&WhX3$u s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
XAb!hc
sca1 = fftshift(fft(s1)); % Take Fourier transform
g]hTz)8fF sca2 = fftshift(fft(s2));
'%2q'LqSA sca3 = fftshift(fft(s3));
tXgsWG?v[H sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
n7r )wy sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
FXi"o
$N sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
TC%ENxDR s3 = ifft(fftshift(sc3));
b;X|[tB s2 = ifft(fftshift(sc2)); % Return to physical space
\ LQ?s)~ s1 = ifft(fftshift(sc1));
#@#/ M) end
2!u4 nxZ. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<oc"!c;T p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
t%`GXJb p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
C{r Sq P1=[P1 p1/p10];
j6NK 7Li P2=[P2 p2/p10];
8 )W{&#C> P3=[P3 p3/p10];
SGuLL+|W#8 P=[P p*p];
Sas &P:# r end
f ;[\'_.* figure(1)
|@a.dgz, plot(P,P1, P,P2, P,P3);
EO<{Bj=2 9HjtWQn 转自：
http://blog.163.com/opto_wang/
