计算脉冲在非线性耦合器中演化的Matlab 程序 g3"`b)M 4xg%OH % This Matlab script file solves the coupled nonlinear Schrodinger equations of
M|76,2u % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
G?YKm1:w % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
UJlK w `4 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<!4'?K -N 3<?(1kSo>> %fid=fopen('e21.dat','w');
.!=2#< N = 128; % Number of Fourier modes (Time domain sampling points)
N<O^%!bu R M1 =3000; % Total number of space steps
@YV-8;hO J =100; % Steps between output of space
o- GHAQ T =10; % length of time windows:T*T0
N "FQMxqm T0=0.1; % input pulse width
=[vT=sHz7 MN1=0; % initial value for the space output location
$FCLo8/= dt = T/N; % time step
kjjO<x?&* n = [-N/2:1:N/2-1]'; % Index
+Fy G{1?< t = n.*dt;
P m
V:J9 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
z q(AN< u20=u10.*0.0; % input to waveguide 2
* 496"kU u1=u10; u2=u20;
_[IN9ZC 2G U1 = u1;
9G 9!=J U2 = u2; % Compute initial condition; save it in U
aq[kKS` ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
}6ec2I%`o w=2*pi*n./T;
m< TKy_C` g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
42X[Huy] L=4; % length of evoluation to compare with S. Trillo's paper
vvdC.4O dz=L/M1; % space step, make sure nonlinear<0.05
:Q!U;33aG for m1 = 1:1:M1 % Start space evolution
\% rX~UhZ= u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
z l@
<X0q u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
B!rY \ ?W ca1 = fftshift(fft(u1)); % Take Fourier transform
zjB8~ku# ca2 = fftshift(fft(u2));
>`\~=ivrD c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
;h3c+7u1 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
>*k3D& u2 = ifft(fftshift(c2)); % Return to physical space
2 ;U(r: ] u1 = ifft(fftshift(c1));
_ jF,
k>F if rem(m1,J) == 0 % Save output every J steps.
EXoT$Wt{$ U1 = [U1 u1]; % put solutions in U array
2Vt iL^;5 U2=[U2 u2];
n: Ka@ MN1=[MN1 m1];
Ws.F=kS>h z1=dz*MN1'; % output location
+-K-CXt end
lc#su$xR> end
M)(
5S1ndq hg=abs(U1').*abs(U1'); % for data write to excel
x4R[Q&:M ha=[z1 hg]; % for data write to excel
jQ(qaX&
t1=[0 t'];
qeHb0G hh=[t1' ha']; % for data write to excel file
3zv_q&+8b %dlmwrite('aa',hh,'\t'); % save data in the excel format
*)H?d figure(1)
k G4v> waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
*8t_$<'dQ figure(2)
9;sebqC? waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
7;0^r#:87# ~Wf&$p<| 非线性超快脉冲耦合的数值方法的Matlab程序 j^m AJ5 FE" ksi 9 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。
$5s?m\!jZz 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
9<G -uF <jY" +@rF ,*wa #[ [N'YFb3"O % This Matlab script file solves the nonlinear Schrodinger equations
m ['UV 2 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
'%l<33* % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Y Dq5%N` % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$0+AR) (O"Wa C=1;
/*B-y$WQk M1=120, % integer for amplitude
-5\hZ!!J2 M3=5000; % integer for length of coupler
bb}|"m . N = 512; % Number of Fourier modes (Time domain sampling points)
1#gveHm]-G dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
2dFC{US' T =40; % length of time:T*T0.
N/4` afiV. dt = T/N; % time step
S[n ;u-U n = [-N/2:1:N/2-1]'; % Index
~jQ|X?tR t = n.*dt;
XcAx@CY9c ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
#kR 8v[Z w=2*pi*n./T;
0 P3^# j g1=-i*ww./2;
JS1$l+1 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
a;r,*z Z=" g3=-i*ww./2;
@6~r7/WD P1=0;
&$:1rA _v P2=0;
xRuAt/aC P3=1;
{ r y v7G P=0;
>;-. rJFr for m1=1:M1
ifHQ2Ug 9 p=0.032*m1; %input amplitude
?>92OuG%W? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
5
<X.1 T1 s1=s10;
*I : ^g s20=0.*s10; %input in waveguide 2
] DHB'NOh, s30=0.*s10; %input in waveguide 3
,9SBGxK5` s2=s20;
=aX ;- s3=s30;
k?zw4S p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
(&H-v'a}3 %energy in waveguide 1
[K1RP. p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
wJ,l"bnq %energy in waveguide 2
Q`j!$r p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
x|g>Zd/n %energy in waveguide 3
j *B ,b4 for m3 = 1:1:M3 % Start space evolution
C @3a/<6m s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
HRS^91aK s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
/@h)IuW s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ve|ig]$5g< sca1 = fftshift(fft(s1)); % Take Fourier transform
plcz m 2 sca2 = fftshift(fft(s2));
K x==vq%39 sca3 = fftshift(fft(s3));
lgWEB3f
. sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
%#kml{I sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
xn|M]E1) sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
lR3 `4bHA s3 = ifft(fftshift(sc3));
G0 * >S`:4 s2 = ifft(fftshift(sc2)); % Return to physical space
`=TV4h4 s1 = ifft(fftshift(sc1));
YGFE(t;lPU end
% xv } p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Q "r QVO p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
j ]Y`L?!Q p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
~U"puEftbs P1=[P1 p1/p10];
;7=pNK P2=[P2 p2/p10];
c~ x P3=[P3 p3/p10];
mu`:@7+Yp P=[P p*p];
}^3CG9% end
Y=0D[o8 figure(1)
[[
{L# plot(P,P1, P,P2, P,P3);
OynQlQD/Eu %QYW0l E 转自：
http://blog.163.com/opto_wang/
