计算脉冲在非线性耦合器中演化的Matlab 程序 g ) 5mr:\ 9 QaE)wt % This Matlab script file solves the coupled nonlinear Schrodinger equations of
O%3Hp.|! % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
|r*)U( c` % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
"M, 1ElQ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
D#AqZS> B S=0DQ19 %fid=fopen('e21.dat','w');
N+ak{3 N = 128; % Number of Fourier modes (Time domain sampling points)
W#%s0EN<_ M1 =3000; % Total number of space steps
(6.u NLr J =100; % Steps between output of space
lXg5UrW T =10; % length of time windows:T*T0
TF%Xb>jy[ T0=0.1; % input pulse width
LFI#wGhXVk MN1=0; % initial value for the space output location
*f3 S tX dt = T/N; % time step
.L+XV y n = [-N/2:1:N/2-1]'; % Index
8L, =E ap t = n.*dt;
+SR{ FF u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
oNtoqYwH u20=u10.*0.0; % input to waveguide 2
hJ$9Hb u1=u10; u2=u20;
n m<?oI*\ U1 = u1;
gfs ;?vP U2 = u2; % Compute initial condition; save it in U
Z,/K$;YWo ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
~ney~Pz_ w=2*pi*n./T;
d\ 8v
VZ
g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
&iInru3 L=4; % length of evoluation to compare with S. Trillo's paper
#R{>@]x` dz=L/M1; % space step, make sure nonlinear<0.05
59O-"Sc[ for m1 = 1:1:M1 % Start space evolution
puJB&u"4L u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Z;%uDlcXI u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
?+))J~@t ca1 = fftshift(fft(u1)); % Take Fourier transform
%rMCiz ca2 = fftshift(fft(u2));
JwB'B c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
bx(@ fl:m c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
b?l>vUgAg u2 = ifft(fftshift(c2)); % Return to physical space
z 7ik/> d? u1 = ifft(fftshift(c1));
{$,\Qg if rem(m1,J) == 0 % Save output every J steps.
t& xoi7!$ U1 = [U1 u1]; % put solutions in U array
ejlns
~ U2=[U2 u2];
rNR7}o~ qo MN1=[MN1 m1];
d ?8OY z1=dz*MN1'; % output location
9H/>M4R T end
|ZL?P qki end
~x^y5[5{ hg=abs(U1').*abs(U1'); % for data write to excel
{_Wrs.a' 8 ha=[z1 hg]; % for data write to excel
0k5 -S~_\ t1=[0 t'];
_"ciHYHBQ hh=[t1' ha']; % for data write to excel file
R kE)2q[5 %dlmwrite('aa',hh,'\t'); % save data in the excel format
!1G
KpL figure(1)
uYMn VE" waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
V9,<> figure(2)
4LKpEl.= waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
u<Kowt<ci Tb$))O} 非线性超快脉冲耦合的数值方法的Matlab程序 hO ]F\0 + tL$,]I$1+ 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。
I&{T 4.B:U 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
==OU d6e} ^Hv&{r77
E.h UDh \%?j % This Matlab script file solves the nonlinear Schrodinger equations
`Pvi+:6\Y % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
&KjMw :l % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
-K 'UXoU1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%dzt'uz [UA*We 1 C=1;
*S ag M1=120, % integer for amplitude
cu N9R G M3=5000; % integer for length of coupler
C < c6Ub N = 512; % Number of Fourier modes (Time domain sampling points)
hOwb
dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Hz.i $ L0} T =40; % length of time:T*T0.
[kg?q5F) dt = T/N; % time step
v>]g="5}8 n = [-N/2:1:N/2-1]'; % Index
?4bYb]8Z t = n.*dt;
k ( :Bl ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
cXPpxRXBD w=2*pi*n./T;
dd g1=-i*ww./2;
iT}>a30]B g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
a9-Mc5^'n g3=-i*ww./2;
@3.Z>KONx P1=0;
% J M$] P2=0;
Voo'ZeZa P3=1;
Y~vk>ZC P=0;
I=kqkuW for m1=1:M1
Kk8wlC p=0.032*m1; %input amplitude
k24I1DlR8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
!T,<p
s1=s10;
,^([aK s20=0.*s10; %input in waveguide 2
UjI./"]O s30=0.*s10; %input in waveguide 3
h9QM
nH' s2=s20;
f)*?Ji|5F s3=s30;
(%X *b.n= p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
!-lI<$S: %energy in waveguide 1
I {89chi p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
p TCD1) %energy in waveguide 2
juR>4SH p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
6TW< ,SM %energy in waveguide 3
y||
n9 for m3 = 1:1:M3 % Start space evolution
d_25]B( s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
v 6
U !(x s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Gd
4S7J E s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
cg8/v:B sca1 = fftshift(fft(s1)); % Take Fourier transform
$mPR)T sca2 = fftshift(fft(s2));
GrLxERf sca3 = fftshift(fft(s3));
jlBsm'M<m sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
@@D/&}#F sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
E{T3X wg sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
zIF1A*UH s3 = ifft(fftshift(sc3));
Xex7Lr & s2 = ifft(fftshift(sc2)); % Return to physical space
!0l|[c4 e> s1 = ifft(fftshift(sc1));
16 AlmegDk end
+S~ u ,= p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
<.ZIhDiE l p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
SD^::bH p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
k9
r49lb P1=[P1 p1/p10];
>V^8<^?G P2=[P2 p2/p10];
q] ="ek&_ P3=[P3 p3/p10];
E <yQB39 P=[P p*p];
a?y ucA end
w~+*Vd~U figure(1)
5$U 49j plot(P,P1, P,P2, P,P3);
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1|p\rHGd 转自：
http://blog.163.com/opto_wang/
