计算脉冲在非线性耦合器中演化的Matlab 程序 &jP1Q3 Xqf,_I =V % This Matlab script file solves the coupled nonlinear Schrodinger equations of
.e~"+Pe6b % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
L'= \ |r % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4Z)s8sD KW % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
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/C7 QKG3>lU %fid=fopen('e21.dat','w');
;g|Vt}a&4 N = 128; % Number of Fourier modes (Time domain sampling points)
hYW9a`Ht/ M1 =3000; % Total number of space steps
3 z8i0 J =100; % Steps between output of space
'C[tPP T =10; % length of time windows:T*T0
|bY@HpMp T0=0.1; % input pulse width
oW3"J6,S MN1=0; % initial value for the space output location
w'
7sh5 dt = T/N; % time step
|b n = [-N/2:1:N/2-1]'; % Index
Px lc RF t = n.*dt;
9bM\ (s/
u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
VXeO }>2S u20=u10.*0.0; % input to waveguide 2
M-o'` e' u1=u10; u2=u20;
&`r/+B_W U1 = u1;
_'=,c" U2 = u2; % Compute initial condition; save it in U
FZHA19Kb ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
JVc{vSa!rm w=2*pi*n./T;
#EPC]jFk g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
zPby+BP L=4; % length of evoluation to compare with S. Trillo's paper
6mM9p)"$ dz=L/M1; % space step, make sure nonlinear<0.05
R f:.'/<^ for m1 = 1:1:M1 % Start space evolution
aFnel8 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
t3;Zx+Br u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
I 1Q!3P ca1 = fftshift(fft(u1)); % Take Fourier transform
]\(8d[ 4 ca2 = fftshift(fft(u2));
KdVKvs[ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~YYnn7) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
GJ ^c ^` u2 = ifft(fftshift(c2)); % Return to physical space
PYkhY;* u1 = ifft(fftshift(c1));
Tq1\ if rem(m1,J) == 0 % Save output every J steps.
EeuYR yK U1 = [U1 u1]; % put solutions in U array
H"A%mrb U2=[U2 u2];
y9:4n1fg MN1=[MN1 m1];
s)^/3 a z1=dz*MN1'; % output location
XqTguO' end
$Z]&3VxxY end
8 x{Owj:Q hg=abs(U1').*abs(U1'); % for data write to excel
IG^@ VQ% ha=[z1 hg]; % for data write to excel
P?0X az t1=[0 t'];
]E`<8hRB hh=[t1' ha']; % for data write to excel file
qN!oN* %dlmwrite('aa',hh,'\t'); % save data in the excel format
a|ufm^ F figure(1)
zx.qN waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
B8@mL-Z-; figure(2)
&LLU@ | waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
uFkl^2 + :MSY p 非线性超快脉冲耦合的数值方法的Matlab程序 ":!$Jnj , R Za/la* 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。
1Viz`y)^ 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
yM_/_V|G ,B <\ a f{sT*_at 3c<aI =$^ % This Matlab script file solves the nonlinear Schrodinger equations
E>~R P^?Uz % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
) c@gRb~ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
hkMeUxS % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
c./\sN @ 6h:QSVfx C=1;
eM7@!CdA9q M1=120, % integer for amplitude
r.C6`
a M3=5000; % integer for length of coupler
\6b~$\~B N = 512; % Number of Fourier modes (Time domain sampling points)
k&Pt\- 9on dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
1/DtF T =40; % length of time:T*T0.
'.A!IGsj dt = T/N; % time step
{U5sRM|I n = [-N/2:1:N/2-1]'; % Index
(v]%kXy/G t = n.*dt;
y{<e4{
! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
o E+'@ w=2*pi*n./T;
G%W9?4 _K g1=-i*ww./2;
A7p4M?09 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
N`8K1{>BH g3=-i*ww./2;
iq&3S 0 P1=0;
i<QDV
W9 P2=0;
s QDgNJbU P3=1;
2#wnJdr6E P=0;
)2f#@0SVL for m1=1:M1
}Fe~XO` p=0.032*m1; %input amplitude
wh:;G`6S s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
i VSNa ra s1=s10;
{R1]tGOf s20=0.*s10; %input in waveguide 2
yV^Yp= f_ s30=0.*s10; %input in waveguide 3
-^p{J
TB+ s2=s20;
(:o F\ s3=s30;
j7I=2xnTWu p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
@6
he!wW %energy in waveguide 1
V?mP7 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
v? 8WQNy %energy in waveguide 2
=EJ&=t p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
w-|Rb~XT
h %energy in waveguide 3
v\x l?F for m3 = 1:1:M3 % Start space evolution
l}nV WuD s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
)nN!% |J s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Jqoo&T") s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
.$U,bE sca1 = fftshift(fft(s1)); % Take Fourier transform
G e k?+|m sca2 = fftshift(fft(s2));
%YG?7PBB sca3 = fftshift(fft(s3));
&PMQ ]B sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
k+QGvgP[4@ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
SmXoNiM"y sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Y\
[|k-6
s3 = ifft(fftshift(sc3));
~&?([}A s2 = ifft(fftshift(sc2)); % Return to physical space
_){ |/Zd s1 = ifft(fftshift(sc1));
z "@^'{.l end
WjV Bz p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
Qz(D1>5I? p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
$QJ3~mG2 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
@-@Coy 4Tt P1=[P1 p1/p10];
z{XB_j6\= P2=[P2 p2/p10];
Mc,79Ix" P3=[P3 p3/p10];
?9 huuJ s7 P=[P p*p];
Ww<Y]H$xZ< end
;*%rFt9FK figure(1)
[S6u:;7 plot(P,P1, P,P2, P,P3);
{gD ED M9"Bx/ 转自：
http://blog.163.com/opto_wang/
