计算脉冲在非线性耦合器中演化的Matlab 程序 9-ozrw8t 79h~w{IT@ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
TLdlPBnr8 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
3"y 6|e/5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
bHwEd%f % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
i5 rkP`)j \/NF??k,jk %fid=fopen('e21.dat','w');
T D _@0Rd N = 128; % Number of Fourier modes (Time domain sampling points)
Q7s@,c !m_ M1 =3000; % Total number of space steps
js_`L#t J =100; % Steps between output of space
[oLV,O|s|j T =10; % length of time windows:T*T0
Gnkar[oa& T0=0.1; % input pulse width
WTvUz.Et MN1=0; % initial value for the space output location
5> x_G#W dt = T/N; % time step
k +-w% n = [-N/2:1:N/2-1]'; % Index
`geHSx_ t = n.*dt;
}E
'r?N u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
~G!JqdKJ0 u20=u10.*0.0; % input to waveguide 2
|YJ83nSO~ u1=u10; u2=u20;
I~GF%$-G U1 = u1;
ZwmucY%3 U2 = u2; % Compute initial condition; save it in U
<S@jf4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Wc3z7xK1@ w=2*pi*n./T;
;5S dx5`_ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
?{ir$M L=4; % length of evoluation to compare with S. Trillo's paper
(
ay AP dz=L/M1; % space step, make sure nonlinear<0.05
j J ,_-ui for m1 = 1:1:M1 % Start space evolution
f O*jCl u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
QZ a.c u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
'/W$9jm ca1 = fftshift(fft(u1)); % Take Fourier transform
PMzPj, ca2 = fftshift(fft(u2));
yayhL
DL c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
c 3vb~l) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
% MHb u2 = ifft(fftshift(c2)); % Return to physical space
-=ZL(r
1 u1 = ifft(fftshift(c1));
b 9.M'P\ if rem(m1,J) == 0 % Save output every J steps.
l:85 _E U1 = [U1 u1]; % put solutions in U array
F/>_PH57 U2=[U2 u2];
^J'_CA MN1=[MN1 m1];
)Z}AhX z1=dz*MN1'; % output location
,lyW'<~gA end
`9~
%6N?7# end
GtA`0B hg=abs(U1').*abs(U1'); % for data write to excel
U ZM #O ha=[z1 hg]; % for data write to excel
{0zn~+ t1=[0 t'];
4.RQ3SoDa hh=[t1' ha']; % for data write to excel file
f-b],YE %dlmwrite('aa',hh,'\t'); % save data in the excel format
!g svF\XDM figure(1)
&.?XntI9O waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
y>^a~}Zq figure(2)
V> Wk\'h waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
{MUB4-@?F$ T{YZ`[ 非线性超快脉冲耦合的数值方法的Matlab程序 * QgKo$IF Uzu6>yT 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。
<wH+\ 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
%`Re {%1; {28| LwmL 4= zs& z kQ[< % This Matlab script file solves the nonlinear Schrodinger equations
_VtQMg|u % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
.HqFdsm % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
"}4%v Zz % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:=*de Z< kB\{ 1; C=1;
&p0e)o~Ux M1=120, % integer for amplitude
UO/sv2CN M3=5000; % integer for length of coupler
VtreOJ+ N = 512; % Number of Fourier modes (Time domain sampling points)
je4l 3Hl dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.g*j]!_] T =40; % length of time:T*T0.
PnlI {d dt = T/N; % time step
Gr"CHz/ n = [-N/2:1:N/2-1]'; % Index
D #ddx t = n.*dt;
\ mqx ' ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
.n-#A w=2*pi*n./T;
$vO&C6m$ g1=-i*ww./2;
x0*{oP g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
QrZ#<{,J5 g3=-i*ww./2;
C0rf P1=0;
ny={OhP- P2=0;
~Bd=]a$mj P3=1;
39 pG-otJ P=0;
*{o7G a for m1=1:M1
SC{m@ p=0.032*m1; %input amplitude
hlTbCl s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
6_LeP9s ) s1=s10;
H=t"qEp s20=0.*s10; %input in waveguide 2
Ucj ?$= s30=0.*s10; %input in waveguide 3
d_RgKdR )k s2=s20;
5of3 & s3=s30;
"
\$^j#o p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
>ZA= 9v %energy in waveguide 1
sE1cvAw9l p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
8a)AuAi?! %energy in waveguide 2
enoj4g7em^ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
7ubz7* %energy in waveguide 3
YF KE>+ for m3 = 1:1:M3 % Start space evolution
Fe+
@; s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
'j1e(wq s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
hy;VvAH 5 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ao(T81 sca1 = fftshift(fft(s1)); % Take Fourier transform
_GOSqu!3Y sca2 = fftshift(fft(s2));
dWqn7+: sca3 = fftshift(fft(s3));
|s| }u`(@9 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
X1 L@
G sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
~z,o):q1 } sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
8H F^^Cva s3 = ifft(fftshift(sc3));
_n&Nw7d2
M s2 = ifft(fftshift(sc2)); % Return to physical space
3} A$+PX s1 = ifft(fftshift(sc1));
U=>S|>daR end
? R RO p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
:P ud% }' p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
n ]ikc| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
V"FQVtTx7 P1=[P1 p1/p10];
V+d_1]
l P2=[P2 p2/p10];
xO$P
C, P3=[P3 p3/p10];
>r.]a ` P=[P p*p];
0.aXg " end
'CLZ7 pV figure(1)
L`NIYH<^ plot(P,P1, P,P2, P,P3);
9 9m2aT() <@<rU:o=V 转自：
http://blog.163.com/opto_wang/
