计算脉冲在非线性耦合器中演化的Matlab 程序 ]6j{@z?{ "#g}ve, % This Matlab script file solves the coupled nonlinear Schrodinger equations of
wC'Szni % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
J<lW<:!3] % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Kc\fu3Q
% pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
R xQ * xoME9u0x4 %fid=fopen('e21.dat','w');
n+R7D.<q!! N = 128; % Number of Fourier modes (Time domain sampling points)
nO-#Q=H, M1 =3000; % Total number of space steps
1xvu<|F J =100; % Steps between output of space
eyxW 0}[ T =10; % length of time windows:T*T0
x4O~q0>:Le T0=0.1; % input pulse width
gRzxLf`K MN1=0; % initial value for the space output location
! 8 b ^, dt = T/N; % time step
DHRlWQox n = [-N/2:1:N/2-1]'; % Index
&7s.` t = n.*dt;
l U] nd[x u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
m4Zk\,1m.| u20=u10.*0.0; % input to waveguide 2
x?<FJ"8"k u1=u10; u2=u20;
Vjp y~iP4B U1 = u1;
%z$#6?OK^ U2 = u2; % Compute initial condition; save it in U
~V6D < ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
"J1
4C9u
w=2*pi*n./T;
1\.pMHv/ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
w32y3~ L=4; % length of evoluation to compare with S. Trillo's paper
~VB1OLgv#. dz=L/M1; % space step, make sure nonlinear<0.05
0*v2y*2V for m1 = 1:1:M1 % Start space evolution
-:rUw$3J u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
T
u'{&
u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
2Khv>#l
ca1 = fftshift(fft(u1)); % Take Fourier transform
W@esITr ca2 = fftshift(fft(u2));
|':{lH6+1 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
_ e2=ado c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d_P` qA u2 = ifft(fftshift(c2)); % Return to physical space
(h
`V+ u1 = ifft(fftshift(c1));
z(~_AN M4, if rem(m1,J) == 0 % Save output every J steps.
$pz/?>! U1 = [U1 u1]; % put solutions in U array
1.>m@Slr> U2=[U2 u2];
ji= "D YtL MN1=[MN1 m1];
3(UVg! t z1=dz*MN1'; % output location
1
TXioDs=_ end
X wtqi@zlE end
2A!FDr~cdT hg=abs(U1').*abs(U1'); % for data write to excel
8?C5L8) ha=[z1 hg]; % for data write to excel
FGkVqZ Y2? t1=[0 t'];
4&iCht
= hh=[t1' ha']; % for data write to excel file
"gwSJ~:ds %dlmwrite('aa',hh,'\t'); % save data in the excel format
D/' dTrR figure(1)
IVmo5,&5( waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
d"Y{UE figure(2)
2t,zLwBdnJ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
"Rl}VeDY i@'dH3-kO
非线性超快脉冲耦合的数值方法的Matlab程序 W_ ZJ0GuE( F:ELPs4" 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
FiU#T.`9' Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Ir]\| t :gC#hmm^ :v 4]D4\o j+Y JbL v % This Matlab script file solves the nonlinear Schrodinger equations
WEpoBP
CL % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
?X;RLpEc|A % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
B/C,.?Or % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
R} e cc : @&/kyGH C=1;
DTs;{c M1=120, % integer for amplitude
']oQ]Yx0 M3=5000; % integer for length of coupler
{>;R?TG]$ N = 512; % Number of Fourier modes (Time domain sampling points)
&.ACd+Cd dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
azU"G(6y?+ T =40; % length of time:T*T0.
F1hHe< ) dt = T/N; % time step
PaN"sf n = [-N/2:1:N/2-1]'; % Index
S[QrS 7 t = n.*dt;
jFb?b6 b ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
DL.!G w=2*pi*n./T;
~{gqsuCCL g1=-i*ww./2;
L=h'Qgk% g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ET >](l9 g3=-i*ww./2;
BORA(, P1=0;
r_.S>] P2=0;
^}C \zW P3=1;
eiOW#_"\ P=0;
@|)Z "m7 for m1=1:M1
^W@5TkkBQq p=0.032*m1; %input amplitude
P>6{&( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
D#z :()VT( s1=s10;
F<w/PMb s20=0.*s10; %input in waveguide 2
'W#D(l9nI s30=0.*s10; %input in waveguide 3
?hM64jI| s2=s20;
>i
O!*&Y> s3=s30;
O1kl70,`R p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
\di = %energy in waveguide 1
)_NO4`ejs/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
DeYV $W
B %energy in waveguide 2
,=N.FS p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
rN{ c7/| %energy in waveguide 3
kNL\m[W8$ for m3 = 1:1:M3 % Start space evolution
WN<zkM~3 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Xry4 7a
) s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
3BLq CZ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
*9i{,I@ sca1 = fftshift(fft(s1)); % Take Fourier transform
.{ KVMc sca2 = fftshift(fft(s2));
lHIM}~#;nd sca3 = fftshift(fft(s3));
KY N0 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
yOKI*.} sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
&VcV$8k sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
o` RKXfCq s3 = ifft(fftshift(sc3));
Y4( s2 = ifft(fftshift(sc2)); % Return to physical space
;UP $yM; s1 = ifft(fftshift(sc1));
snikn& end
Ic4H# w p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
>"<Wjr8W!$ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
4Z,!zFS$` p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
]0\MmAJRn P1=[P1 p1/p10];
s|ITsz0,td P2=[P2 p2/p10];
cs'{5!i] P3=[P3 p3/p10];
2Wb]4- P=[P p*p];
F sryEHz end
Xs ?o{]Fe figure(1)
)F2OT<]m, plot(P,P1, P,P2, P,P3);
:a)u&g @G I!?}jo3 转自：
http://blog.163.com/opto_wang/
