计算脉冲在非线性耦合器中演化的Matlab 程序 .jj$ Kh q] 3;a<_cE*@ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
u?9" jX % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
6C-z=s)P& % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/c,(8{(O % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
\|K;-pL !H ~<
%fid=fopen('e21.dat','w');
|m2X+s9 N = 128; % Number of Fourier modes (Time domain sampling points)
;$z$@@WC M1 =3000; % Total number of space steps
/ 4lvP J =100; % Steps between output of space
s&NX@ T =10; % length of time windows:T*T0
9 -rNw?7 T0=0.1; % input pulse width
435;Vns\n MN1=0; % initial value for the space output location
&9Xhl'' dt = T/N; % time step
0@EwM n = [-N/2:1:N/2-1]'; % Index
Z.M ,NR t = n.*dt;
c_V;DcZ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
N2w"R{) j\ u20=u10.*0.0; % input to waveguide 2
(7 r<'' u1=u10; u2=u20;
`(3 /$% U1 = u1;
. Z%{'CC U2 = u2; % Compute initial condition; save it in U
"U\4:k`: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
TY Qwy* w=2*pi*n./T;
1Uqu> ' g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
t
89!Ihk L=4; % length of evoluation to compare with S. Trillo's paper
q=#}
yEG dz=L/M1; % space step, make sure nonlinear<0.05
G8;w{-{m for m1 = 1:1:M1 % Start space evolution
bP^Je&nS* u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
0)m(;> '70 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
K#U<ib-v ca1 = fftshift(fft(u1)); % Take Fourier transform
PP!SK2u "L ca2 = fftshift(fft(u2));
a AB`G3 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
yUp,NfS]o c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
' Tc]KXD6 u2 = ifft(fftshift(c2)); % Return to physical space
zF`c8Tsx]) u1 = ifft(fftshift(c1));
?| 39u{ if rem(m1,J) == 0 % Save output every J steps.
Y_QH&GZ U1 = [U1 u1]; % put solutions in U array
? 8LX P U2=[U2 u2];
ma((2My'H MN1=[MN1 m1];
tuhA
9}E z1=dz*MN1'; % output location
[AW"
D3 end
FD8 N"p end
-k"^o!p hg=abs(U1').*abs(U1'); % for data write to excel
I hA* " ha=[z1 hg]; % for data write to excel
vo# UtN:q t1=[0 t'];
V?=8".GiX hh=[t1' ha']; % for data write to excel file
DuOG { %dlmwrite('aa',hh,'\t'); % save data in the excel format
%b"\bH H figure(1)
@0SC"CqM waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
TqddOp figure(2)
19j+ lCSvH waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
1Y]TA3: G rk@dZI 非线性超快脉冲耦合的数值方法的Matlab程序 kJ Mf -]t,E,(! 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
qIAoA . Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.;*s`t {1b Zg pb=c B Z$ ,Y>Bex_v % This Matlab script file solves the nonlinear Schrodinger equations
U~ck!\0&T % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Gqy,u3lE % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
f?'JAC* % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
fOMvj%T@2 ;asP4R= C=1;
uI DuGrt M1=120, % integer for amplitude
KFFSv{m[ M3=5000; % integer for length of coupler
kVy\b E0o N = 512; % Number of Fourier modes (Time domain sampling points)
57g</ p dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
cJL'$`gWf T =40; % length of time:T*T0.
:bC40@ dt = T/N; % time step
[ U w i n = [-N/2:1:N/2-1]'; % Index
DmOyBtj t = n.*dt;
Y>&Ew*Y ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
m:/ wG&
! w=2*pi*n./T;
,Uy|5zv g1=-i*ww./2;
2[ r^M'J g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
jWY V#ifs2 g3=-i*ww./2;
Z%x\~ ) ~ P1=0;
E_bO9nRHV P2=0;
}ga@ />Sl& P3=1;
QQV~?iW{~ P=0;
{4-[r#R<M for m1=1:M1
b@2J]Ay E* p=0.032*m1; %input amplitude
A4]s~Ur s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
e@ \p0( s1=s10;
d S5a
s20=0.*s10; %input in waveguide 2
[ V)
L s30=0.*s10; %input in waveguide 3
~O1&@xX s2=s20;
aN ,M64F s3=s30;
m,t|IgDh p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
h)Ff2tX %energy in waveguide 1
NmSo4Dg`U p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
+
Q6l*:<|c %energy in waveguide 2
^'ryNa;" p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
w$u3W*EoU^ %energy in waveguide 3
Q
pmsOp| for m3 = 1:1:M3 % Start space evolution
e A}%C.ZR s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
<$h u s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
g=e71DXG2 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
zH*KYB sca1 = fftshift(fft(s1)); % Take Fourier transform
d%0~c'D8a sca2 = fftshift(fft(s2));
nQ/E5y
sca3 = fftshift(fft(s3));
shM SN]S_x sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
!Lh^oPT"I sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
SC-
$B sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
eBJUv]o % s3 = ifft(fftshift(sc3));
8zBWIi s2 = ifft(fftshift(sc2)); % Return to physical space
wG ZR31 s1 = ifft(fftshift(sc1));
"$}vP<SM end
_ Dwqy( p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
@GvztVYo p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
>X51$ wBL p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
ZZyDG9a>7 P1=[P1 p1/p10];
Vy|6E#U P2=[P2 p2/p10];
OGY"<YH6 P3=[P3 p3/p10];
U5 r7j P=[P p*p];
o^V(U~m] end
kVD(Q ~< figure(1)
)<xypDQ plot(P,P1, P,P2, P,P3);
f
+hjC T_lsGu/ 转自：
http://blog.163.com/opto_wang/
