计算脉冲在非线性耦合器中演化的Matlab 程序 d#ld*\| X?>S24I"9 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
#A:I|Q 1$g % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
jJ55Az?t: % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
xg'0YZ\t % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
JB+pd_>5 Nj#!L~^h, %fid=fopen('e21.dat','w');
Zs+6Zd4f N = 128; % Number of Fourier modes (Time domain sampling points)
^Xa-)Pu M1 =3000; % Total number of space steps
hH"3 Y}U@ J =100; % Steps between output of space
w$Dp m.0( T =10; % length of time windows:T*T0
%=#&\ldPS T0=0.1; % input pulse width
*>_:E6) MN1=0; % initial value for the space output location
Ba`]Sm= dt = T/N; % time step
G9E?
n = [-N/2:1:N/2-1]'; % Index
Q=e?G300#L t = n.*dt;
WpTC,~- u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
p@cPm8L3 u20=u10.*0.0; % input to waveguide 2
@|-ydm0 u1=u10; u2=u20;
M?}2 U1 = u1;
sB7DF<91 U2 = u2; % Compute initial condition; save it in U
R0. `2= ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
kdxs {b"t w=2*pi*n./T;
jy&p_v1 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
qmxkmO+Qur L=4; % length of evoluation to compare with S. Trillo's paper
50_%Tl[ dz=L/M1; % space step, make sure nonlinear<0.05
vf5[x!4 for m1 = 1:1:M1 % Start space evolution
NKGo E/ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
&]#D`u u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
mT!~;] RrF ca1 = fftshift(fft(u1)); % Take Fourier transform
w?Q@"^IL ca2 = fftshift(fft(u2));
S vI c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
^gb2=gWZ< c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
;y H A.} u2 = ifft(fftshift(c2)); % Return to physical space
WqYl=%x"{V u1 = ifft(fftshift(c1));
2a?
d:21 B if rem(m1,J) == 0 % Save output every J steps.
"G`)x+<~Z8 U1 = [U1 u1]; % put solutions in U array
nHZ 4):` U2=[U2 u2];
F+hsIsQ MN1=[MN1 m1];
6 _7 3 z1=dz*MN1'; % output location
E(u[? end
l8^^ O end
YjHGdacs hg=abs(U1').*abs(U1'); % for data write to excel
.Ta$@sP h} ha=[z1 hg]; % for data write to excel
zlSwKd ( t1=[0 t'];
]&}?J:+?0E hh=[t1' ha']; % for data write to excel file
,
/ 4}CM %dlmwrite('aa',hh,'\t'); % save data in the excel format
'BUdySng figure(1)
J3q}DDnEo waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
tM@TT@.t~ figure(2)
oO= 6Kd+T waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
2H]&3kM3X Zqx5I~ 非线性超快脉冲耦合的数值方法的Matlab程序 j4 G, Z4 >aa-ix
& 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
ky!'.3yoI Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[dt1%DD`M /]+t$K\cBq hP 9+|am% :+[q ` % This Matlab script file solves the nonlinear Schrodinger equations
\f % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
{ 0Leua % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
g VZ~OcB!W % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
)0UQy#r $9hOWti C=1;
Cu/w><h) M1=120, % integer for amplitude
Rl 6E M3=5000; % integer for length of coupler
Gc
SX5c N = 512; % Number of Fourier modes (Time domain sampling points)
rJ<v1Yb dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
<Pf W T =40; % length of time:T*T0.
:L\@+}{( c dt = T/N; % time step
e%UFY-2 n = [-N/2:1:N/2-1]'; % Index
{},G xrQm t = n.*dt;
! JrV h$K ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
2abWIw4 w=2*pi*n./T;
y;Dw%m g1=-i*ww./2;
>TtkG|/U-T g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
#kV= ;(lq g3=-i*ww./2;
jUjQ{eT P1=0;
K3\U'bRO P2=0;
ii~~xt1 P3=1;
r! #a. P=0;
d3Y#_! ) for m1=1:M1
m3,]j\ p=0.032*m1; %input amplitude
Kb4u)~S: s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
&LYU#$sj s1=s10;
Iy`Zh@"~ s20=0.*s10; %input in waveguide 2
rGq~e|.O3 s30=0.*s10; %input in waveguide 3
=\_MJ? A$ s2=s20;
8 Z#)Xb4 s3=s30;
Vl'|l)b4W p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
30F&FT W %energy in waveguide 1
e
`_ [+y p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
^#"!uCq]gM %energy in waveguide 2
~W`upx) j p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
9~u1fk { %energy in waveguide 3
x ~Pv for m3 = 1:1:M3 % Start space evolution
9~>;sjJk s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
6' ?Y ]K s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
BIX%Bu0'f s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
KZ<zsHX8H sca1 = fftshift(fft(s1)); % Take Fourier transform
ZEHz/Y% sca2 = fftshift(fft(s2));
H\)on" sca3 = fftshift(fft(s3));
X"' }1o sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
9Y*6AaKE6 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
tQUp1i{j\ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
w{Dk,9 >w) s3 = ifft(fftshift(sc3));
Z mYp!B_~ s2 = ifft(fftshift(sc2)); % Return to physical space
>mh:OJH45 s1 = ifft(fftshift(sc1));
:IS]|3wD end
VN;Sz,1Z p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
.cle^P p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
#9p{Y}2# p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
w,JB`jS)/ P1=[P1 p1/p10];
Ok
O;V6` P2=[P2 p2/p10];
Ks!.$y:x P3=[P3 p3/p10];
qb
"H&)aHw P=[P p*p];
0y|}}92: end
l<^#@S H figure(1)
f'R^MX2 plot(P,P1, P,P2, P,P3);
}U+gJkY2 GD.mB[f* 转自：
http://blog.163.com/opto_wang/
