计算脉冲在非线性耦合器中演化的Matlab 程序 M !6Fnj PzP NvV/o % This Matlab script file solves the coupled nonlinear Schrodinger equations of
%<kfW&_>w % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Kyh6QA^ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
w9Yx 2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.
Z&5TK4I QjLU@?& %fid=fopen('e21.dat','w');
IGTO|sT" N = 128; % Number of Fourier modes (Time domain sampling points)
1t e^dh:Vp M1 =3000; % Total number of space steps
JM ;bNW8 J =100; % Steps between output of space
!IOmJpl ' T =10; % length of time windows:T*T0
}#1. $a T0=0.1; % input pulse width
wwl,F=| Y MN1=0; % initial value for the space output location
)FwOg;=3M" dt = T/N; % time step
ftY&Q#[ n = [-N/2:1:N/2-1]'; % Index
D:9^^uVp t = n.*dt;
4&NB xe u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
a >fA-@ u20=u10.*0.0; % input to waveguide 2
KJFQ)#SW! u1=u10; u2=u20;
gp9O%g3' U1 = u1;
MNs <yQ9I' U2 = u2; % Compute initial condition; save it in U
| Kd6.Mx ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
@zS/J,:v} w=2*pi*n./T;
G 5qsnTxUJ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
'\{ OQ H L=4; % length of evoluation to compare with S. Trillo's paper
Sp[9vlo8 dz=L/M1; % space step, make sure nonlinear<0.05
N,w6 for m1 = 1:1:M1 % Start space evolution
Fe[6Y<x+: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
rX$-K\4W u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
5V<6_ o ca1 = fftshift(fft(u1)); % Take Fourier transform
!$HuH6_[ ca2 = fftshift(fft(u2));
s-*N_Dv c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
X:Y1g)|K c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
%;4#?.W8 u2 = ifft(fftshift(c2)); % Return to physical space
n^QDMyC;I u1 = ifft(fftshift(c1));
q"Bd-?9 if rem(m1,J) == 0 % Save output every J steps.
S*}GW-) oA U1 = [U1 u1]; % put solutions in U array
g S(JgN U2=[U2 u2];
c Mi9 Z] MN1=[MN1 m1];
K/( LF} z1=dz*MN1'; % output location
?Ho$f Gz end
<;i&-, end
~oOv/1v}, hg=abs(U1').*abs(U1'); % for data write to excel
NTJ,U2 ha=[z1 hg]; % for data write to excel
{;bec%pq0 t1=[0 t'];
j 1 'H| 4 hh=[t1' ha']; % for data write to excel file
'NWvQR<X %dlmwrite('aa',hh,'\t'); % save data in the excel format
Jur$O,u40l figure(1)
6AD&%v waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
'
Sd&I:? figure(2)
R GV{KL waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
gu3)HCZ C Ws;1`aP 非线性超快脉冲耦合的数值方法的Matlab程序 e7 G>'K &\?{%xj 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
w}}+8mk[ Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
N0fE *xo j5Yli6r?3- p"\-iY] Y\!:/h]E& % This Matlab script file solves the nonlinear Schrodinger equations
nb5%a % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
F`Vp % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
\mN?5QCcE % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
( `n*d3 -GgV&%'a C=1;
gKU*@`6G M1=120, % integer for amplitude
=L$RY2S" M3=5000; % integer for length of coupler
]H:K $nmX N = 512; % Number of Fourier modes (Time domain sampling points)
AO$aW y I dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
[\HAJ A, T =40; % length of time:T*T0.
C~iFFh6: dt = T/N; % time step
bv[ *jr;45 n = [-N/2:1:N/2-1]'; % Index
/9y'UKl7[ t = n.*dt;
a(o[ bH.|; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
/7*qa G w=2*pi*n./T;
1?+)T%" g1=-i*ww./2;
RmN\;G?} g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Q6Zh%\+h( g3=-i*ww./2;
'\m\$
{ P1=0;
`0ju=FP'u5 P2=0;
=7P; /EV P3=1;
N_!Zn"J P=0;
;+qPV7Z for m1=1:M1
q33!X!br p=0.032*m1; %input amplitude
CQY/q@7 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
8&f"")m s1=s10;
!as< UH"\ s20=0.*s10; %input in waveguide 2
}\ui} \ s30=0.*s10; %input in waveguide 3
Df/f&;` s2=s20;
1/q iE{NW s3=s30;
J2#=`|t" p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
ZsPBs4<p
%energy in waveguide 1
Ah2XwFg? p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
I p0@Q}^ %energy in waveguide 2
.J\U|r p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
[76m g j!K %energy in waveguide 3
cfe[6N for m3 = 1:1:M3 % Start space evolution
qXW2a '~ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
/[#{#:lo2 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Y=rW.yK8 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
j'0*|f ^z sca1 = fftshift(fft(s1)); % Take Fourier transform
vrW9<{ sca2 = fftshift(fft(s2));
7#|NQ=yd sca3 = fftshift(fft(s3));
7erao- sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
GrQAho sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Y.* lO sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
qaGIU`}:$A s3 = ifft(fftshift(sc3));
C1rCKKh s2 = ifft(fftshift(sc2)); % Return to physical space
iii$)4 V s1 = ifft(fftshift(sc1));
(U dDp"/ end
w)8@Tu:Q p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
$BBfsaJPT p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
|)Joxq R p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
.y2<2eW P1=[P1 p1/p10];
>qUO_> P2=[P2 p2/p10];
s* YFN#Wuc P3=[P3 p3/p10];
>a-+7{}; P=[P p*p];
a@r K% Iff end
sBu"$ "] figure(1)
".i{WyTt plot(P,P1, P,P2, P,P3);
h+^T);h};| /eMZTh*1P 转自：
http://blog.163.com/opto_wang/
