计算脉冲在非线性耦合器中演化的Matlab 程序 G/w&yd4 O=9mLI6 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
9qHbV
9,M % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
bK 7j" % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
) sh+cfTCb % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
~; emUU { NS6y \, %fid=fopen('e21.dat','w');
exn F y- N = 128; % Number of Fourier modes (Time domain sampling points)
Yb~[XS |p M1 =3000; % Total number of space steps
: d Zq!1~t J =100; % Steps between output of space
?3x7_=4t@ T =10; % length of time windows:T*T0
I1IuvH6 T0=0.1; % input pulse width
U|Du9_0 MN1=0; % initial value for the space output location
~BS Ip
. dt = T/N; % time step
z^KMYvH
g n = [-N/2:1:N/2-1]'; % Index
y" (-O%Pe t = n.*dt;
@-7h}2P Q u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
-UHa;W H u20=u10.*0.0; % input to waveguide 2
%LH~Im= u1=u10; u2=u20;
E>bK-j G U1 = u1;
:#?Z)oQpT U2 = u2; % Compute initial condition; save it in U
Vd VUYp ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
W!R}eLf@ w=2*pi*n./T;
J`&*r;"" V g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
dK 5|tWJX L=4; % length of evoluation to compare with S. Trillo's paper
D9cpw0{nc dz=L/M1; % space step, make sure nonlinear<0.05
2=&4@c|cn for m1 = 1:1:M1 % Start space evolution
wNHvYu lI u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
:U,n[.$5' u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
aCq ) hR ca1 = fftshift(fft(u1)); % Take Fourier transform
wRa$b ca2 = fftshift(fft(u2));
yc#0c[ZQu c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
? !h
jI;_& c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
gJkk0wok C u2 = ifft(fftshift(c2)); % Return to physical space
lk$@8h$vS u1 = ifft(fftshift(c1));
0 e}N{,&Y if rem(m1,J) == 0 % Save output every J steps.
Fp_?1 y U1 = [U1 u1]; % put solutions in U array
qqmhh_[T U2=[U2 u2];
n#{z"G MN1=[MN1 m1];
O% 1X[ z1=dz*MN1'; % output location
D8`dEB2|S end
-v '|#q end
O?6ph4' hg=abs(U1').*abs(U1'); % for data write to excel
m0: IFE($ ha=[z1 hg]; % for data write to excel
@Kx@ 2#~b t1=[0 t'];
~^&]8~m*d hh=[t1' ha']; % for data write to excel file
O}Ipg[h %dlmwrite('aa',hh,'\t'); % save data in the excel format
Rl. YF+YH figure(1)
@w8MOT$ waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
S? -6hGA
j figure(2)
b5-W K; waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
h!vq~g x&n gCB@O 非线性超快脉冲耦合的数值方法的Matlab程序 r )EuH.z _'W en 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。
}mZ sK> 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
l *v6U'J j 4!g&F _y l,I[r$TCf ]vFtByqn % This Matlab script file solves the nonlinear Schrodinger equations
=54"9* % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
mbij& 0 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Lrr 1) h % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
%u t^ O 9 kpCn.rJ C=1;
#RJFJb/ M1=120, % integer for amplitude
% yVboA1 M3=5000; % integer for length of coupler
4
Qo(Wl N = 512; % Number of Fourier modes (Time domain sampling points)
w7(j SPB dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
bv%A ; T =40; % length of time:T*T0.
# QWG5 dt = T/N; % time step
"JH
/ ODm n = [-N/2:1:N/2-1]'; % Index
zKnHo:SV t = n.*dt;
>+9f{FP
9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
dbmt y|d w=2*pi*n./T;
\-Oq/g{j g1=-i*ww./2;
Po
,zTz g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ls^| j%$J g3=-i*ww./2;
8 2EH'C P1=0;
H{XD> q. P2=0;
lZt{L0 P3=1;
wDL dmrB P=0;
xE[CNJ%t^, for m1=1:M1
+2ZBj6 e9 p=0.032*m1; %input amplitude
I^CK q?V?: s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
rA">< pH s1=s10;
B. J_(V+ s20=0.*s10; %input in waveguide 2
!oJ226>WI s30=0.*s10; %input in waveguide 3
#dd-rooQuD s2=s20;
p ^E}%0# s3=s30;
" ,qcqG( p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
bG'"l qn %energy in waveguide 1
0Rme}&$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
8,5H^Bi %energy in waveguide 2
w
b@Zna p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
.y)Y20=o! %energy in waveguide 3
M)<4|x for m3 = 1:1:M3 % Start space evolution
>z, SN s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
A#WvN> s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
S~Z`?qHWh s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
&3o[^_Ti sca1 = fftshift(fft(s1)); % Take Fourier transform
W@T_-pTCjK sca2 = fftshift(fft(s2));
!,I530eh7 sca3 = fftshift(fft(s3));
Q9\6P n ]T sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
:epjJ1mW sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ftw@ nQNU sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
XW^Sw;[efZ s3 = ifft(fftshift(sc3));
x+X^K_* s2 = ifft(fftshift(sc2)); % Return to physical space
",pN.<F9O s1 = ifft(fftshift(sc1));
`X =2Ff end
=L UDg7P p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
dV:vM9+x p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
DaK 2P;WP p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
r
N.<S[ P1=[P1 p1/p10];
^< }>]F_ P2=[P2 p2/p10];
r=`]L-}V P3=[P3 p3/p10];
t!u{sr{j= P=[P p*p];
UImd* ;2TE end
\0^ZNa? figure(1)
: kaHvf plot(P,P1, P,P2, P,P3);
{e3XmVA I :We}l;.jQ 转自：
http://blog.163.com/opto_wang/
