计算脉冲在非线性耦合器中演化的Matlab 程序 u%'\UmE w Ai D [SR % This Matlab script file solves the coupled nonlinear Schrodinger equations of
XLMb=T~S % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
# :T-hRu % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S+TOSjfis % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4f(Kt,0 cYXM__ %fid=fopen('e21.dat','w');
pP(XIC N = 128; % Number of Fourier modes (Time domain sampling points)
FU=w(< R; M1 =3000; % Total number of space steps
>0p$(>N] J =100; % Steps between output of space
qfcY E= T =10; % length of time windows:T*T0
GUsl PnG T0=0.1; % input pulse width
}|%eCVB MN1=0; % initial value for the space output location
4v[~r1!V dt = T/N; % time step
[{C )LDN n = [-N/2:1:N/2-1]'; % Index
&3J@BMYp t = n.*dt;
=] 3tUD u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
FKe, qTqa u20=u10.*0.0; % input to waveguide 2
5NJ4 u1=u10; u2=u20;
oD}uOC}FS{ U1 = u1;
]Qm]I1P U2 = u2; % Compute initial condition; save it in U
NBb6T
V}j ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
czlFr|O; w=2*pi*n./T;
eT2*W$ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
s+:= I
e L=4; % length of evoluation to compare with S. Trillo's paper
5>AX*]c dz=L/M1; % space step, make sure nonlinear<0.05
fwzb!"!.@ for m1 = 1:1:M1 % Start space evolution
Y.^= ]-n, u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
h*ZC*eV> u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
=_Y G#yS ca1 = fftshift(fft(u1)); % Take Fourier transform
t4?DpE ca2 = fftshift(fft(u2));
+2 A f&~T c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
$ cj>2. c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
R *F l8
u2 = ifft(fftshift(c2)); % Return to physical space
XD"_Iq! u1 = ifft(fftshift(c1));
^&g=u5
d0 if rem(m1,J) == 0 % Save output every J steps.
?W E U1 = [U1 u1]; % put solutions in U array
u^029sH6j U2=[U2 u2];
B c2p(z4 MN1=[MN1 m1];
_HhbIU z1=dz*MN1'; % output location
Nan[< end
:x_'i_w end
IHRGw hg=abs(U1').*abs(U1'); % for data write to excel
OzC\9YeA ha=[z1 hg]; % for data write to excel
'U'yC2BI n t1=[0 t'];
bTQNb!& hh=[t1' ha']; % for data write to excel file
<V>dM 4Mkr %dlmwrite('aa',hh,'\t'); % save data in the excel format
B:7mpSnEQ figure(1)
}B~If}7 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
{\[5}nV figure(2)
;2Q~0a| waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
?)e37 %c[ V 非线性超快脉冲耦合的数值方法的Matlab程序 KN-avu_Ix B7]MGXC 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
Pb*5eXk Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
"Ky; a?Y Ks}Xgc\ 2k<;R': GRY2?' ` % This Matlab script file solves the nonlinear Schrodinger equations
LY+|[qka % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
qTQBt} % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
*{+G=d % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
2h%z ("3/ ~Ch+5A; C=1;
-kbg\,PW M1=120, % integer for amplitude
r [ K5w M3=5000; % integer for length of coupler
`mN4_\] N = 512; % Number of Fourier modes (Time domain sampling points)
S]E.KLR?[; dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
IT$25ZF T =40; % length of time:T*T0.
(e"iO`H dt = T/N; % time step
t'ZWc\ n = [-N/2:1:N/2-1]'; % Index
$ [yFsA6 t = n.*dt;
xZV1k~C ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
VWO9=A*Y| w=2*pi*n./T;
VcoOeAKL g1=-i*ww./2;
Q?X>E3=U g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
MM j9{ou g3=-i*ww./2;
H8 "@ iE, P1=0;
}K3x P2=0;
~/*MY P3=1;
GaSPJt P=0;
~,*b }O for m1=1:M1
<mAhr p=0.032*m1; %input amplitude
+5XpzZ{#Wa s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
2+X\}s1vN s1=s10;
MR}Agu#LG s20=0.*s10; %input in waveguide 2
!>1@HH?I\/ s30=0.*s10; %input in waveguide 3
XU"~h64] s2=s20;
cH>%r^G\ s3=s30;
|7zd%! p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
P@FHnh3}Z$ %energy in waveguide 1
;amXY@RmH p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
l<);s %energy in waveguide 2
` Jdb ; p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
t]-5 ]oI %energy in waveguide 3
k-}b{ for m3 = 1:1:M3 % Start space evolution
7.`fJf? s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
[Jv@J\ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
O?|gp<=d s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
&?(?vDFfZ sca1 = fftshift(fft(s1)); % Take Fourier transform
q`r**N+zn sca2 = fftshift(fft(s2));
/E\%>wv sca3 = fftshift(fft(s3));
Jke k-m sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
p a# IJ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
Hhh0 T>gi sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
z[;z>8|c s3 = ifft(fftshift(sc3));
f`Fi# EKT s2 = ifft(fftshift(sc2)); % Return to physical space
w`5xrqt@ s1 = ifft(fftshift(sc1));
0L/n ?bf end
"
W|%~h p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vuYSVI2=H p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
V 0rZz p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
=&:Y6XP P1=[P1 p1/p10];
R47\Y P2=[P2 p2/p10];
0vw4?>Jf@ P3=[P3 p3/p10];
@< x*.8 P=[P p*p];
&c,kQo+pA end
=y-@AU8 figure(1)
J Px~VnE%% plot(P,P1, P,P2, P,P3);
G I1 1 .6:# 转自：
http://blog.163.com/opto_wang/
