计算脉冲在非线性耦合器中演化的Matlab 程序 gM;m{gXYK z{w %pUn } % This Matlab script file solves the coupled nonlinear Schrodinger equations of
jR[c3EA
; % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
_,(s % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
XK/l1E3N % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
w8Z#]kRv TS+jDs %fid=fopen('e21.dat','w');
F5cN F 5 N = 128; % Number of Fourier modes (Time domain sampling points)
$},XRo&R M1 =3000; % Total number of space steps
H3R{+ 7 J =100; % Steps between output of space
D- C]0Jf3 T =10; % length of time windows:T*T0
;4b=/ 1M' T0=0.1; % input pulse width
}F.k,2 MN1=0; % initial value for the space output location
)6p6<y dt = T/N; % time step
j G{?>^ n = [-N/2:1:N/2-1]'; % Index
;DnUeE 8 t = n.*dt;
#>:S&R?2t u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
1I69O6" u20=u10.*0.0; % input to waveguide 2
&gS-.{w " u1=u10; u2=u20;
d{NMG)`x\ U1 = u1;
PH8
88O U2 = u2; % Compute initial condition; save it in U
,@;|+C ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
j~ds)dW%`& w=2*pi*n./T;
/"A= Yf g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Y(1?uVYW\d L=4; % length of evoluation to compare with S. Trillo's paper
Tb2#y ]27 dz=L/M1; % space step, make sure nonlinear<0.05
`G: 1 for m1 = 1:1:M1 % Start space evolution
xL.m <XDL u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
k -R"e u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
_MIh eCvV ca1 = fftshift(fft(u1)); % Take Fourier transform
V 1d#7rP ca2 = fftshift(fft(u2));
PbvA~gm c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
v07A 3oj c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
#P}n+w_@ u2 = ifft(fftshift(c2)); % Return to physical space
o@360#njF u1 = ifft(fftshift(c1));
.J @mpJdY if rem(m1,J) == 0 % Save output every J steps.
ESoC7d&.K{ U1 = [U1 u1]; % put solutions in U array
Gq[5H(0/c U2=[U2 u2];
ALF21e*n MN1=[MN1 m1];
Q wG_- z1=dz*MN1'; % output location
nTGf end
3D@3jyo: end
7\g#'#K hg=abs(U1').*abs(U1'); % for data write to excel
}[!=O+g O ha=[z1 hg]; % for data write to excel
xq g4b{ t1=[0 t'];
F` e E*& hh=[t1' ha']; % for data write to excel file
yLCMu | + %dlmwrite('aa',hh,'\t'); % save data in the excel format
L |#0CRiN figure(1)
*u|1Z%XO waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
;?iu@h figure(2)
} L|B@fW waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
M'R
] '' Y[PC<-fyf 非线性超快脉冲耦合的数值方法的Matlab程序 F%lC%~ -qh 6l4= 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。
ipGxi [Vav 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
q!U$\ Q& g ^|R;s{ 0w TOdCvmb R%2.N!8 v % This Matlab script file solves the nonlinear Schrodinger equations
qk^/ &j % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
=IX-n$d`> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
NM:$Q< n % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
SfY 5Xgp *wJz0ex7R/ C=1;
C]JK'K<7- M1=120, % integer for amplitude
H2[0@|<< M3=5000; % integer for length of coupler
9L-jlAo< N = 512; % Number of Fourier modes (Time domain sampling points)
M/[_~ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
4/ *@cW T =40; % length of time:T*T0.
P $y'`` dt = T/N; % time step
z8kebS&5 n = [-N/2:1:N/2-1]'; % Index
[+A]E,pv]1 t = n.*dt;
E%8uQ2p( ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
ydY( *] w=2*pi*n./T;
J1gnR g1=-i*ww./2;
*(vh | g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
t&x\@p9 g3=-i*ww./2;
Au)~"N~p? P1=0;
vA op#V P2=0;
YE*|KL^ P3=1;
s}UJv\* P=0;
FY )]yz for m1=1:M1
F}[!OYy g p=0.032*m1; %input amplitude
zNo"P[J8 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
:}#)ip r s1=s10;
mb3aUFxA; s20=0.*s10; %input in waveguide 2
L|(U %$ s30=0.*s10; %input in waveguide 3
SQ+r'g s2=s20;
BL>~~ s3=s30;
UB8n,+R p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
qG~6YCqii %energy in waveguide 1
s%vy^x29 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
jd5kkX8= %energy in waveguide 2
Q q j9o2 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
x7gd6"10^ %energy in waveguide 3
:nl,A c for m3 = 1:1:M3 % Start space evolution
y eIS} O s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
?A .ah s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
csJ )Pt?d s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
L|s\IM1g sca1 = fftshift(fft(s1)); % Take Fourier transform
I!kR:Z sca2 = fftshift(fft(s2));
Hc|cA(9sh9 sca3 = fftshift(fft(s3));
87S,6 Y sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
bV'r9&[_6 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
D-i, C~W sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
X6t9* |C s3 = ifft(fftshift(sc3));
WH7UJ CQ s2 = ifft(fftshift(sc2)); % Return to physical space
726 UO#* s1 = ifft(fftshift(sc1));
>6WZSw/Hq end
iY,oaC~?"N p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
d2U?rw_ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Q3bU"f p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Lq.2vfA> P1=[P1 p1/p10];
8vR'<_>Q P2=[P2 p2/p10];
1!U:M8T| P3=[P3 p3/p10];
Xnh&Kyz`v P=[P p*p];
Y1ca=ewFx end
-j rAk figure(1)
GCw4sb4~w plot(P,P1, P,P2, P,P3);
;iJxJX\+ %yfl-c(u 转自：
http://blog.163.com/opto_wang/
