计算脉冲在非线性耦合器中演化的Matlab 程序 t]y
D-3'l& !/}O>v~o % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Q<h-FW8z % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
tZ}
v%3 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
q*\x0"mS/ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8TGOx%}i ;3d"wW]}7K %fid=fopen('e21.dat','w');
}Mf!-g N = 128; % Number of Fourier modes (Time domain sampling points)
^* J2'X38I M1 =3000; % Total number of space steps
Wc,~ { J =100; % Steps between output of space
4]h
=yc R T =10; % length of time windows:T*T0
J?Ra bYd ~ T0=0.1; % input pulse width
N}pw74=1 MN1=0; % initial value for the space output location
}`W){]{k O dt = T/N; % time step
p[hZ@f(z n = [-N/2:1:N/2-1]'; % Index
(@%gS[ ] t = n.*dt;
=+U `-J} g u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
PJ]];MQ u20=u10.*0.0; % input to waveguide 2
]$Yvj!K*Q u1=u10; u2=u20;
: YXX8|> U1 = u1;
&j4 xgh 9 U2 = u2; % Compute initial condition; save it in U
N['qgO/ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
e ?7& M w=2*pi*n./T;
k 8UO9r[ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
|?qquD 4= L=4; % length of evoluation to compare with S. Trillo's paper
GliwY_ dz=L/M1; % space step, make sure nonlinear<0.05
i\KQ!f>A for m1 = 1:1:M1 % Start space evolution
JHz
[ 7 u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Po ZuMF u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
R] OpQ[k ca1 = fftshift(fft(u1)); % Take Fourier transform
|K.m P4CKY ca2 = fftshift(fft(u2));
2.% .Z_k) c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
k\WR ] c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
|/09<F:L[ u2 = ifft(fftshift(c2)); % Return to physical space
Qp/QaVQ+ u1 = ifft(fftshift(c1));
t.laO. 3 if rem(m1,J) == 0 % Save output every J steps.
n^z]q;IN2. U1 = [U1 u1]; % put solutions in U array
:^kZ.6Q@ U2=[U2 u2];
gW-V=LV ( MN1=[MN1 m1];
g=QDu7Ux z1=dz*MN1'; % output location
H-~6Z",1 end
@xbQ Ye%J end
(vb
SM}P hg=abs(U1').*abs(U1'); % for data write to excel
f>W - ha=[z1 hg]; % for data write to excel
W}5xmz t1=[0 t'];
,=Mt`aN hh=[t1' ha']; % for data write to excel file
c- }X_)U } %dlmwrite('aa',hh,'\t'); % save data in the excel format
:/ Q figure(1)
b]x4o #t waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
/Y'Vh^9/T figure(2)
/4g1zrU waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
"tB;^jhRs !{ ^PO <9 非线性超快脉冲耦合的数值方法的Matlab程序 =K6($|'= DpUbzr41+k 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。
-?mfE+kt 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
E=>FjCsu<- Cq%IE^g< a{R%#e\n kP-3"AC G % This Matlab script file solves the nonlinear Schrodinger equations
sOU1n % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
~} ,=OF-b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
[/e<l&y % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
1`a5C.v Ib+Y~
XYR C=1;
n
p\TlUc M1=120, % integer for amplitude
go'-5 in( M3=5000; % integer for length of coupler
Zo g']= N = 512; % Number of Fourier modes (Time domain sampling points)
BK,{N0 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
-( f)6a+H T =40; % length of time:T*T0.
Of4^?`
^ dt = T/N; % time step
_Em. n = [-N/2:1:N/2-1]'; % Index
X22[tqg;& t = n.*dt;
U c@Ao: ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
g7O qX \ w=2*pi*n./T;
H;YP8MoQ g1=-i*ww./2;
HbXPok g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
Hm%;=`:' g3=-i*ww./2;
DV<` K$ET P1=0;
,u`B<heoLU P2=0;
d`
jjGEj P3=1;
A29gz:F( P=0;
!V
i@1E for m1=1:M1
(Q.waI p=0.032*m1; %input amplitude
_Ou WB" s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
a2
Y;xe s1=s10;
9J9) AV s20=0.*s10; %input in waveguide 2
p2DrEId s30=0.*s10; %input in waveguide 3
;|vpwB@B s2=s20;
aVK3?y2 s3=s30;
PYM(Xz $ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
N6 ( %energy in waveguide 1
dIRm q+d^ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
hvDNz"ec{ %energy in waveguide 2
CS==A57I p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
E#u l IgD %energy in waveguide 3
l zYnw)Pv for m3 = 1:1:M3 % Start space evolution
:9$F'd\ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
E}40oID s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
.p N`;*7` s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
-Xxqm%([71 sca1 = fftshift(fft(s1)); % Take Fourier transform
`"&d a#N] sca2 = fftshift(fft(s2));
:k.NbN$i\ sca3 = fftshift(fft(s3));
^xi j{W`| sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
rld67'KcE sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
]8 f ms( sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
k;w- E s3 = ifft(fftshift(sc3));
1Dv R[Lx% s2 = ifft(fftshift(sc2)); % Return to physical space
2Fq<*pxAY
s1 = ifft(fftshift(sc1));
o[cV 1G end
ZE2$I^DY- p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
i1>- QDYnJ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
IF DZf x p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
($}`R
xj1@ P1=[P1 p1/p10];
rfN m&!K P2=[P2 p2/p10];
d"6&AJ5a P3=[P3 p3/p10];
sI K;x]Q) P=[P p*p];
tb$LriN end
V\^EfQ figure(1)
L (khAmm plot(P,P1, P,P2, P,P3);
s;64N'HH #1c_ev H 转自：
http://blog.163.com/opto_wang/
