计算脉冲在非线性耦合器中演化的Matlab 程序 NV:>a +*n] tlk % This Matlab script file solves the coupled nonlinear Schrodinger equations of
63.( j P1; % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
.JNcY]V# % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
'n>K^rA % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
?x:m;z / 9Kc0&?q@D %fid=fopen('e21.dat','w');
{V.Wk N = 128; % Number of Fourier modes (Time domain sampling points)
vZ:G8K)o( M1 =3000; % Total number of space steps
+z+ F- J =100; % Steps between output of space
7Aqn[1{_O T =10; % length of time windows:T*T0
Xxh sPFv T0=0.1; % input pulse width
=\M)6" }y} MN1=0; % initial value for the space output location
:b"= KQ dt = T/N; % time step
I9;xz ES n = [-N/2:1:N/2-1]'; % Index
VxNX d? t = n.*dt;
U> W|( Y u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
]n~yp5Nbr u20=u10.*0.0; % input to waveguide 2
$6 W3EOl u1=u10; u2=u20;
5n:nZ _D U1 = u1;
]Fxku<z7| U2 = u2; % Compute initial condition; save it in U
>Q&CgGpW $ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
9p5= _ w=2*pi*n./T;
wc"9A~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
`q^(SM L=4; % length of evoluation to compare with S. Trillo's paper
64SW dz=L/M1; % space step, make sure nonlinear<0.05
Ys-^7
y_ for m1 = 1:1:M1 % Start space evolution
V>6QPA^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
D2{L= u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
cxgE\4_u" ca1 = fftshift(fft(u1)); % Take Fourier transform
1y 7y0V ca2 = fftshift(fft(u2));
TFo}\ B7 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
S,XKW(5 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
U4=]#=R~o u2 = ifft(fftshift(c2)); % Return to physical space
2bkJ /u`i u1 = ifft(fftshift(c1));
k<!<<,Z if rem(m1,J) == 0 % Save output every J steps.
iZC>)&ax U1 = [U1 u1]; % put solutions in U array
F9%,MSt U2=[U2 u2];
7vw;Egd@@- MN1=[MN1 m1];
E!uJ 6\ z1=dz*MN1'; % output location
/\d(c/, 4 end
[M`=HhJ4 end
$_wo6/J5+D hg=abs(U1').*abs(U1'); % for data write to excel
f`,-b ha=[z1 hg]; % for data write to excel
hv3;irK]& t1=[0 t'];
g rc:Y hh=[t1' ha']; % for data write to excel file
a%v>eXc %dlmwrite('aa',hh,'\t'); % save data in the excel format
D '<$ g figure(1)
_p0)vT waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Zd$JW=KR]l figure(2)
Gt C7^ Z&E waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
eIsT!V" 7 w E?CvL 非线性超快脉冲耦合的数值方法的Matlab程序 g@Ld"5$^2 #,TELzUVE 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。
"w9`cz9a~J 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
qIz}$%!A 7_KXD# 7|Xe &o <n C!5I?z& % This Matlab script file solves the nonlinear Schrodinger equations
f9a$$nb3` % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
0Q`&inwh % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Xo \S9,s{ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
*Z; r
B Je 31". C=1;
*,0+RAS vq M1=120, % integer for amplitude
?,>5[Ha^? M3=5000; % integer for length of coupler
V:Oi W"/ N = 512; % Number of Fourier modes (Time domain sampling points)
&sdx`, dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
bJwc1AJgH T =40; % length of time:T*T0.
ctHEEFWm dt = T/N; % time step
T{tn.sT n = [-N/2:1:N/2-1]'; % Index
Q(e{~
]* t = n.*dt;
tvGlp)?. ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
x}|+sS,g w=2*pi*n./T;
YQYX, b g1=-i*ww./2;
JCD?qeTg g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
IT18v[-G g3=-i*ww./2;
l#$TYJi P1=0;
>azEed<B P2=0;
t!:)L+$3 P3=1;
4gb'7' P=0;
AuXs B for m1=1:M1
('JKN"3 p=0.032*m1; %input amplitude
H{%H^ t> s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
WL1\y| s1=s10;
H99xZxHZ{ s20=0.*s10; %input in waveguide 2
v%nP*i9 s30=0.*s10; %input in waveguide 3
'g hys1H s2=s20;
b ]i>Bv s3=s30;
n]iyFZ`9 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
CdL .?^ %energy in waveguide 1
@$c!/ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
K{2h9 ]VF %energy in waveguide 2
#x)8f3I p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
Mg\TH./Y: %energy in waveguide 3
$UC {"0 for m3 = 1:1:M3 % Start space evolution
$w/E9EJ)3A s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
#ouE r -= s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
PS}73Y # s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
d @ (vg sca1 = fftshift(fft(s1)); % Take Fourier transform
({ k7#1
h8 sca2 = fftshift(fft(s2));
>pdnCv_c sca3 = fftshift(fft(s3));
?oKL &I@ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
i/*,N&^ sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
ISBF\ wQY sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
*)D1!R<\,R s3 = ifft(fftshift(sc3));
>f@ G>H )+ s2 = ifft(fftshift(sc2)); % Return to physical space
]2$x| #Gg} s1 = ifft(fftshift(sc1));
`{o$F ::( end
O aaH$B p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
* |KVN&# p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
UP8{5fx ' p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
bLlH//ZRH P1=[P1 p1/p10];
:,~K]G P2=[P2 p2/p10];
f3#X0.': P3=[P3 p3/p10];
SiTeB)/ P=[P p*p];
:tbd,Uo end
c1#+Vse figure(1)
$ >r5>6 plot(P,P1, P,P2, P,P3);
V|: qow:F U\bC0q 转自：
http://blog.163.com/opto_wang/
