计算脉冲在非线性耦合器中演化的Matlab 程序 ^JVP2L>o* &j@J <*k % This Matlab script file solves the coupled nonlinear Schrodinger equations of
+4nR&1z$ % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
A.x} %v,E % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^? xJpr%) % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
:;Rt#! 207oE O] %fid=fopen('e21.dat','w');
%
j{pz N = 128; % Number of Fourier modes (Time domain sampling points)
e+ w M1 =3000; % Total number of space steps
:k/U7 2 J =100; % Steps between output of space
"g1;TT:1~ T =10; % length of time windows:T*T0
!!O{ ppM T0=0.1; % input pulse width
'nt,+`.y6 MN1=0; % initial value for the space output location
b!~%a dt = T/N; % time step
`(suRp8! n = [-N/2:1:N/2-1]'; % Index
0F'UFn>{ t = n.*dt;
d;:&3r|X u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
xKzFrP;/{ u20=u10.*0.0; % input to waveguide 2
yzR=:0J u1=u10; u2=u20;
Hf!4 (\yN U1 = u1;
Vzm+Ew
_ U2 = u2; % Compute initial condition; save it in U
D\*_ulc] ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
6="&K _Q7 w=2*pi*n./T;
at]Q4 g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
o (NyOC L=4; % length of evoluation to compare with S. Trillo's paper
?s} E<Kr dz=L/M1; % space step, make sure nonlinear<0.05
|aJ6363f. for m1 = 1:1:M1 % Start space evolution
Ic!83- u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Q f(e 'e u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
0BE^qe ca1 = fftshift(fft(u1)); % Take Fourier transform
<OfzE5 ca2 = fftshift(fft(u2));
BXw,Rz } c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
)K3
vzX c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
<qY>d,+E' u2 = ifft(fftshift(c2)); % Return to physical space
A@AGu#W u1 = ifft(fftshift(c1));
o`! :Q!+ if rem(m1,J) == 0 % Save output every J steps.
L([ >yQZ U1 = [U1 u1]; % put solutions in U array
pAmI ]( U2=[U2 u2];
rL3Vogw'e MN1=[MN1 m1];
6mpUk.M" z1=dz*MN1'; % output location
e"mfJY end
'X< u G
x end
{ ;M/J hg=abs(U1').*abs(U1'); % for data write to excel
J c^ozw ha=[z1 hg]; % for data write to excel
x99
Oq! t1=[0 t'];
Vn; ] ''_ hh=[t1' ha']; % for data write to excel file
0j MI)aY. %dlmwrite('aa',hh,'\t'); % save data in the excel format
F|{?GV%hF figure(1)
)p9n|C waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
6WM_V9Tidq figure(2)
7N=VVD~!b waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
j/|qge4 5D*V%v 非线性超快脉冲耦合的数值方法的Matlab程序 FWTl:LqFO ]%h I- 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。
(1]@ fCd + 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
u Aa>6R x[6 Bc 8}T3Fig,q x:lf=D lA % This Matlab script file solves the nonlinear Schrodinger equations
RE$-{i % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
E |3aiC,5 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
dsuW4 ^ l % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
Te #[+B? yo6IY C=1;
_'a4I ; M1=120, % integer for amplitude
\D a$bJ M3=5000; % integer for length of coupler
i mQNfNm N = 512; % Number of Fourier modes (Time domain sampling points)
6I![ 5j dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
O0YGjS|d T =40; % length of time:T*T0.
d^^>3L!h dt = T/N; % time step
3$;v# P$%N n = [-N/2:1:N/2-1]'; % Index
*E_= 8OV t = n.*dt;
T/5U lW|\ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
G [,VP C= w=2*pi*n./T;
DR8dJ# g1=-i*ww./2;
y&]D 2"I g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
QLl44*@ g3=-i*ww./2;
,1L^#?Q~ P1=0;
J1t?Qj;f3 P2=0;
H/f=
2b P3=1;
S/jHyJ, P=0;
WU_Q
7%+QS for m1=1:M1
&>{L"{ p=0.032*m1; %input amplitude
0AenDm@9 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
5w3'yA<vE s1=s10;
Ml a,"~4D5 s20=0.*s10; %input in waveguide 2
%SXqJW^: s30=0.*s10; %input in waveguide 3
"H@AT$Ny( s2=s20;
n\U6oJN s3=s30;
rD?o97 p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
N@S;{uK %energy in waveguide 1
enM 3 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
'"a8< 7 %energy in waveguide 2
\g/E4U .+ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
v<4zcMv %energy in waveguide 3
{S!~pn& ^Y for m3 = 1:1:M3 % Start space evolution
p9J( ,} s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
Ycm1 _z s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
5T`39[Fya s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
q~C6+ sca1 = fftshift(fft(s1)); % Take Fourier transform
YQJ _t@0C sca2 = fftshift(fft(s2));
FliN@RNo sca3 = fftshift(fft(s3));
**"sru;@= sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
uIBV1Qz sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
S1JB]\ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
UPsh Y s3 = ifft(fftshift(sc3));
?##GY;# s2 = ifft(fftshift(sc2)); % Return to physical space
FMiYZ1^r s1 = ifft(fftshift(sc1));
hQO~9mQ+! end
'yqp p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
h/ic-iH(> p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
'_8Vay ~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
+8"H%#~ P1=[P1 p1/p10];
{S c1! 2q P2=[P2 p2/p10];
3%k+<ho( P3=[P3 p3/p10];
Q_S
fFsY P=[P p*p];
6O?O6Ub end
UHH e~L figure(1)
h fNBWN plot(P,P1, P,P2, P,P3);
<?eZ9eB hLF@'ln 转自：
http://blog.163.com/opto_wang/
