计算脉冲在非线性耦合器中演化的Matlab 程序 6xvy hg#B x)5# *Q % This Matlab script file solves the coupled nonlinear Schrodinger equations of
Q3'\Vj,S& % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
`p Oiv&> % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
S3A OT % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
="JLUq*]s ldO6W7 G|h %fid=fopen('e21.dat','w');
~;9B\fE` N = 128; % Number of Fourier modes (Time domain sampling points)
H<Ed"-n$I< M1 =3000; % Total number of space steps
u#ag|b/C: J =100; % Steps between output of space
f@]4udc e T =10; % length of time windows:T*T0
$x)C_WZj? T0=0.1; % input pulse width
-[^aWNqyJ MN1=0; % initial value for the space output location
uF/l,[0v dt = T/N; % time step
E0o= n = [-N/2:1:N/2-1]'; % Index
L?23Av0W t = n.*dt;
%n SLe~b u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
YP5V~-O/ u20=u10.*0.0; % input to waveguide 2
~L<q9B( @ u1=u10; u2=u20;
^~E?7{BL U1 = u1;
\,+act "v U2 = u2; % Compute initial condition; save it in U
4U( W~O ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
h}nceH0s3d w=2*pi*n./T;
8F9sKRq|rO g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
PVC\&YF L=4; % length of evoluation to compare with S. Trillo's paper
Z ^zUb dz=L/M1; % space step, make sure nonlinear<0.05
* _)xlpy for m1 = 1:1:M1 % Start space evolution
ou0(C ` u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
F]:@?}8R u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
{R5Q{]dK 3 ca1 = fftshift(fft(u1)); % Take Fourier transform
mQ*:?\@ ca2 = fftshift(fft(u2));
o4^rE<vJ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
FZ)_WaqG f c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
/ q *n*j u2 = ifft(fftshift(c2)); % Return to physical space
Y &6v TU u1 = ifft(fftshift(c1));
tF}Vs} if rem(m1,J) == 0 % Save output every J steps.
B{hP#bYK U1 = [U1 u1]; % put solutions in U array
!vH7 vq U2=[U2 u2];
X~(%Y#6 MN1=[MN1 m1];
^rO3B? _ z1=dz*MN1'; % output location
f| P% end
<x e=G]v end
T:p,!?kc7 hg=abs(U1').*abs(U1'); % for data write to excel
2K 0HN ha=[z1 hg]; % for data write to excel
:FcYjw t1=[0 t'];
'85 @U`e. hh=[t1' ha']; % for data write to excel file
= Bz yI %dlmwrite('aa',hh,'\t'); % save data in the excel format
_BHR ?I[w figure(1)
Ou/ JN+2A waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
~ M 7
J{hK figure(2)
+ KGZk?% waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
E2+x?Sc+ ~<!b}Hv 非线性超快脉冲耦合的数值方法的Matlab程序 ,1J+3ugp& ;<i `6e 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。
*.nC'$-2r 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
Y??8P nK=-SQ sq1Z;l31" zX *+J"x % This Matlab script file solves the nonlinear Schrodinger equations
XaOq &7 % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
g b:)t }| % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
cyu)YxT % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
.hd<,\nW RKB--$ibj C=1;
$Pv;>fHu M1=120, % integer for amplitude
j{PuZ^v 1 M3=5000; % integer for length of coupler
& c a- N = 512; % Number of Fourier modes (Time domain sampling points)
?|Y/&/;%I dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
K.'II9-{ T =40; % length of time:T*T0.
J}a 8N.S dt = T/N; % time step
\ @6P A n = [-N/2:1:N/2-1]'; % Index
I`"B<=zi t = n.*dt;
2O}UVp> ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
rN* , U\q w=2*pi*n./T;
?+EN.P[;3 g1=-i*ww./2;
PO9<g% qTf g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
5[NF g3=-i*ww./2;
`uK_}Vy_ P1=0;
(9R;a np P2=0;
qC<!!473 ? P3=1;
a:nMW '! P=0;
Hp`Mp )1s for m1=1:M1
DY]\@<ez p=0.032*m1; %input amplitude
:{2exu s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
(KQAKEhD! s1=s10;
t<'-?B2g s20=0.*s10; %input in waveguide 2
m<]b] FQ s30=0.*s10; %input in waveguide 3
aDr 46TB`J s2=s20;
j n[%@zD } s3=s30;
[;O 6)W p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
7/^` y') %energy in waveguide 1
/Hxz@=LC1 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
GMD>Ih.k:9 %energy in waveguide 2
zyey 5Z:7 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
D4jf%7X!Lu %energy in waveguide 3
NY]`1yy for m3 = 1:1:M3 % Start space evolution
T^'NC8v s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
5G-)> s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
GWP;; x% s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
-8 F~Tffx sca1 = fftshift(fft(s1)); % Take Fourier transform
OG}auM4
sca2 = fftshift(fft(s2));
X[pk9mha sca3 = fftshift(fft(s3));
) {=2td$=$ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Nc4e,>$]& sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
z>_jC+ sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
$'M: H_T s3 = ifft(fftshift(sc3));
("HT0 &#a s2 = ifft(fftshift(sc2)); % Return to physical space
{-X8MisI s1 = ifft(fftshift(sc1));
e*[M*u end
8p3 pw=p p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
3PS( 1 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~c8Z9[QW p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
Rx e
sK P1=[P1 p1/p10];
i7^_y3dG P2=[P2 p2/p10];
?V|t7^+: P3=[P3 p3/p10];
j\t"4=,n P=[P p*p];
S].=gR0: end
pfCNFF*" figure(1)
dL9QYIfP plot(P,P1, P,P2, P,P3);
gwFHp .mE d9/YW#tm 转自：
http://blog.163.com/opto_wang/
