计算脉冲在非线性耦合器中演化的Matlab 程序 }AfPBfgC1z "RX5] eJc\ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
xR6IXF>* % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
64j 4P 7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
C>;8`6_!gU % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
iiDk k PC7 .+;1 %fid=fopen('e21.dat','w');
B148wh#r N = 128; % Number of Fourier modes (Time domain sampling points)
q9(}wvtr M1 =3000; % Total number of space steps
v@s`l# J =100; % Steps between output of space
5BO!K$6 T =10; % length of time windows:T*T0
F"TI 9ib T0=0.1; % input pulse width
~u& O MN1=0; % initial value for the space output location
{O oNhN9 dt = T/N; % time step
")gCA:1- n = [-N/2:1:N/2-1]'; % Index
q5?mP6 t = n.*dt;
[bVP2j u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
EUS]Se2 u20=u10.*0.0; % input to waveguide 2
RSeezP6# u1=u10; u2=u20;
> -+X; 0& U1 = u1;
M#2U'jy U2 = u2; % Compute initial condition; save it in U
LVtQ^ 5>8 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Sf: lN4 w=2*pi*n./T;
_1%^ ibn g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
=YsTF T L=4; % length of evoluation to compare with S. Trillo's paper
d~$t{ 46 dz=L/M1; % space step, make sure nonlinear<0.05
hs uJ;4}$q for m1 = 1:1:M1 % Start space evolution
s'=]a-l~ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
>c>ar>4xF u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Q >*K/%KD ca1 = fftshift(fft(u1)); % Take Fourier transform
r+Cha%&D ca2 = fftshift(fft(u2));
bu5)~|?{t c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
AG0x) c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
g<c^\WG u2 = ifft(fftshift(c2)); % Return to physical space
<W^~Y31:0 u1 = ifft(fftshift(c1));
uCr if rem(m1,J) == 0 % Save output every J steps.
\R t U1 = [U1 u1]; % put solutions in U array
UzwI V{ U2=[U2 u2];
IT33E%G MN1=[MN1 m1];
tR/
JY;jn z1=dz*MN1'; % output location
}`]^LFU5 end
0evZg@JP` end
(ajX ;/ hg=abs(U1').*abs(U1'); % for data write to excel
x;a Z& ha=[z1 hg]; % for data write to excel
&!MKq J@t t1=[0 t'];
\hc9R k hh=[t1' ha']; % for data write to excel file
[]^>QsS(X %dlmwrite('aa',hh,'\t'); % save data in the excel format
2*FZ@?X@r figure(1)
_{);n$ ` waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Vi-@z;k
figure(2)
8Qy |;T} waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
<[~M|OL9q, 9V!K. _Cb 非线性超快脉冲耦合的数值方法的Matlab程序
fE}}> QKQy)g 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。
G;+ 0V0K 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
%"V,V3kw4 @@&;gWr; H# akE\, zqn*DbT
% This Matlab script file solves the nonlinear Schrodinger equations
)[.URp& % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
_JoA=< O! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
p]HtJt|] % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
ibL;99 # `R;X N- C=1;
m0YDO 0 M1=120, % integer for amplitude
~Q\[b%>J M3=5000; % integer for length of coupler
GM~jR-F Z N = 512; % Number of Fourier modes (Time domain sampling points)
Pr' py dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
KDk^)zv%! T =40; % length of time:T*T0.
<#i'3TUR dt = T/N; % time step
-K4RQ{=>UZ n = [-N/2:1:N/2-1]'; % Index
='azVw%_ t = n.*dt;
V#Eq74ic ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
[;+YO) w=2*pi*n./T;
0jMrL\>C g1=-i*ww./2;
b9Nw98` g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
c$TBHK;c g3=-i*ww./2;
-#h
\8Xl P1=0;
kS>j!U(%d P2=0;
A,@"(3 P3=1;
&3M He$ P=0;
j\<S 6%p#R for m1=1:M1
+ `xp+Q p=0.032*m1; %input amplitude
Gl(,%~F9i s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
iZF{9@ s1=s10;
+{&g|V s20=0.*s10; %input in waveguide 2
B _ >|Mo/ s30=0.*s10; %input in waveguide 3
Fej$`2mRH s2=s20;
"wc $'7M s3=s30;
7}MWmS^8j p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=W?c1EPLCx %energy in waveguide 1
l\)Q3.w p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
'=5N ?) %energy in waveguide 2
Q{l;8M CL p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l
}[
4 %energy in waveguide 3
0nX5
$Kn for m3 = 1:1:M3 % Start space evolution
5 ,HNb s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
(s~hh s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
v%r! }s s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
D UeT sca1 = fftshift(fft(s1)); % Take Fourier transform
/TdTo@ sca2 = fftshift(fft(s2));
S<44{
oH sca3 = fftshift(fft(s3));
#HML=qK~ sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
f>o@Y]/l sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
FM5$83Q sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Sq ,x@ s3 = ifft(fftshift(sc3));
$%<gp@Gz s2 = ifft(fftshift(sc2)); % Return to physical space
x:(e: I8x( s1 = ifft(fftshift(sc1));
D N+iS end
&,+ZN A`P p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
"o`(
kYSF p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
,b/0_ Q p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
6%? NNEM P1=[P1 p1/p10];
B}p/ ,4x6 P2=[P2 p2/p10];
Q{ RHW@_/ P3=[P3 p3/p10];
m@ ~HHwj P=[P p*p];
}-!$KR]:s end
a&&EjI figure(1)
d7 @ N~<n plot(P,P1, P,P2, P,P3);
$O[ut.
W*
YfyM 转自：
http://blog.163.com/opto_wang/
