计算脉冲在非线性耦合器中演化的Matlab 程序 AK =k@hT 1gJ!!SHPo % This Matlab script file solves the coupled nonlinear Schrodinger equations of
+s}28U! % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
B=Os?'2[ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
= x}/q4}L % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
quYZD6IH 5ntP{p%> %fid=fopen('e21.dat','w');
R[;Z<K\Nn? N = 128; % Number of Fourier modes (Time domain sampling points)
Y<XDR:]A, M1 =3000; % Total number of space steps
|M_Bbo@ud J =100; % Steps between output of space
zOw]P6Gk T =10; % length of time windows:T*T0
'5--eYG T0=0.1; % input pulse width
!%@{S8IP.v MN1=0; % initial value for the space output location
H5 {J2M,f dt = T/N; % time step
/H% pOL6(r n = [-N/2:1:N/2-1]'; % Index
)%7A. UO) t = n.*dt;
\^cn}db) u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
{xX|5/z u20=u10.*0.0; % input to waveguide 2
)J0V B't u1=u10; u2=u20;
&Te:l-x U1 = u1;
L8 J/GVmj U2 = u2; % Compute initial condition; save it in U
o<4LL7$A! ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<k!G%R<9 w=2*pi*n./T;
10&A3C(E g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Zn/ /u<D L=4; % length of evoluation to compare with S. Trillo's paper
e1-=|!U7# dz=L/M1; % space step, make sure nonlinear<0.05
.YkKIei for m1 = 1:1:M1 % Start space evolution
{Hv=iVmt u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
2 H#vA u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
4hs4W,2! ca1 = fftshift(fft(u1)); % Take Fourier transform
'Bx7b(xqk ca2 = fftshift(fft(u2));
C@-JH\{\T# c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
^ytd~iK8 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
F t}tIP7 u2 = ifft(fftshift(c2)); % Return to physical space
j;
C(:6#J u1 = ifft(fftshift(c1));
Y>+ D\|%Q if rem(m1,J) == 0 % Save output every J steps.
n_<]9 U1 = [U1 u1]; % put solutions in U array
^9nM)[/C? U2=[U2 u2];
o%.cQo=v* MN1=[MN1 m1];
rSk $]E ]Z z1=dz*MN1'; % output location
"n:9Jq Pb end
83a
Rq&(R end
b/EvcN8 } hg=abs(U1').*abs(U1'); % for data write to excel
a #1X )ot ha=[z1 hg]; % for data write to excel
F\e'z t1=[0 t'];
^ =ikxZyO hh=[t1' ha']; % for data write to excel file
vIJdl2(^E %dlmwrite('aa',hh,'\t'); % save data in the excel format
|]Xw1.S.L figure(1)
u+'=EGl waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
P<hqr; figure(2)
~"N]%Cu waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
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! yBoZ@9Do 非线性超快脉冲耦合的数值方法的Matlab程序 ;,1i,? + uA<g` 4 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
KK+Mxoj, Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+C kK4<dF =aCv
Xa&, X%dOkHarB +*dJddz % This Matlab script file solves the nonlinear Schrodinger equations
:97`IV% % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
K6X1a7 % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
/_O-m8+ 4m % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
}oG&zw Uu(W62 C=1;
F8/@/B M1=120, % integer for amplitude
L,<.rr$: M3=5000; % integer for length of coupler
;@L#0 N = 512; % Number of Fourier modes (Time domain sampling points)
u-Vnmig9 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
/vhh2` T =40; % length of time:T*T0.
+G~b-} dt = T/N; % time step
;kbz( :wA n = [-N/2:1:N/2-1]'; % Index
=p"0G %+% t = n.*dt;
QUNsS9 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Q3D xjD w=2*pi*n./T;
=[WccF g1=-i*ww./2;
_D:/?=y;e g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
V= _8G3 g3=-i*ww./2;
j\a?n4g - P1=0;
Rz)#VVYC= P2=0;
/~yqZD<O P3=1;
Cw_ <t P=0;
DlP}Fp { for m1=1:M1
,[~EThcq p=0.032*m1; %input amplitude
Or t\J~ O s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
li{_biey} s1=s10;
4MIVlg9 s20=0.*s10; %input in waveguide 2
Np<A ak s30=0.*s10; %input in waveguide 3
k @ 2gw]y" s2=s20;
82<L07fB s3=s30;
FD*y[A
? p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
pv T!6+
%energy in waveguide 1
Qhr:d`@^] p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
SbZk{lWcq %energy in waveguide 2
L.R p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
v/.2Z(sZ %energy in waveguide 3
8,R]R= for m3 = 1:1:M3 % Start space evolution
D >m LSh s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
p|((r?{ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
'L,rJ =M3 s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
IV *}w"r sca1 = fftshift(fft(s1)); % Take Fourier transform
J kA~Ol sca2 = fftshift(fft(s2));
H [v~ sca3 = fftshift(fft(s3));
z TK sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
"7 l}X{b sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
w+}dm ^X sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
YZk& 'w s3 = ifft(fftshift(sc3));
YMWy5 \ s2 = ifft(fftshift(sc2)); % Return to physical space
l YhwV\3 s1 = ifft(fftshift(sc1));
[bcqaT end
2vXMrh\ p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
BoXCc"q[ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
^;2L` U@5 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
iZ:-V8{ P1=[P1 p1/p10];
M *}$$Fe| P2=[P2 p2/p10];
i2*nYd`K P3=[P3 p3/p10];
t.w?OyO P=[P p*p];
pZR^ HOq end
d.
a> (G figure(1)
OT [t
EqQ plot(P,P1, P,P2, P,P3);
&a0%7ea`.S Z+}SM]m 转自：
http://blog.163.com/opto_wang/
