计算脉冲在非线性耦合器中演化的Matlab 程序 $6 Q^u r: 9 " q-Bb % This Matlab script file solves the coupled nonlinear Schrodinger equations of
}O*` I( % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
qS\#MMsTd % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
e4` L8 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
3'.@aMA@ J-
S.m( %fid=fopen('e21.dat','w');
1<G+KC[F N = 128; % Number of Fourier modes (Time domain sampling points)
N#l2 wT M1 =3000; % Total number of space steps
K ~mUO J =100; % Steps between output of space
jae9!W i T =10; % length of time windows:T*T0
I Id4w~| T0=0.1; % input pulse width
O?X [&t
MN1=0; % initial value for the space output location
^i%S}V K dt = T/N; % time step
gbuh04#~ n = [-N/2:1:N/2-1]'; % Index
ULA r! t = n.*dt;
bq ED5;d'# u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
Ef#LRcG-Z u20=u10.*0.0; % input to waveguide 2
upuN$4m&{ u1=u10; u2=u20;
?:wb#k)Z/ U1 = u1;
W#bYz{s. U2 = u2; % Compute initial condition; save it in U
KzVi: Hm ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
O#U maNj/ w=2*pi*n./T;
Qel)%|dOn g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
m'N AM%$}J L=4; % length of evoluation to compare with S. Trillo's paper
n.+ '9Fj dz=L/M1; % space step, make sure nonlinear<0.05
(j'\h/ for m1 = 1:1:M1 % Start space evolution
M<Wi:r: u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
Y_CVDKdcY u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
To*+Z3Wd ca1 = fftshift(fft(u1)); % Take Fourier transform
y`va6 %u{ ca2 = fftshift(fft(u2));
w5 . ^meU c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
cp@Fj" c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
8Nzn%0(Q u2 = ifft(fftshift(c2)); % Return to physical space
- UkK$wP5 u1 = ifft(fftshift(c1));
B4b' 0p if rem(m1,J) == 0 % Save output every J steps.
:gV~L3YW5 U1 = [U1 u1]; % put solutions in U array
9InP2u\&: U2=[U2 u2];
kxhsDD$@p MN1=[MN1 m1];
ARu_S
B z1=dz*MN1'; % output location
NVb}uH*i end
R@K\ end
k K=VG<
:M hg=abs(U1').*abs(U1'); % for data write to excel
%NQ%6 B ha=[z1 hg]; % for data write to excel
6X@z(EEL t1=[0 t'];
hH`x*:Qja hh=[t1' ha']; % for data write to excel file
Be|! S_Y P %dlmwrite('aa',hh,'\t'); % save data in the excel format
zgGysjV figure(1)
r)|~Rs!y, waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
4fKvB@O@. figure(2)
9} 6 _B| waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
NIQ}A-b w<H Xe 非线性超快脉冲耦合的数值方法的Matlab程序 Rmw=~NP5 A1p~K*[[ 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。
nG'Yo8I^5 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
5$ =[x!x ;$iT]S sg,\!' Ln# o:" E % This Matlab script file solves the nonlinear Schrodinger equations
5}G_2<G % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
@m5J%8>k % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
<~dfp % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+DRt2a # eF%M2:&c; C=1;
STwGp<8 M1=120, % integer for amplitude
~Fb@E0 }! M3=5000; % integer for length of coupler
MQP9^+f)O? N = 512; % Number of Fourier modes (Time domain sampling points)
O H>.N"IG dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
w<B
S T =40; % length of time:T*T0.
z h2<!MH dt = T/N; % time step
wK2$hsque n = [-N/2:1:N/2-1]'; % Index
x~5,v5R^] t = n.*dt;
c6F?#@? ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
eA1g}ipm w=2*pi*n./T;
,&,%B|gT] g1=-i*ww./2;
K RxJ2 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
.8 QhJHwd g3=-i*ww./2;
W%+0 2_/) P1=0;
m^oG9&" ; P2=0;
'yCVB&`b P3=1;
.h
<=C&Yg P=0;
V30w`\1A for m1=1:M1
O + aK#eF p=0.032*m1; %input amplitude
Tp-W/YC s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
#MY oy7= s1=s10;
1?QVt fwY s20=0.*s10; %input in waveguide 2
Oey
Ph9^V s30=0.*s10; %input in waveguide 3
yr+QV:oVA s2=s20;
)s>|;K{ s3=s30;
h.?<( I p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
YQD `4ND %energy in waveguide 1
<p<6!tdO p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
lai@,_<GV %energy in waveguide 2
U)'YR$2< p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
uB+#<F/c %energy in waveguide 3
^JxVs
7 for m3 = 1:1:M3 % Start space evolution
fP<== DK s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
RK@K>)"f s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
jkl dr@t s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
p Imq< Z sca1 = fftshift(fft(s1)); % Take Fourier transform
r4u ,I<ZbH sca2 = fftshift(fft(s2));
?MywA'N@x sca3 = fftshift(fft(s3));
^N7cX K* sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
iJh{ ,0))g sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
8o :h/F sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
2. nT k s3 = ifft(fftshift(sc3));
O)^F z: s2 = ifft(fftshift(sc2)); % Return to physical space
~<u\YIJ s1 = ifft(fftshift(sc1));
d0T 8Cwc b end
?6*\ M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
CHS}tCfos> p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~Q"qz<WO p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
rui 8x4c P1=[P1 p1/p10];
EiD41N P2=[P2 p2/p10];
ipu~T ) } P3=[P3 p3/p10];
[|$C 2Dhw= P=[P p*p];
kK6t|Yn& end
,^CG\); figure(1)
sz%]rN6$ plot(P,P1, P,P2, P,P3);
@ [FO;4w UK'8cz9 转自：
http://blog.163.com/opto_wang/
