计算脉冲在非线性耦合器中演化的Matlab 程序 9}G.F r ;hz m&My % This Matlab script file solves the coupled nonlinear Schrodinger equations of
H}vq2 |MN % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
GI']&{ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
f-$%Ck$%, % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
@M=xdZNyJ 4C m+xAXG %fid=fopen('e21.dat','w');
;tg9$P<85 N = 128; % Number of Fourier modes (Time domain sampling points)
$^~dqmE2, M1 =3000; % Total number of space steps
,%Sf,h?" ^ J =100; % Steps between output of space
TuR.'kE@ T =10; % length of time windows:T*T0
w\SfzJN T0=0.1; % input pulse width
.Aj4?AXWc MN1=0; % initial value for the space output location
J7a_a >Y dt = T/N; % time step
^I! u H1G n = [-N/2:1:N/2-1]'; % Index
m}`!FaB # t = n.*dt;
f i#p('8 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
A43 mX !g\ u20=u10.*0.0; % input to waveguide 2
|&wwH&<[z u1=u10; u2=u20;
V[#eeH)/ U1 = u1;
uPh/u! U2 = u2; % Compute initial condition; save it in U
Lgr(j60 s ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
a\_?zi]s&, w=2*pi*n./T;
#ATV#/hW g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
{&3{_Ml L=4; % length of evoluation to compare with S. Trillo's paper
>_esLsPWh] dz=L/M1; % space step, make sure nonlinear<0.05
EUGN`t-M for m1 = 1:1:M1 % Start space evolution
(58}G2}q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
,;%F\<b u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
K-X@3&X} ca1 = fftshift(fft(u1)); % Take Fourier transform
D0 5JQ* ca2 = fftshift(fft(u2));
_|1m]2'9 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
Wks?9 )Is c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
ZlEQzL~ u2 = ifft(fftshift(c2)); % Return to physical space
?R#?=<VkG u1 = ifft(fftshift(c1));
*gGL5<%T: if rem(m1,J) == 0 % Save output every J steps.
4C]>{osv U1 = [U1 u1]; % put solutions in U array
>n(Ga9E U2=[U2 u2];
&[#iM0;)W0 MN1=[MN1 m1];
Z~[E ZgIg z1=dz*MN1'; % output location
R%EpF'[~[ end
K."%PdC end
E=3UaYr hg=abs(U1').*abs(U1'); % for data write to excel
S:F8` Gh ha=[z1 hg]; % for data write to excel
Aq3.%,X2H t1=[0 t'];
u*w'.5l hh=[t1' ha']; % for data write to excel file
FV~ENpncP %dlmwrite('aa',hh,'\t'); % save data in the excel format
d$ f3 Cre figure(1)
K3* 8-Be waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
J
n~t>? figure(2)
X<p'& waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
J>w3>8!>7 0D==0n 非线性超快脉冲耦合的数值方法的Matlab程序 XSBh+ )0Ww %Eq4>o?D 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。
V(#z{! 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
8
o^ h\9I .).}ffhOL G?$0OU : *g3PhNE % This Matlab script file solves the nonlinear Schrodinger equations
L!qXt(` % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
0pW?v: !H % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
7c8A|E0\mF % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
n,l{1 q 0r/pZ3/ C=1;
5`t MH gQO M1=120, % integer for amplitude
1&2X*$]y M3=5000; % integer for length of coupler
P-Up v6J3 N = 512; % Number of Fourier modes (Time domain sampling points)
u6#FG9W 7 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
Gm1 [PAj T =40; % length of time:T*T0.
a9%^Jvm" dt = T/N; % time step
{];8jdg/? n = [-N/2:1:N/2-1]'; % Index
aK +jpi4? t = n.*dt;
0x1#^dII ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
I&Dp~aEM] w=2*pi*n./T;
-ufO,tJRLL g1=-i*ww./2;
]>_Ie?L)< g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
] - +%]' g3=-i*ww./2;
e6y,)W"WW2 P1=0;
"54t7 P2=0;
k. @OFkX. P3=1;
7Z7e}|
\W P=0;
|XV@/ZGl~ for m1=1:M1
z]d2
rzV(_ p=0.032*m1; %input amplitude
&ZR} Z7E*= s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Bsc&# s1=s10;
~k[mowz0 s20=0.*s10; %input in waveguide 2
kKlcK_b; s30=0.*s10; %input in waveguide 3
u |eV'-R)s s2=s20;
G9qN1q~ s3=s30;
yKb+bm&5:' p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
HQ0fY %energy in waveguide 1
,e93I6 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
~u^MRe|` %energy in waveguide 2
a 9H^e<g p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
l2|[ %energy in waveguide 3
WJ[ybzV j for m3 = 1:1:M3 % Start space evolution
-RK R. , s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
N)0V 6 q" s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
^f?>;,<& s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
E|~)"= sca1 = fftshift(fft(s1)); % Take Fourier transform
D.;iz>_}Y sca2 = fftshift(fft(s2));
oEN^O:9e sca3 = fftshift(fft(s3));
Jb1L[sT2 sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Ng 3r`S"_< sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
|08'd 5 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
duT'$}2@> s3 = ifft(fftshift(sc3));
tX'2 $} s2 = ifft(fftshift(sc2)); % Return to physical space
='z4bU s1 = ifft(fftshift(sc1));
0*{ 2^\ end
BSd\Sg4 p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
[19QpK WM p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
Eb.k:8?Tn p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
aFf( m- P1=[P1 p1/p10];
q3 7d:Hp P2=[P2 p2/p10];
"' @>cJ= P3=[P3 p3/p10];
H7Y :l0b P=[P p*p];
\:Vm7Zg end
q1_iV.G< figure(1)
hwj:$m R plot(P,P1, P,P2, P,P3);
.d?2Kc)SV\ 57~/QEdy 转自：
http://blog.163.com/opto_wang/
