计算脉冲在非线性耦合器中演化的Matlab 程序 6`0mta Q qw7@(R'" % This Matlab script file solves the coupled nonlinear Schrodinger equations of
JCPUM *g8 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
%&->%U| ' % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
!@ x+q)2 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^ K7ic,{ {&P
FXJ %fid=fopen('e21.dat','w');
R*oXmuOsYA N = 128; % Number of Fourier modes (Time domain sampling points)
I=7Y]w= M1 =3000; % Total number of space steps
@WQK>-=(3 J =100; % Steps between output of space
[6)UhS8 T =10; % length of time windows:T*T0
ly4s"4v T0=0.1; % input pulse width
d{3@h +zL MN1=0; % initial value for the space output location
JXixYwm dt = T/N; % time step
I.Y['%8,5~ n = [-N/2:1:N/2-1]'; % Index
ZT[3aXS t = n.*dt;
B nCKSg7V u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
R64!>o"nED u20=u10.*0.0; % input to waveguide 2
Ul_M3"Z u1=u10; u2=u20;
?9 HhG?_x U1 = u1;
Qd_Y\PzS U2 = u2; % Compute initial condition; save it in U
gP-nluq ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
QD TBWM% w=2*pi*n./T;
osOVg0Gyj g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
Io|X#\K L=4; % length of evoluation to compare with S. Trillo's paper
5jgdbHog] dz=L/M1; % space step, make sure nonlinear<0.05
C@Nv;;AlU for m1 = 1:1:M1 % Start space evolution
^pS+/ZSi^ u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
xy8#2 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
6oinidB[l ca1 = fftshift(fft(u1)); % Take Fourier transform
*d(SI<j ca2 = fftshift(fft(u2));
X; 5Jb c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
=?])['VaA c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
d'*]ns u2 = ifft(fftshift(c2)); % Return to physical space
lJzl6& u1 = ifft(fftshift(c1));
X53mzs if rem(m1,J) == 0 % Save output every J steps.
ESg+n(R U1 = [U1 u1]; % put solutions in U array
[xfaj'j=@ U2=[U2 u2];
h 6%[q x< MN1=[MN1 m1];
'q>2t}K G z1=dz*MN1'; % output location
ExSO|g]% end
>tG+?Y'{ end
FG%j {_Ez hg=abs(U1').*abs(U1'); % for data write to excel
TZ;p0^( ha=[z1 hg]; % for data write to excel
7
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ZpD t1=[0 t'];
:s-o0$PlJ hh=[t1' ha']; % for data write to excel file
D Y{cQb %dlmwrite('aa',hh,'\t'); % save data in the excel format
nRb^<cZf figure(1)
KECEl K3uj waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Nwc!r ( figure(2)
v)f7};"z waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
/ahNnCtu?1 1|ZhPsD.}g 非线性超快脉冲耦合的数值方法的Matlab程序 3L _I[T$s 1/ZR*f a 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。
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! 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
o5Y2vmz?9 6al=Cwf 9p@C4oen ~AG$5 ! % This Matlab script file solves the nonlinear Schrodinger equations
p O~c<d}b % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
BHj\G7,S % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
fd8!KO % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
kax\h U@Tj B C=1;
JR9$. fGJ M1=120, % integer for amplitude
D H^T x M3=5000; % integer for length of coupler
Y-~~,Yl~ N = 512; % Number of Fourier modes (Time domain sampling points)
td{O}\s7D dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
.5> 20\b2 T =40; % length of time:T*T0.
wP"q<W
g dt = T/N; % time step
.wK1El{bf n = [-N/2:1:N/2-1]'; % Index
?@R")$ t = n.*dt;
u-DK_^v4M ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
HFo-4 " w=2*pi*n./T;
LS.r%:$mb g1=-i*ww./2;
0 nW F g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
M R'o{?{e` g3=-i*ww./2;
XD-^w_ P1=0;
mzD^ Y<LTd P2=0;
zzZg$9PT[ P3=1;
uH\kQ9f P=0;
*s)}Bj for m1=1:M1
RbQ < m!A p=0.032*m1; %input amplitude
+`bC%\T8? s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
ad n|N s1=s10;
>O]s&34 s20=0.*s10; %input in waveguide 2
z, *:x4}F s30=0.*s10; %input in waveguide 3
7;LO2<|1 s2=s20;
~fzuwz s3=s30;
Y:x/!- p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
H5nS%D %energy in waveguide 1
vz`@x45K p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
N
dR ] %energy in waveguide 2
l Q*eH1 0H p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
?\H.S9 CZ^ %energy in waveguide 3
rOl6lQW for m3 = 1:1:M3 % Start space evolution
A8?[6^%O | s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
;RN8\re s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
=^h~! ovj: s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
o ;`!kIQ sca1 = fftshift(fft(s1)); % Take Fourier transform
Jp;k+ "<q sca2 = fftshift(fft(s2));
8&}~'4[b[$ sca3 = fftshift(fft(s3));
'pP-rdx sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
@?&W m3x9 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
$W!]fc ZlB sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
hSqMaX%G s3 = ifft(fftshift(sc3));
P#G.lft"O s2 = ifft(fftshift(sc2)); % Return to physical space
zp=!8 Av s1 = ifft(fftshift(sc1));
o;J;*~g end
X<MpN5%|Wo p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
f\ "` 7 p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
~v: #zU p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
8?jxDW
a P1=[P1 p1/p10];
p/|(,)'+jx P2=[P2 p2/p10];
: d'65KMi P3=[P3 p3/p10];
x3p9GAd# P=[P p*p];
T$b\Q end
9NIy# figure(1)
4nX(:K}> plot(P,P1, P,P2, P,P3);
Uh6mGL z*& c %<2z 转自：
http://blog.163.com/opto_wang/
