计算脉冲在非线性耦合器中演化的Matlab 程序 &r 5&6p "(HA9: % This Matlab script file solves the coupled nonlinear Schrodinger equations of
qr<-eJf % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
FV vv % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
8Izn'>" % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4EaS g# @8 oDy$j %fid=fopen('e21.dat','w');
[~Z'xY
y N = 128; % Number of Fourier modes (Time domain sampling points)
,YAPCj M1 =3000; % Total number of space steps
5kRwSOG%' J =100; % Steps between output of space
]%WD} 4e T =10; % length of time windows:T*T0
GDNh?R T0=0.1; % input pulse width
a
V+o\fId MN1=0; % initial value for the space output location
S1x.pLHj8 dt = T/N; % time step
B~ 'VDOG$Z n = [-N/2:1:N/2-1]'; % Index
buxI- wv t = n.*dt;
<?=mLOo = u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
^R 8U-V8: u20=u10.*0.0; % input to waveguide 2
O[5_ 9W
4 u1=u10; u2=u20;
pJ)+}vascR U1 = u1;
{YO%JTQ U2 = u2; % Compute initial condition; save it in U
uZ=UBir ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
jU3 ;jm.) w=2*pi*n./T;
XeIUdg4>R g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
6|"!sW`%N L=4; % length of evoluation to compare with S. Trillo's paper
b[&,%Sm+6 dz=L/M1; % space step, make sure nonlinear<0.05
U`8^N.Snrp for m1 = 1:1:M1 % Start space evolution
I ]WeZ,E u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
7/U<\(V!g u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
JtrDZ;^@
ca1 = fftshift(fft(u1)); % Take Fourier transform
"Wn?8vR ca2 = fftshift(fft(u2));
zw%n!wc_\ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
+{=_| 3( c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
aJa^~*N/Aa u2 = ifft(fftshift(c2)); % Return to physical space
Kt!IyIa;Ht u1 = ifft(fftshift(c1));
HHu7{, if rem(m1,J) == 0 % Save output every J steps.
9Sj:nn^/u U1 = [U1 u1]; % put solutions in U array
lu@>?,< U2=[U2 u2];
e k;&<Z_ ] MN1=[MN1 m1];
a h!O&ECh z1=dz*MN1'; % output location
5[j!\d }U end
rO?x/{;ai end
|q.:hWYFpM hg=abs(U1').*abs(U1'); % for data write to excel
mZ0oa-Iy ha=[z1 hg]; % for data write to excel
;MR C~F= t1=[0 t'];
pJ*#aH[ySP hh=[t1' ha']; % for data write to excel file
:?:j$
=nWN %dlmwrite('aa',hh,'\t'); % save data in the excel format
v<J;S9u= figure(1)
gt t$O waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
N;`[R>Z~ figure(2)
g0:4zeL waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
!qw=I( ? m_R U 非线性超快脉冲耦合的数值方法的Matlab程序 : ! iPn% :2U C{_ 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。
Pq J* 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%LB|(@j{ >eG&gc@$1$ `j!2uRFe> yL3<X w| % This Matlab script file solves the nonlinear Schrodinger equations
H T,kx % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
g=YiR/O1QN % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
,I&0#+}n % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
<
8 Y<w|Hh k'I_,Z<, C=1;
-ynLuq#1A M1=120, % integer for amplitude
C}P
\kDM M3=5000; % integer for length of coupler
T;[c<gc/ N = 512; % Number of Fourier modes (Time domain sampling points)
~h^}W$pO dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
> v !c\ T =40; % length of time:T*T0.
%Rsf6 rJ dt = T/N; % time step
R5;eR(24G n = [-N/2:1:N/2-1]'; % Index
L I|HET_ t = n.*dt;
Nj-rZ%& ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
lQ<n
dt ~ w=2*pi*n./T;
hHl-;%# g1=-i*ww./2;
ocuVD C g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
B{o\RN U g3=-i*ww./2;
nk3< ]u P1=0;
+l?ro[#6&. P2=0;
,f0g|5yDf P3=1;
\y )4`A P=0;
@oc%4~zl for m1=1:M1
E e \-q p=0.032*m1; %input amplitude
+j: Ld( s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
K J^GUqVl s1=s10;
Ufe s20=0.*s10; %input in waveguide 2
rUpAiZfz > s30=0.*s10; %input in waveguide 3
%V1T !< s2=s20;
vgW1hWmHJ s3=s30;
(`y |AOs p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
I.0P7eA- %energy in waveguide 1
W]}V<S$ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
= 4WZ r %energy in waveguide 2
k mr
4cU5 p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
"gikX/Co= %energy in waveguide 3
-zLI!F 0 for m3 = 1:1:M3 % Start space evolution
G1^!e j s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
L8tLW09 s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
<d&)|W s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
8Pdn w/W sca1 = fftshift(fft(s1)); % Take Fourier transform
DD$P r&~= sca2 = fftshift(fft(s2));
cA SH gm sca3 = fftshift(fft(s3));
ftH%, /, sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
"sx& 8H" sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
, Y8X"~{A sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
5YH
mp7c-z s3 = ifft(fftshift(sc3));
LLY;IUK!R s2 = ifft(fftshift(sc2)); % Return to physical space
*#^1rKGWK s1 = ifft(fftshift(sc1));
OHnjI> / end
$(L 7/M p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
w:zC/5x` p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
/P"\ +Qp p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
to|9)\ P1=[P1 p1/p10];
h}&Il DG P2=[P2 p2/p10];
?[B[ F P3=[P3 p3/p10];
Dj. +5f' P=[P p*p];
XK-x*| end
T<?BIQz(} figure(1)
7<o;3gR7Kj plot(P,P1, P,P2, P,P3);
vGHYB1=~ DMN H?6 转自：
http://blog.163.com/opto_wang/
