计算脉冲在非线性耦合器中演化的Matlab 程序 N"zg)MsX #
9@K % This Matlab script file solves the coupled nonlinear Schrodinger equations of
*K'_"2J % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
+U^H`\EUr % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
Q&?^eOI&#( % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
4))5l9kc. 1Z_2s2`p %fid=fopen('e21.dat','w');
6Q x[W>I N = 128; % Number of Fourier modes (Time domain sampling points)
!8@8 M1 =3000; % Total number of space steps
~:xR0dqx J =100; % Steps between output of space
h(4&!x
T =10; % length of time windows:T*T0
AK_,$'f T0=0.1; % input pulse width
12 TX _ 0 MN1=0; % initial value for the space output location
v"v -c!k dt = T/N; % time step
? `+G0VT n = [-N/2:1:N/2-1]'; % Index
%Mxc"% w t = n.*dt;
jiGXFM2 u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
0/4"Jh$t u20=u10.*0.0; % input to waveguide 2
k )=Gyv < u1=u10; u2=u20;
mJYG k_ua U1 = u1;
14S_HwX U2 = u2; % Compute initial condition; save it in U
'mm ~+hp ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
:={rPj-nU w=2*pi*n./T;
k"pN g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
C lWxL#L6~ L=4; % length of evoluation to compare with S. Trillo's paper
K j/{V dz=L/M1; % space step, make sure nonlinear<0.05
\<kQ::o1y for m1 = 1:1:M1 % Start space evolution
`Re {j{~s u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
x4Wu`-4^ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
3 :mZ1+ ca1 = fftshift(fft(u1)); % Take Fourier transform
y py ca2 = fftshift(fft(u2));
?C`&*+ c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
~LU$ n o^ c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
["~T)d' u2 = ifft(fftshift(c2)); % Return to physical space
4DV@- u1 = ifft(fftshift(c1));
,1e\}^ if rem(m1,J) == 0 % Save output every J steps.
+ :;6kyM6X U1 = [U1 u1]; % put solutions in U array
gaC [%M U2=[U2 u2];
E (miQ MN1=[MN1 m1];
y.,li< z1=dz*MN1'; % output location
k* e $_ end
_(J4 end
Y0;66bfh} hg=abs(U1').*abs(U1'); % for data write to excel
m;oCi }fL ha=[z1 hg]; % for data write to excel
DPBWw[ t1=[0 t'];
R^Y>v5jAe hh=[t1' ha']; % for data write to excel file
w%uM=YmuT %dlmwrite('aa',hh,'\t'); % save data in the excel format
rGgP9
( figure(1)
Mq Q'Kjo waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
f|NWn`#bY figure(2)
,UATT]> waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
Dwbt^{N ^ 8\BYm|%aa 非线性超快脉冲耦合的数值方法的Matlab程序 G"|c_qX BRF4 p: 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
[+ (fN Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
X( qs]: ! vGJ 7 ?O.'_YS >)8 <d3 m % This Matlab script file solves the nonlinear Schrodinger equations
w1:%P36H % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
! D~\uW1b % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
5]F4.sa % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
5{\ ;7( 7$A=|/'nSA C=1;
7f ]O / M1=120, % integer for amplitude
%~E Oq\& M3=5000; % integer for length of coupler
P:k!dRb9{ N = 512; % Number of Fourier modes (Time domain sampling points)
|TRl >1rv dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
sL4+O P- T =40; % length of time:T*T0.
q?=_{oH9 dt = T/N; % time step
jVInTR0f[ n = [-N/2:1:N/2-1]'; % Index
Gi Max t = n.*dt;
j UCDf-_ m ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
'~ n=< Y w=2*pi*n./T;
h{.x:pPXy g1=-i*ww./2;
b.mWB`59 g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
ds:&{~7L<T g3=-i*ww./2;
nV>=n, +s" P1=0;
JVq`v#8 P2=0;
i/aj;t P3=1;
B/gI~e0 P=0;
3 adF) mh for m1=1:M1
5@yBU wMSj p=0.032*m1; %input amplitude
)vy_m_f& s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
Wf>=^ ~` s1=s10;
#/o1D^ s20=0.*s10; %input in waveguide 2
O_^
u Lp s30=0.*s10; %input in waveguide 3
.v[!_bk8C s2=s20;
jM;?);Dd s3=s30;
)@E'yHYO> p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
g<s;uRA4O9 %energy in waveguide 1
7~2V5 @{< p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
y7-dae k %energy in waveguide 2
$x;(C[ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
F:'>zB]-} %energy in waveguide 3
+{[E Ow for m3 = 1:1:M3 % Start space evolution
Bt(U,nFB s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
-MuKeCg i s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
VNHt ]Ewj s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
`(VVb@:o sca1 = fftshift(fft(s1)); % Take Fourier transform
L] 3gHq sca2 = fftshift(fft(s2));
]6;oS-4gu? sca3 = fftshift(fft(s3));
x_OZdI sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
& n9 srs sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
^k4 n sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
/A>1TPb09" s3 = ifft(fftshift(sc3));
MUR Hv3 s2 = ifft(fftshift(sc2)); % Return to physical space
g{^(EZ, s1 = ifft(fftshift(sc1));
z.0!FUd end
"xp>Vj p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
8rM1kOCf p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
'OvyQ/T
p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
%)PQomn? P1=[P1 p1/p10];
DP=\FG"}x P2=[P2 p2/p10];
L ]QBh\ P3=[P3 p3/p10];
H;Cv] - P=[P p*p];
Q)ZbnR2Z8 end
{z*`*
O@ figure(1)
% QI6`@Y" plot(P,P1, P,P2, P,P3);
d1hXzJs 'jj J[16"d 转自：
http://blog.163.com/opto_wang/
