计算脉冲在非线性耦合器中演化的Matlab 程序 A#:8X1w 7jezw'\=~ % This Matlab script file solves the coupled nonlinear Schrodinger equations of
@aB9%An1 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
$5/\Z % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
92(~'5Qr % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
FuMq|S M'| )dM| %fid=fopen('e21.dat','w');
S _T N = 128; % Number of Fourier modes (Time domain sampling points)
`V~LV<v5 M1 =3000; % Total number of space steps
n8FT<pUq J =100; % Steps between output of space
JFJIls T =10; % length of time windows:T*T0
-RC v7U` T0=0.1; % input pulse width
(6#M9XL MN1=0; % initial value for the space output location
B? TpBd dt = T/N; % time step
El 1:?4; n = [-N/2:1:N/2-1]'; % Index
z[FI 2jl t = n.*dt;
4^ MSX+zt u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
gL,"ef+nM u20=u10.*0.0; % input to waveguide 2
Cji#?!Ra? u1=u10; u2=u20;
$:]tcY-L9 U1 = u1;
7BrV<)ih{* U2 = u2; % Compute initial condition; save it in U
?k
w/S4 ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
)T<D6l
Lt w=2*pi*n./T;
X o_] v g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
zK /f$} L=4; % length of evoluation to compare with S. Trillo's paper
v+ 7*R)/ dz=L/M1; % space step, make sure nonlinear<0.05
t_Z _!Qy for m1 = 1:1:M1 % Start space evolution
MyM+C} u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
L+(C5L93} u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
{SHqW5VX ca1 = fftshift(fft(u1)); % Take Fourier transform
x{QBMe` ca2 = fftshift(fft(u2));
,?#*eJD c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
8q{1E ];:q c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
I<9n(rA u2 = ifft(fftshift(c2)); % Return to physical space
)j( fWshP u1 = ifft(fftshift(c1));
mj,qQ=n;p if rem(m1,J) == 0 % Save output every J steps.
!}j,TPpG U1 = [U1 u1]; % put solutions in U array
^VC7C~NZ!M U2=[U2 u2];
^h"n03VFA MN1=[MN1 m1];
u[:
P z1=dz*MN1'; % output location
,?;sT`Mh) end
g!.Ut:8L9 end
#EEG>M*xB hg=abs(U1').*abs(U1'); % for data write to excel
9DY|Sa]#= ha=[z1 hg]; % for data write to excel
f^yw W[dF t1=[0 t'];
7s$6XO! hh=[t1' ha']; % for data write to excel file
)fy <P;g %dlmwrite('aa',hh,'\t'); % save data in the excel format
Y+OYo I figure(1)
% Mw' e/? waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
EK: Y2W Z figure(2)
N!.k q4$. waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
q!9^#c '?z9,oW{ 非线性超快脉冲耦合的数值方法的Matlab程序 1Q0%7zRirI @-}D7? 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。
y`\mQ48V 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
pqk cf \ ^#}dPGm Ny]'RS- X9DM ^tt % This Matlab script file solves the nonlinear Schrodinger equations
mQmBf|Rl % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
-??!@R7V % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
DBLA% {05 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
^l&nB . l@~1CMyN C=1;
d.L OyO M1=120, % integer for amplitude
g & |4 M3=5000; % integer for length of coupler
J2)-cY5G N = 512; % Number of Fourier modes (Time domain sampling points)
YG -Z.{d5Z dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
JTSq{NN T =40; % length of time:T*T0.
AB/,S dt = T/N; % time step
`WraOsoY n = [-N/2:1:N/2-1]'; % Index
XKpL4]{&q4 t = n.*dt;
HKq2Js ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
XhQw+j~1. w=2*pi*n./T;
W\nHX I g1=-i*ww./2;
YJ &lB&xH g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
4jDs 0Hn" g3=-i*ww./2;
"
whO} P1=0;
iMP*]K-O P2=0;
bbfDt^ P3=1;
oV%(
37W9= P=0;
D2>hMc for m1=1:M1
^zBjG/'7 p=0.032*m1; %input amplitude
</K%i;l s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~E^yM=:h s1=s10;
n25irCD` s20=0.*s10; %input in waveguide 2
K> c8r8! s30=0.*s10; %input in waveguide 3
va`l*N5 s2=s20;
2r PcNh9 s3=s30;
\O8Y3|< p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
d ,h~u{ %energy in waveguide 1
^8o_Iz)r, p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
pDLu + }@ %energy in waveguide 2
hj[+d%YZY" p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
k X ~-g %energy in waveguide 3
XgwMppacw for m3 = 1:1:M3 % Start space evolution
{ r< (t# s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
>%PL_<Vbv s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
hLDch5J5~ s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
KdB q@ sca1 = fftshift(fft(s1)); % Take Fourier transform
LUe>)eqw sca2 = fftshift(fft(s2));
1Y F+(fk sca3 = fftshift(fft(s3));
el2*\(XT sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
_IQU<Za sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
4yJ*85e] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Q1O_CC} s3 = ifft(fftshift(sc3));
Gvt;Q,hH s2 = ifft(fftshift(sc2)); % Return to physical space
reqfgNg s1 = ifft(fftshift(sc1));
Lo$Z>u4(c end
;~'cITL p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
vp )}/&/ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
2A@Y&g(6T7 p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
5 WN`8? P1=[P1 p1/p10];
/pAm8vK P2=[P2 p2/p10];
EPE!V> P3=[P3 p3/p10];
cuV8# :
i P=[P p*p];
L5 -T6CD end
LK
figure(1)
w (vE2Y ? plot(P,P1, P,P2, P,P3);
d'lr:=GQ 'XZI{q2i 转自：
http://blog.163.com/opto_wang/
