计算脉冲在非线性耦合器中演化的Matlab 程序 S<9gyW FF jRf % This Matlab script file solves the coupled nonlinear Schrodinger equations of
w#rVSSXQ3 % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
3jS7 uU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
^} tuP % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
U(!?d ]en {F/q{c~] %fid=fopen('e21.dat','w');
Z] 7tjRvq) N = 128; % Number of Fourier modes (Time domain sampling points)
oHk27U G M1 =3000; % Total number of space steps
d&?F#$> 7| J =100; % Steps between output of space
mfz"M)1p1 T =10; % length of time windows:T*T0
^t7_3%%w T0=0.1; % input pulse width
y s/vI/e\ MN1=0; % initial value for the space output location
c{ 7<H dt = T/N; % time step
vU7&'ca n = [-N/2:1:N/2-1]'; % Index
y{?Kao7Ij t = n.*dt;
:Nkz,R? u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
zv,\@Z9.($ u20=u10.*0.0; % input to waveguide 2
`LqnEutzc u1=u10; u2=u20;
n}f3Vrl U1 = u1;
vyujC`61d U2 = u2; % Compute initial condition; save it in U
HMhLTl{; ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
51z / w=2*pi*n./T;
! *9FKDB{ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
X& /(x L=4; % length of evoluation to compare with S. Trillo's paper
2G H)iUmc dz=L/M1; % space step, make sure nonlinear<0.05
$Q=$?>4U for m1 = 1:1:M1 % Start space evolution
KjC[q u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
w gmWo8 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
v, 8Si'"i+ ca1 = fftshift(fft(u1)); % Take Fourier transform
@\+%GDv ca2 = fftshift(fft(u2));
f^~2^p
1te c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
7WX iG0 c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
K[n<+e;G u2 = ifft(fftshift(c2)); % Return to physical space
t6j-?c(' u1 = ifft(fftshift(c1));
3mybG%39 if rem(m1,J) == 0 % Save output every J steps.
vu44 !c@ U1 = [U1 u1]; % put solutions in U array
7bHE!#L`0 U2=[U2 u2];
>}mN i:6xq MN1=[MN1 m1];
6<#Sl w [ z1=dz*MN1'; % output location
f]hBPk Z6 end
$x/J+9Ww end
ykJ+%gla hg=abs(U1').*abs(U1'); % for data write to excel
DZ,<Jmg&e* ha=[z1 hg]; % for data write to excel
mSy|&(l t1=[0 t'];
vs* >onCf hh=[t1' ha']; % for data write to excel file
e#K rgUG %dlmwrite('aa',hh,'\t'); % save data in the excel format
* q+oeAYX figure(1)
LE<:.?<Z- waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
PE^eP}O1 figure(2)
]Qh[%GD waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
iOKr9%9?Z :vw0r` 非线性超快脉冲耦合的数值方法的Matlab程序 ZBPd(;"x+ 2-QuT"Gkd 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
}5QZ6i# Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
tWcizj;?wK kx:c*3q.k NJ.rv o7m99( % This Matlab script file solves the nonlinear Schrodinger equations
tX+0 GLz % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
Q S 5dP % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
fLLnf]. O % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
f34_?F<h zuK/(q Z C=1;
d&O'r[S M1=120, % integer for amplitude
tq2-.]Y@U M3=5000; % integer for length of coupler
B?$S~5
} N = 512; % Number of Fourier modes (Time domain sampling points)
Q]yV:7 dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
^qE<yn T =40; % length of time:T*T0.
.`:oP&9r dt = T/N; % time step
Z|V"8jE n = [-N/2:1:N/2-1]'; % Index
4x=V|" t = n.*dt;
XYz,NpK ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
xgZV0!% w=2*pi*n./T;
er&uC4Y]a g1=-i*ww./2;
Y{+zg9L* g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
=>gyc;{2K< g3=-i*ww./2;
!%SdTaC{T P1=0;
yg]suU<z] P2=0;
Oz"@yL} P3=1;
W@R$' r,@O P=0;
rD:gN%B= for m1=1:M1
x.j Yip p=0.032*m1; %input amplitude
ls8olLM> s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
_ C7abw- s1=s10;
$)kk8Q4 +K s20=0.*s10; %input in waveguide 2
IKNFYe[9e s30=0.*s10; %input in waveguide 3
}CB=c]p s2=s20;
o=mq$Z:} s3=s30;
fvAh?<Ul p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
G%V=idU*" %energy in waveguide 1
r[C3u[ p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
eO|^Lu]+ %energy in waveguide 2
'6Pu[^x p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
:F!dTD$ %energy in waveguide 3
@m !9"QhC for m3 = 1:1:M3 % Start space evolution
[TiT ff&LV s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
pgLzFY[' s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
N7RG5 ? s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
ae9k[=- sca1 = fftshift(fft(s1)); % Take Fourier transform
3Hb .Z LE# sca2 = fftshift(fft(s2));
.N2nJ/ sca3 = fftshift(fft(s3));
$sd3h\P&R sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,d9%Ce.$2 sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
=]5DYRhX] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
|!jYv'% s3 = ifft(fftshift(sc3));
ZNL;8sI?> s2 = ifft(fftshift(sc2)); % Return to physical space
0- ;DN:> s1 = ifft(fftshift(sc1));
mVc'%cPaw end
zm;*:]S p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
?<>,XyY p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
S*2L4Uj`| p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
z[0LU]b< P1=[P1 p1/p10];
E :' P2=[P2 p2/p10];
d[P>jl%7 P3=[P3 p3/p10];
wB1-|= K1 P=[P p*p];
!}Woo$#ND end
(dO'_s&M]/ figure(1)
o3\SO plot(P,P1, P,P2, P,P3);
*_"c! eW 8JjU 9# 转自：
http://blog.163.com/opto_wang/
