计算脉冲在非线性耦合器中演化的Matlab 程序 lN7YU-ygz 9w-;d =(Q % This Matlab script file solves the coupled nonlinear Schrodinger equations of
tY60~@YO& % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
&7KX`%K"D % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
uC? /p1 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
$Q`\- G4"n`89LK %fid=fopen('e21.dat','w');
Hm_&``=' N = 128; % Number of Fourier modes (Time domain sampling points)
Rc}#4pM8 M1 =3000; % Total number of space steps
%Z yt ;p2 J =100; % Steps between output of space
.19_E Q >+ T =10; % length of time windows:T*T0
UM. Se(kS T0=0.1; % input pulse width
o 'Z W MN1=0; % initial value for the space output location
D\ P-|} dt = T/N; % time step
-_f-j n = [-N/2:1:N/2-1]'; % Index
2K 2_- t = n.*dt;
>n5Kz]]% u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
7/bF0 4~% u20=u10.*0.0; % input to waveguide 2
'3B7F5uLx" u1=u10; u2=u20;
1+Bj` ACP U1 = u1;
g? > U2 = u2; % Compute initial condition; save it in U
#3YYE5cB ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
o6 8; -b'n w=2*pi*n./T;
Cil1wFBb g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
ZU5; w L=4; % length of evoluation to compare with S. Trillo's paper
n0w0]dJ&lc dz=L/M1; % space step, make sure nonlinear<0.05
nD Xy$ f8 for m1 = 1:1:M1 % Start space evolution
WU6F-{M"? u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
uC"Gm;0 u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
dEfP2 72M ca1 = fftshift(fft(u1)); % Take Fourier transform
|qb-iXW= ca2 = fftshift(fft(u2));
]GzfU'fOn| c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
9iGp0_J c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
BsYJIKfW u2 = ifft(fftshift(c2)); % Return to physical space
-V:7j8 u1 = ifft(fftshift(c1));
UL3u2g;d if rem(m1,J) == 0 % Save output every J steps.
|w.5*]?H U1 = [U1 u1]; % put solutions in U array
0~ cbB U2=[U2 u2];
y9 K'(/ MN1=[MN1 m1];
kQ .3J.Q5 z1=dz*MN1'; % output location
B{NGrC`5) end
\5F
{MBx ! end
/z4n?&tM hg=abs(U1').*abs(U1'); % for data write to excel
@eRv`O" ha=[z1 hg]; % for data write to excel
I_ na^s h* t1=[0 t'];
l6-%)6u> hh=[t1' ha']; % for data write to excel file
u@kr;^m %dlmwrite('aa',hh,'\t'); % save data in the excel format
!3Q^oR figure(1)
Edl .R}&1 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
+ $/mh figure(2)
=Ka :i> waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
8LlWXeD9 :Q>{Y 非线性超快脉冲耦合的数值方法的Matlab程序 (&qjY
I )IGx3+I
, 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
%F] :nk` Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
z5t"o ! 3 Oe\l[?$; " = * Wq*W+ 7=. % This Matlab script file solves the nonlinear Schrodinger equations
qZX\riR % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
v;IuB % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
%~qY\> % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_Zbgma sb c 4L++
u# C=1;
MW)=l
| G M1=120, % integer for amplitude
"ax"k0 M3=5000; % integer for length of coupler
E=l^&[dIl N = 512; % Number of Fourier modes (Time domain sampling points)
eed!SmP dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
),f d, T =40; % length of time:T*T0.
qr? RU .W dt = T/N; % time step
vkW]?::Cfd n = [-N/2:1:N/2-1]'; % Index
q#.+P1"U t = n.*dt;
0/zgjT|fe ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
R TeG\U w=2*pi*n./T;
Y !AQ7F g1=-i*ww./2;
axdRV1+s g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
KgEfh O$W g3=-i*ww./2;
r<-@.$lf P1=0;
6q~*\KRk P2=0;
f=nVK4DuZ P3=1;
be~'}`> P=0;
yx/.4DW1Ua for m1=1:M1
w&LL-~KI+ p=0.032*m1; %input amplitude
M}`G}* s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
_u8d`7$*% s1=s10;
S{c;n*x f s20=0.*s10; %input in waveguide 2
C9E@$4* s30=0.*s10; %input in waveguide 3
A@JZK+WB} s2=s20;
ph=U<D4 s3=s30;
G:{\-R' p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
kB ;!EuL %energy in waveguide 1
l*n4d[0J p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
firiYL"=44 %energy in waveguide 2
`i3fC&?C p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
7|q _JdKoU %energy in waveguide 3
u
YJL^I8M' for m3 = 1:1:M3 % Start space evolution
)`
90* s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
w}``2djR'W s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
'@eH)wh@m) s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
!gFUC<4bu sca1 = fftshift(fft(s1)); % Take Fourier transform
</Ry4x^A sca2 = fftshift(fft(s2));
73kL>u sca3 = fftshift(fft(s3));
pN7 v7rs sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
2V = bE- sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
R%^ AW2 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
[;hCwj# s3 = ifft(fftshift(sc3));
FK.Qj P: s2 = ifft(fftshift(sc2)); % Return to physical space
t+Hx&_pMj s1 = ifft(fftshift(sc1));
V NWa3`w end
g'1 ASMuR p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
x>~.cey p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
A0 1 D-) p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
(Y$48@x P1=[P1 p1/p10];
q. NvwJ P2=[P2 p2/p10];
ouR(l; P3=[P3 p3/p10];
rty&\u @} P=[P p*p];
odC}RdN end
9 aZ^m$tAt figure(1)
6`;+| H<$ plot(P,P1, P,P2, P,P3);
:Y2J7p[+ T&~7*j(|e 转自：
http://blog.163.com/opto_wang/
