计算脉冲在非线性耦合器中演化的Matlab 程序 dpZ7eJ nen6!bw4 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
kR^7Z7+#* % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
~D@V@sX % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
k(=\&T % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
jCW>=1:JGY fj0+a0h %fid=fopen('e21.dat','w');
qt/syF&s N = 128; % Number of Fourier modes (Time domain sampling points)
=/6.4;8 M1 =3000; % Total number of space steps
Z/q%%(fh 0 J =100; % Steps between output of space
`m3@mJ!>\ T =10; % length of time windows:T*T0
z:u`W#Rf T0=0.1; % input pulse width
T_Z@uZom. MN1=0; % initial value for the space output location
eN/sW!:P| dt = T/N; % time step
c/;t.+g n = [-N/2:1:N/2-1]'; % Index
L)8 +/+ t = n.*dt;
E=~H,~ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
s%GiM u20=u10.*0.0; % input to waveguide 2
><LIOFqsS u1=u10; u2=u20;
~Zl`Ap U1 = u1;
-J[zJ4z# U2 = u2; % Compute initial condition; save it in U
Cb=r 8C ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
T~"tex] w=2*pi*n./T;
C>v g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
(n" ) L=4; % length of evoluation to compare with S. Trillo's paper
@kvp2P+O dz=L/M1; % space step, make sure nonlinear<0.05
OOl{ for m1 = 1:1:M1 % Start space evolution
vR,HCI u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
t)cG_+rJ u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
a:zx&DwM ca1 = fftshift(fft(u1)); % Take Fourier transform
YL){o$-N"J ca2 = fftshift(fft(u2));
32~Tf, c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
W U<#_by
g c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
X&wK< u2 = ifft(fftshift(c2)); % Return to physical space
+ W@r p# u1 = ifft(fftshift(c1));
~|DF-t
V if rem(m1,J) == 0 % Save output every J steps.
V]q{N-Iq U1 = [U1 u1]; % put solutions in U array
?b#?Vz U2=[U2 u2];
QMtt:f]?i MN1=[MN1 m1];
ATnD~iACY z1=dz*MN1'; % output location
]2h[.qa end
wW%I < M end
Lj~lfO hg=abs(U1').*abs(U1'); % for data write to excel
I,YGm
ha=[z1 hg]; % for data write to excel
P?9CBhN t1=[0 t'];
]VwAHT&je hh=[t1' ha']; % for data write to excel file
jQb=N%5s %dlmwrite('aa',hh,'\t'); % save data in the excel format
7]nPWz1%* figure(1)
_Fz)2h,3 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
I]k'0LG*^ figure(2)
gKYn* waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
o8s&n3mY}y XX6&%7( 非线性超快脉冲耦合的数值方法的Matlab程序 LL[+QcH hJ}G5pX 在研究脉冲在非线性耦合器中的演变时,我们需要求解非线性偏微分方程组。在如下的
论文中,我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
G x,D'H' Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+vU.#C_2 SbGp {;p/V\ Ix(4<s % This Matlab script file solves the nonlinear Schrodinger equations
5Q%#Z
L/' % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
qb" ! % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
4k#B5^iJ % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
[")0{LSA= y:,{U*49 C=1;
8vT:icl M1=120, % integer for amplitude
A%GJ|h,i M3=5000; % integer for length of coupler
3/ [= N = 512; % Number of Fourier modes (Time domain sampling points)
PH7L#H^ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
]$L[3qA. T =40; % length of time:T*T0.
?BLOc;I&a dt = T/N; % time step
3YLnh@- n = [-N/2:1:N/2-1]'; % Index
1B1d>V$* t = n.*dt;
+$UfP(XmH ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
<=zGaU, w=2*pi*n./T;
<;XJ::d g1=-i*ww./2;
|hdh4P$+| g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
B}M J?uvA g3=-i*ww./2;
/C(L(X P1=0;
fk"{G>&8 P2=0;
8odVdivh P3=1;
.H>Rqikj P=0;
K&X'^|en for m1=1:M1
I}q-J~s p=0.032*m1; %input amplitude
Gt1Up~\s s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
AH7k|6ku<* s1=s10;
)a}5\V s20=0.*s10; %input in waveguide 2
9.@(& s30=0.*s10; %input in waveguide 3
3jI.!xD` s2=s20;
g@U#Y#b@" s3=s30;
H 0h p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
=CVw0'yZ %energy in waveguide 1
asF-mf;D p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
2tbqmWw/s %energy in waveguide 2
H,I}R p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
cpy"1=K~M %energy in waveguide 3
O<E0L&4-& for m3 = 1:1:M3 % Start space evolution
oby*.61?5l s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
]SPB c s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
~H$XSNPi s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
C=]3NB>Jc sca1 = fftshift(fft(s1)); % Take Fourier transform
e56#Qb@$\ sca2 = fftshift(fft(s2));
jG2w(h/" sca3 = fftshift(fft(s3));
Cn55%: sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
MvW>ktkU sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
U;nC)'~YW9 sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
{L=[1 s3 = ifft(fftshift(sc3));
x3P@AC$\ s2 = ifft(fftshift(sc2)); % Return to physical space
t,+S~Cj| s1 = ifft(fftshift(sc1));
nZT@d;]U9 end
j*zK"n p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
N:<O p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
5_`}$"<~ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
J#kdyBmuO P1=[P1 p1/p10];
G<z)Ydh_ P2=[P2 p2/p10];
f8 jaMn9o P3=[P3 p3/p10];
xHGoCFB P=[P p*p];
yRznP) end
nT12[@:Tr figure(1)
;1dz?'%V plot(P,P1, P,P2, P,P3);
Chua>p!$g J
v#^GNm 转自:
http://blog.163.com/opto_wang/