计算脉冲在非线性耦合器中演化的Matlab 程序 `nAR/Ye :6k8\{^9"D % This Matlab script file solves the coupled nonlinear Schrodinger equations of
UF3g]>* % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
B$R"Ntp % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
f tS^|%p % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
_4eSDO[h \LYB% K} %fid=fopen('e21.dat','w');
+Bg$]~ T N = 128; % Number of Fourier modes (Time domain sampling points)
0E*q-$P M1 =3000; % Total number of space steps
C| #GODA J =100; % Steps between output of space
Y>Oh]? T =10; % length of time windows:T*T0
KIyhvY~ T0=0.1; % input pulse width
N03)G2 MN1=0; % initial value for the space output location
b@GL*Z dt = T/N; % time step
h(q,-')l_ n = [-N/2:1:N/2-1]'; % Index
9 7/"5i9 t = n.*dt;
F E`4%X u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
!GB\-( u20=u10.*0.0; % input to waveguide 2
#&fi[|%X$ u1=u10; u2=u20;
- ~ w5 yd U1 = u1;
eIZ7uSl U2 = u2; % Compute initial condition; save it in U
cK( )_RB# ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
&J>XKO nl w=2*pi*n./T;
D hN{Y8'~ g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
j#}wg`P"A L=4; % length of evoluation to compare with S. Trillo's paper
I4[sf dz=L/M1; % space step, make sure nonlinear<0.05
rG#o*oA for m1 = 1:1:M1 % Start space evolution
#~3$4j2U(y u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
]i$ <<u u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
8>U{>]WG ca1 = fftshift(fft(u1)); % Take Fourier transform
<c` + f PW ca2 = fftshift(fft(u2));
( (.b & c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
/INjP~ C c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
MK"p~b0-> u2 = ifft(fftshift(c2)); % Return to physical space
D<V[:~-o u1 = ifft(fftshift(c1));
VFm G \ if rem(m1,J) == 0 % Save output every J steps.
)4nf={iM U1 = [U1 u1]; % put solutions in U array
+<l6!r2Z U2=[U2 u2];
z|KQiLza MN1=[MN1 m1];
yf >
r G z1=dz*MN1'; % output location
pr\wI?:k end
^("23mhfJ end
\nfjz\"R?b hg=abs(U1').*abs(U1'); % for data write to excel
f*Z8C9) ha=[z1 hg]; % for data write to excel
v'0WE t1=[0 t'];
$N
!l-lu= hh=[t1' ha']; % for data write to excel file
*Sd}cD CO% %dlmwrite('aa',hh,'\t'); % save data in the excel format
LS"_-4I} figure(1)
y\a@'LFL waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
BM~>=emc figure(2)
a ~ waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
P\j n ht [h5~1N 非线性超快脉冲耦合的数值方法的Matlab程序 n(}cK@ ;u:A:Y4V 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
^bD )Tg5 K Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
U z* 7J n j90`O.K AVn?86ri 3np |\i % This Matlab script file solves the nonlinear Schrodinger equations
?* {Vn5aX{ % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
u&M:w5EM % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
9$
VudE>; % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
`G@(Z:]f,t J!\Cs1 !f C=1;
`>HM<Nn-0 M1=120, % integer for amplitude
=pT}] M3=5000; % integer for length of coupler
!7r k>YrY N = 512; % Number of Fourier modes (Time domain sampling points)
.RazjXAY dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
a^#\" c T =40; % length of time:T*T0.
-`f 1l8LD2 dt = T/N; % time step
s%bm1$} n = [-N/2:1:N/2-1]'; % Index
MvCB|N"q y t = n.*dt;
h^B~Fv> ~ ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
hL?"! w=2*pi*n./T;
nB|m!fi< g1=-i*ww./2;
Ii .0Bul g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
x(]Um! g3=-i*ww./2;
U } K]W>Z P1=0;
8wf[*6VwV P2=0;
- X]?ql*%` P3=1;
Ii.?|
u P=0;
s u}n3NsJ for m1=1:M1
c,yjsxETW p=0.032*m1; %input amplitude
M#u~] ?hS s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
>h
Rq s1=s10;
+|w%}/N s20=0.*s10; %input in waveguide 2
"<N 2TDF5 s30=0.*s10; %input in waveguide 3
Q i;62M s2=s20;
yq=rv$.s s3=s30;
BJDSk#!J!{ p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
V * I2
%energy in waveguide 1
%a=^T?8 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
DtFzT>$^F %energy in waveguide 2
W2w A66MB p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
K ; e R) %energy in waveguide 3
[ uLpm*7 for m3 = 1:1:M3 % Start space evolution
UhX)?'J s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
W<c95QD. s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
8XG|K`'u s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
PAy/"R9DT- sca1 = fftshift(fft(s1)); % Take Fourier transform
}2]m]D@%7 sca2 = fftshift(fft(s2));
FoW|BGA~ sca3 = fftshift(fft(s3));
KsDovy< sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
s?yl4\]Muf sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
lD-H Q d sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
bH Nf> s3 = ifft(fftshift(sc3));
]r(&hqdR s2 = ifft(fftshift(sc2)); % Return to physical space
\c\z 6;j s1 = ifft(fftshift(sc1));
(7 O?NS end
0F-%C>&g p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
\%czNF p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
8dUP_t~d#q p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
W @]t P1=[P1 p1/p10];
\sEH)$R' P2=[P2 p2/p10];
%jh
gKq P3=[P3 p3/p10];
nrM_ay P=[P p*p];
= ,J-D6J? end
>$:_M*5 figure(1)
v\G+t2{ plot(P,P1, P,P2, P,P3);
2DX V~> TMG|"| 转自：
http://blog.163.com/opto_wang/
