计算脉冲在非线性耦合器中演化的Matlab 程序 &?gvW//L2 G@Y!*ZH*f % This Matlab script file solves the coupled nonlinear Schrodinger equations of
1O,<JrE+- % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
Yx{q VU % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
k(.6K[ b % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
8RJ^e[?o( 'lD"{^ %fid=fopen('e21.dat','w');
0xQ="aXE N = 128; % Number of Fourier modes (Time domain sampling points)
_]# ^2S M1 =3000; % Total number of space steps
HRxA0y= J =100; % Steps between output of space
y q2pg8% T =10; % length of time windows:T*T0
~t-!{F T0=0.1; % input pulse width
J"Z=`I)KON MN1=0; % initial value for the space output location
lboi\GP| dt = T/N; % time step
@?r[
$Ea1M n = [-N/2:1:N/2-1]'; % Index
f Nnemn@> t = n.*dt;
ht 1d[ u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
HM(S}> u20=u10.*0.0; % input to waveguide 2
e=m=IVY #W u1=u10; u2=u20;
CFU' -
#b U1 = u1;
e7^B3FOx U2 = u2; % Compute initial condition; save it in U
^<VJ8jk< ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
jA}b=c w=2*pi*n./T;
- .EH?{i g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
;9rS[$ ^$O L=4; % length of evoluation to compare with S. Trillo's paper
byTTLs,}d dz=L/M1; % space step, make sure nonlinear<0.05
` oq][| for m1 = 1:1:M1 % Start space evolution
3pF7} P u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
#7}1W[y9}l u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
Ghb Jty` ca1 = fftshift(fft(u1)); % Take Fourier transform
awic9 uMH ca2 = fftshift(fft(u2));
Ob#d;F c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
*l T: P- c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
=
olmBXn/ u2 = ifft(fftshift(c2)); % Return to physical space
dRD t.U!T u1 = ifft(fftshift(c1));
(6Tvu5*4U if rem(m1,J) == 0 % Save output every J steps.
aF41?.s U1 = [U1 u1]; % put solutions in U array
;0c
-+, U2=[U2 u2];
-FGQn
|h4 MN1=[MN1 m1];
:K)7_]y z1=dz*MN1'; % output location
(Iz$_( end
^f%hhpV@ end
/ Q nq,`z hg=abs(U1').*abs(U1'); % for data write to excel
>{HQ"{Q ha=[z1 hg]; % for data write to excel
y`| 86`
Y t1=[0 t'];
t3//
U # hh=[t1' ha']; % for data write to excel file
P ` xQL %dlmwrite('aa',hh,'\t'); % save data in the excel format
f"}g5eg+ figure(1)
e#t7 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
P< 5v\\ figure(2)
FP_q?=~rFs waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
(/a#1Pd& ^.HvuG},O 非线性超快脉冲耦合的数值方法的Matlab程序 6B=: P3Y !5}u \ 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。
U7do,jCoa 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
L<62-+e` 1X pG7 R0A|} Ee* 9 k.5'# % This Matlab script file solves the nonlinear Schrodinger equations
' %&gER % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
G=ly . % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
=} D9sT % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
6^l|/\ Y{ p Rys 5/&v C=1;
:2zga=)g M1=120, % integer for amplitude
J_S8=`f% M3=5000; % integer for length of coupler
`]7==c #Y N = 512; % Number of Fourier modes (Time domain sampling points)
Ht9QINo dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
je`Ysbe n T =40; % length of time:T*T0.
YstR
T1 dt = T/N; % time step
8= kwc n = [-N/2:1:N/2-1]'; % Index
YLsOA`5X t = n.*dt;
90 [6PSXk ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
R0 g^0K. w=2*pi*n./T;
kfV}ta'^S g1=-i*ww./2;
e=^^TX`I g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
,`
64t'g g3=-i*ww./2;
!*1 $j7`tP P1=0;
v8} vk]b P2=0;
@u @~gEt P3=1;
[o"<DP6w P=0;
('k9X cTPP for m1=1:M1
!sG# 3sUe[ p=0.032*m1; %input amplitude
]?6Pt: N2 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
fg)VO6Wo& s1=s10;
:;hz!6! s20=0.*s10; %input in waveguide 2
l@)`Q s30=0.*s10; %input in waveguide 3
;l %$-/% s2=s20;
;aN_!!
r s3=s30;
}6_*i!68"U p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
@ tvz9N %energy in waveguide 1
/rIyW?& f p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
K0YQ b&*k %energy in waveguide 2
s(Bcw`'# p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
b}
0G~oLP %energy in waveguide 3
- |GKtZ]} for m3 = 1:1:M3 % Start space evolution
ZXIw^!8@/ s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
hYht8?6}m s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
^B)f!HtU s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
AU1U?En sca1 = fftshift(fft(s1)); % Take Fourier transform
\$4 [qG= sca2 = fftshift(fft(s2));
o (k{Ed sca3 = fftshift(fft(s3));
"ze-Mb sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
@-ml=S7;Sz sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
)dd1B>ej] sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
/go|r ' s3 = ifft(fftshift(sc3));
Q+oV?
S3{ s2 = ifft(fftshift(sc2)); % Return to physical space
]h?q1
s1 = ifft(fftshift(sc1));
`Gj (>z* end
Z)}UCi+/". p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
N; '] & f p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
p|C[T]J\@ p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
0NeIQr1N_ P1=[P1 p1/p10];
yeI> b 1>Q P2=[P2 p2/p10];
.ht-* P3=[P3 p3/p10];
o "6
2 ~ P=[P p*p];
1<t J3>Xl end
g/FZ?Wo figure(1)
/&c2O X|Z plot(P,P1, P,P2, P,P3);
mqj-/DN6* " Lh&s<[ 转自：
http://blog.163.com/opto_wang/
