计算脉冲在非线性耦合器中演化的Matlab 程序 =_TCt H {y :/9 % This Matlab script file solves the coupled nonlinear Schrodinger equations of
lS}5bcjR=k % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
u0N1+-6kr+ % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
dGZVWEaPfx % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
PF4Cs3m/ Ff.gR x %fid=fopen('e21.dat','w');
+8v !vuO' N = 128; % Number of Fourier modes (Time domain sampling points)
B<+}_3. M1 =3000; % Total number of space steps
[<bfwTFsl J =100; % Steps between output of space
8_W<BXW T =10; % length of time windows:T*T0
Z!tt(y\ T0=0.1; % input pulse width
V5M_ N;h MN1=0; % initial value for the space output location
'%)7%O,2 dt = T/N; % time step
0gx bo n = [-N/2:1:N/2-1]'; % Index
tTC[^Dji t = n.*dt;
tZ4W]od u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
o^gqpQv u20=u10.*0.0; % input to waveguide 2
1) M3*h3 u1=u10; u2=u20;
:h?Zg(l U1 = u1;
,p0R 4gi U2 = u2; % Compute initial condition; save it in U
ck-w Md ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
lO)p w=2*pi*n./T;
O+c@B}[! g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
spgY &OI; L=4; % length of evoluation to compare with S. Trillo's paper
NNS n]LP dz=L/M1; % space step, make sure nonlinear<0.05
|VTm5.23 for m1 = 1:1:M1 % Start space evolution
0 E{ $u u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
BpRQG]L u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
T|r@:t [ ca1 = fftshift(fft(u1)); % Take Fourier transform
?GX 5Pvg ca2 = fftshift(fft(u2));
6?z&G6 c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
v?5Xx{ym c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
omY%sQ{) u2 = ifft(fftshift(c2)); % Return to physical space
#;>J<> u1 = ifft(fftshift(c1));
)k=8.j4 if rem(m1,J) == 0 % Save output every J steps.
7G!SlC
X}W U1 = [U1 u1]; % put solutions in U array
Lab{?!E>U U2=[U2 u2];
iiKFV>;t/ MN1=[MN1 m1];
mI "`. z1=dz*MN1'; % output location
8gr&{-5 end
cKdy)T%; end
CQQ X7Y\ hg=abs(U1').*abs(U1'); % for data write to excel
U*1rA/"n ha=[z1 hg]; % for data write to excel
@4_W}1W t1=[0 t'];
I3p ~pt2 hh=[t1' ha']; % for data write to excel file
DBb mM*r %dlmwrite('aa',hh,'\t'); % save data in the excel format
=^O8 4Cp 6 figure(1)
1KAA(W;nq waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
M"ZP s figure(2)
qqLmjDv waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
)%f]` < o !JJCG 非线性超快脉冲耦合的数值方法的Matlab程序 G{$9e}# XBdC/DM[ 在研究脉冲在非线性耦合器中的演变时，我们需要求解非线性偏微分方程组。在如下的
论文中，我们提出了一种简洁的数值方法。 这里我们提供给大家用Matlab编写的计算程序。
n-}.Yc Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
+7^{T:^ht NhS0D=v6 iMYvC w/t6 e*: [#LJ]C % This Matlab script file solves the nonlinear Schrodinger equations
e#)}.
% for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
]Y}faW(&Y % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
&(IL` % % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
/ <Zy-+3 t-3wjS1v C=1;
45> w=O M1=120, % integer for amplitude
R1\cAP^ 0 M3=5000; % integer for length of coupler
>5i1M ^g( N = 512; % Number of Fourier modes (Time domain sampling points)
0&$e:O'v dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
LPvyfD;Zy T =40; % length of time:T*T0.
cg}46)^<QH dt = T/N; % time step
]nEN3RJ n = [-N/2:1:N/2-1]'; % Index
`3*>tq t = n.*dt;
&W)k s ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
0[x?Q[~S_0 w=2*pi*n./T;
TJ
;4QL g1=-i*ww./2;
)|q,RA n g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
gjk=`lU g3=-i*ww./2;
> rB7ms/@E P1=0;
EAqTXB@XU P2=0;
QS mE:Y P3=1;
N|WnUlf]: P=0;
Z[slN5]([ for m1=1:M1
)U`H 7\*) p=0.032*m1; %input amplitude
72@8 M s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
^kch]?
s1=s10;
oy;N 3 s20=0.*s10; %input in waveguide 2
4Q,HhqV' s30=0.*s10; %input in waveguide 3
v'2EYTVNJD s2=s20;
bv)E>%Yy s3=s30;
I^ qk` 5w p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
r9yUye} %energy in waveguide 1
(uD( ,3/Cw p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
- $.$6"] %energy in waveguide 2
3Yp_k p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
N`Zm[Sv7 %energy in waveguide 3
] j}zN2[A for m3 = 1:1:M3 % Start space evolution
N_= 7 s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
,D
[ s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
4&R\6!*s s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
0v,DQJ?w8 sca1 = fftshift(fft(s1)); % Take Fourier transform
jcYI"f"~ sca2 = fftshift(fft(s2));
{o*z iZh sca3 = fftshift(fft(s3));
.1t$(]CyC sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
Go^W\y
sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
aGr(djD sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
6<(HT#=# s3 = ifft(fftshift(sc3));
P(VQ D>G s2 = ifft(fftshift(sc2)); % Return to physical space
qWy{{ A+ s1 = ifft(fftshift(sc1));
~lzV=c$t end
k(3 s^B p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
bsR^H5O@ p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
@433?g`2b p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
st :[ |` P1=[P1 p1/p10];
'N,x=1R5 P2=[P2 p2/p10];
i/y+kL P3=[P3 p3/p10];
Yc"G="XP; P=[P p*p];
;TEZD70r end
"Y7RvL!U figure(1)
Yu9Ccj` plot(P,P1, P,P2, P,P3);
F<Z "W}I+6 0;!aO.l]K 转自：
http://blog.163.com/opto_wang/
