计算脉冲在非线性耦合器中演化的Matlab 程序 \bx~*FaX tdF9NFMD % This Matlab script file solves the coupled nonlinear Schrodinger equations of
U5] pi +r % soliton in 2 cores coupler. The output pulse evolution plot is shown in Fig.1 of
m"9XT)N % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
$) 5Bf3P0 % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
zj|/ CxV '>v^6i S %fid=fopen('e21.dat','w');
1,V`8 [ N = 128; % Number of Fourier modes (Time domain sampling points)
Ji;mHFZ*FU M1 =3000; % Total number of space steps
2F8|I7R J =100; % Steps between output of space
YUdxG/~' T =10; % length of time windows:T*T0
H \GkW6 T0=0.1; % input pulse width
f2,1<^{ MN1=0; % initial value for the space output location
CVi`bO 4\ dt = T/N; % time step
sgr=w+",Q n = [-N/2:1:N/2-1]'; % Index
?K@t0a
t = n.*dt;
oR*=|B u10=1.*sech(1*t); % input to waveguide1 amplitude: power=u10*u10
e2C<PGUUB u20=u10.*0.0; % input to waveguide 2
)=Q)BN[ u1=u10; u2=u20;
Q8MS ,7y/ U1 = u1;
XTDE53Js& U2 = u2; % Compute initial condition; save it in U
cMzkL% ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
GyC /_ntn w=2*pi*n./T;
- ~4+w g=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./T
w#^U45y1v L=4; % length of evoluation to compare with S. Trillo's paper
IF@HzT;Q dz=L/M1; % space step, make sure nonlinear<0.05
~^vC,]hU for m1 = 1:1:M1 % Start space evolution
p[2GkP u1 = exp(dz*i*(abs(u1).*abs(u1))).*u1; % 1st sSolve nonlinear part of NLS
~B$b)`* u2 = exp(dz*i*(abs(u2).*abs(u2))).*u2;
AA:no= ca1 = fftshift(fft(u1)); % Take Fourier transform
,5|d3 dJS ca2 = fftshift(fft(u2));
gq5qRi`q c2=exp(g.*dz).*(ca2+i*1*ca1.*dz); % approximation
@+_&Y] c1=exp(g.*dz).*(ca1+i*1*ca2.*dz); % frequency domain phase shift
somfv$'B u2 = ifft(fftshift(c2)); % Return to physical space
F pt-V u1 = ifft(fftshift(c1));
=raA?Bp3;( if rem(m1,J) == 0 % Save output every J steps.
E-1"+p U1 = [U1 u1]; % put solutions in U array
(}:C+p
'I U2=[U2 u2];
X;! D};;M MN1=[MN1 m1];
&D#+6M&LK{ z1=dz*MN1'; % output location
<SVmOmJ-K end
x "(9II* end
K<v:-TjQZ: hg=abs(U1').*abs(U1'); % for data write to excel
e(1k0W4 B ha=[z1 hg]; % for data write to excel
?G? gy2 t1=[0 t'];
m h;X~.98 hh=[t1' ha']; % for data write to excel file
>m _v5K %dlmwrite('aa',hh,'\t'); % save data in the excel format
iS@\ =CK figure(1)
e@F|NCQ.9 waterfall(t',z1',abs(U1').*abs(U1')) % t' is 1xn, z' is 1xm, and U1' is mxn
Y~n` ~( figure(2)
tL0`Rvl waterfall(t',z1',abs(U2').*abs(U2')) % t' is 1xn, z' is 1xm, and U1' is mxn
S)%_we LW7 &B!%fd .' 非线性超快脉冲耦合的数值方法的Matlab程序 v6e% # = J fcMca 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。
3z{S}~ 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 '[?9/T ,2 WH/" |ia@,*KD ;^l_i4A % This Matlab script file solves the nonlinear Schrodinger equations
>kd M:MK % for 3 cores nonlinear coupler. The output plot is shown in Fig.2 of
R V!o4"\] % Youfa Wang and Wenfeng Wang, “A simple and effective numerical method for nonlinear
~hURs;Sb % pulse propagation in N-core optical couplers”, IEEE Photonics Technology lett. Vol.16, No.4, pp1077-1079, 2004
v5T9Y-{` )u@t.)ChAV C=1;
<?$kI>Ot M1=120, % integer for amplitude
lv:U%+A M3=5000; % integer for length of coupler
Q2C)tVK+ N = 512; % Number of Fourier modes (Time domain sampling points)
R9. HD?H@ dz =3.14159/(sqrt(2.)*C)/M3; % length of coupler is divided into M3 segments, make sure nonlinearity<0.05.
>,h1 N$A+ T =40; % length of time:T*T0.
zj]b&In6; dt = T/N; % time step
Z|^MGyn n = [-N/2:1:N/2-1]'; % Index
2H&{1f\Bf t = n.*dt;
gw Qvao ww = 4*n.*n*pi*pi/T/T; % Square of frequency. Note i^2=-1.
Xa`(;CLW? w=2*pi*n./T;
7o{*Z g1=-i*ww./2;
+0pW/4x g2=-i*ww./2; % w=2*pi*f*n./N, f=1/dt=N/T,so w=2*pi*n./TP=0;
$
u2Cd4 g3=-i*ww./2;
Sa] mm/ G P1=0;
PO
ko]@~!i P2=0;
U($^E}I2( P3=1;
k)E ;( P=0;
K[ ?R[ for m1=1:M1
tE!'dpG5) p=0.032*m1; %input amplitude
\7E`QY4 s10=p.*sech(p.*t); %input soliton pulse in waveguide 1
~eo^`4O{{ s1=s10;
|vy]8?Ak s20=0.*s10; %input in waveguide 2
*1;23BiH - s30=0.*s10; %input in waveguide 3
0|2%# E s2=s20;
jA2ofC s3=s30;
ci7~Ke wJ* p10=dt*(sum(abs(s10').*abs(s10'))-0.5*(abs(s10(N,1)*s10(N,1))+abs(s10(1,1)*s10(1,1))));
\ j]~>9 %energy in waveguide 1
?"@ET9 p20=dt*(sum(abs(s20').*abs(s20'))-0.5*(abs(s20(N,1)*s20(N,1))+abs(s20(1,1)*s20(1,1))));
N^@
\tg = %energy in waveguide 2
;4d.)-<No_ p30=dt*(sum(abs(s30').*abs(s30'))-0.5*(abs(s30(N,1)*s30(N,1))+abs(s30(1,1)*s30(1,1))));
N &B>#: %energy in waveguide 3
ZA.fa0n for m3 = 1:1:M3 % Start space evolution
Cnur"?w@o s1 = exp(dz*i*(abs(s1).*abs(s1))).*s1; % 1st step, Solve nonlinear part of NLS
y@9Y,ZR* s2 = exp(dz*i*(abs(s2).*abs(s2))).*s2;
Kcn \g. s3 = exp(dz*i*(abs(s3).*abs(s3))).*s3;
fI[dh d6 sca1 = fftshift(fft(s1)); % Take Fourier transform
$i&\\QNn sca2 = fftshift(fft(s2));
70<K .T<b sca3 = fftshift(fft(s3));
4 ? {*( sc1=exp(g1.*dz).*(sca1+i*C*sca2.*dz); % 2nd step, frequency domain phase shift
,i OZ | sc2=exp(g2.*dz).*(sca2+i*C*(sca1+sca3).*dz);
G4yUC<TqBP sc3=exp(g3.*dz).*(sca3+i*C*sca2.*dz);
Orc>.~+f%A s3 = ifft(fftshift(sc3));
&9 h s2 = ifft(fftshift(sc2)); % Return to physical space
Ao!=um5D J s1 = ifft(fftshift(sc1));
)tPl<lb end
Fhi5LhWe+. p1=dt*(sum(abs(s1').*abs(s1'))-0.5*(abs(s1(N,1)*s1(N,1))+abs(s1(1,1)*s1(1,1))));
aa= b<Cd p2=dt*(sum(abs(s2').*abs(s2'))-0.5*(abs(s2(N,1)*s2(N,1))+abs(s2(1,1)*s2(1,1))));
<W|1<=z( p3=dt*(sum(abs(s3').*abs(s3'))-0.5*(abs(s3(N,1)*s3(N,1))+abs(s3(1,1)*s3(1,1))));
[Ye5Y? P1=[P1 p1/p10];
LO> 8 j: P2=[P2 p2/p10];
)GCLK<,swu P3=[P3 p3/p10];
|
W?[,|e P=[P p*p];
./!KE"! end
Ko-QR( figure(1)
Rc%PZ}es plot(P,P1, P,P2, P,P3);
N('3oy#8 7X:hIl 转自：
http://blog.163.com/opto_wang/
