dE
2
0L =dt ¼ G 0 Á E
2
0L Á N L À E
2
0L =T 0F ,
dN L =dt ¼ α N00 Á J 0L þ α N01 Á J 1L À
N 0L
T 1
À G 0 N L E
2
0L ,
dφ=dt ¼ 2πν 0P N L
ð ÞÀ2πν 0 þ σ 0L þ ρ 0L E
2
0L ,
d
2 J 1L
dt 2 þ
1
T F
dJ 1L
dt
þ 2π f eF0
ð
Þ
2 J 1L ¼ S NY E
2
0L K FOS K PD ,J 1L t À T DL
ð
Þ
Â
à dJ 1L t À T DL
ð
Þ
dt
,
8
> > > > > > > <
> > > > > > > :
ð5:18Þ
where the transfer function K DL ¼ K FOS K PD , K FOS is the transfer function of FOS,
which contains the optical fiber of two fibers of different length, K PD is the transfer
function of the photodetector, which were defined in Chap. 2.
Now we present for comparison similar to Eq. (5.18) system from four timeequation for OEO MZ with QWLD:
dE
2
0L =dt¼G 0 E
2
0L N L ÀE
2
0L =T 0F ,
dN L =dt¼ α N00 ÁJ 0L À
N L
T 1L
ÀG 0 N L E
2
0L ,
dφ=dt¼2πν 0P ðN L ÞÀ2πν 0 þσ 0L þρ 0L E
2
0L ,
d
2 U
dt 2 þ
1
T F
dU
dt
þð2π f eF0 Þ
2 U ¼S NY ½E
2
0L K MZ K FOS K PD ÁUðtÀT FODL ފ
dUðtÀT FODL Þ
dt
:
8
> > > > > > > <
> > > > > > > :
ð5:19Þ
5.2.1.1 The Symbolic Form of the Equation System of OEO DM
and OEO MZ
Now we introduce the Laplace operator p ¼
d
dt in Eq. (5.19) and obtain the system of
three symbolic equations for OEO DM with QWLD:
pE
2
0L ¼ G 0 E
2
0L N 0L À E
2
0L =T 0F ,
pN L ¼ α N00 Á J 0L þ α N01 Á J 1L À 1=T 1
ð
ÞN L À G 0 N L E
2
0L ,
p
2
þ
1
T F
p þ 2π f eF0 Æ ν 0F
ð
Þ
2
!
J 1L ¼ pS NY E
2
0L K FOS K PD J 1L
Â
Ã
:
8
> > > <
> > > :
ð5:20Þ
Below we present for comparison the similar to Eq. (5.20) system of three
symbolic equations for OEO MZ with QWLD:
216
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .