P 0G ¼
α e00
β e00
1 À
1
P 0L K FOLD
j
jα e00 β e00
%
α e00
β e00
1 À
1
2
N 02 ÀN 01
ð
Þ h
N 02 ε n
T 0F
T 1
K FOLD
j
jα e00 β e00
!
:
ð5:72Þ
Similarly to Eq. (5.69) for the laser PSD, from the general symbolic equation
(Eq. 5.67), we obtain the equation for PSD S Ψ for the OEO phase noise. The PSD S Ψ
reduced to the power P 0G of RF oscillation is determined by the following expression according to the Evtianov–Kuleshov method:
S ¼
S Ψ
P 0G
¼
Y a Re À σ U
ð
Þ
2 S ImFDNY þ Y
2
aIm S Re FDNY
P 0G Y a Re À σ U
½
ŠY a Re À 1
½
Šþ Y aIm
½
Š
2
n
o 2 ,
ð5:73Þ
where S ImFDNY , S ReFDNY are in-phase and quadrature components of fluctuations,
which are determined by the mutual noises of the laser, the photodiode and the
amplifier of the OEO closed loop; Y aRe , Y aIm are in-phase and quadrature components of OEO controlling conductance (abbreviated representations)
(Y a ¼ Y aRe + jY aIm ):
Y a Re ¼ y M
1 þ FT F
ð
Þcos FT FOLD
ð
Þ
P 0L K FODL
j
j
% y M
1 þ FT F
ð
Þcos FT FOS
ð
Þ
P 0L K FODL
j
j
,
ð5:74Þ
Y aIm ¼ y M
1 þ FT F
ð
Þsin FT FOLD
ð
Þ
P 0L K FODL
j
j
% y M
1 þ FT F
ð
Þsin FT FOS
ð
Þ
P 0L K FODL
j
j
,
ð5:75Þ
where the offset frequency F ¼ 2π( f À f 0 ) is difference of frequency of analysis f and
frequency of OEO generation f 0 ; |K FODL | is the module of the transfer function of the
S , dB/Hz
–100
–110
–90
–120
5
10
50
F 00L
F, kHz
100
2
1
500 1000
Fig. 5.8 PSD of the laser
phase noise (curve 1) and
PSD of the OEO MZ phase
noise (curve 2)
254
5 Optoelectronic oscillator (OEO) Differential Equations as the Laser System with. . .