K FOS Á K PD R NA S NA0 ), ReK S ¼ K FOS K PD R NA S NA0 cos (FT FOS ), ImK S ¼
K FOS K PD R NA S NA0 sin (FT FOS ), the amplitude and phase noises of QWLD optical
oscillations and of RF oscillations in OEO DM essentially decrease. The phase
noises of OEO DM at small frequency offsets from the carrier are determined by the
quadrature component of the laser spontaneous noise ξ Lφ /( jω). At offset frequencies
close to the frequency of the photon–electron resonance ω
2
¼ ω
2
00L Á 1 À K S =G
ð
Þ ,
the value of the phase noise is inversely proportional to the laser damping decrement
α 00l . Taking into account that the transfer function K S ¼ Re K DL R NA S NA0 ¼
K FOS Á K PD R NA S NA0 contains the optical fiber with (in potential) the retarded time
T BZ , then, the laser phase noise and the RF phase noise of OEO decrease with
account of the stabilization effect on the long delay line. Amplitude noises are
defined by the carrier noise of QWLD and by the noise of the optical phase.
Now we examine the structure of OEO DM at open feedback loop, i.e., at zero
transfer function of feedback K S ¼ 0. Neglecting of small emission frequency
modulation and of the influence of amplitude variations of the laser emission
intensity upon the phase, we take into consideration that K S ¼ 0 and the determinants
for differential equations are:
Δ
jω
¼ ω
2
À α 00l À 1
ð
Þ G À jωα 00l ¼ ω
2
À ω
2
00L À jωα 00l ,
ð7:65Þ
Δ 2
jωT 1L
¼f α 00l À 1
ð
Þ ξ Ln þ ξ Lφ1
À
Á þ ξ Le jω þ α 00l
ð
Þþ2πv 00 C N T 1L
½
þ jω þ α 00l
ð
Þ ξ Lφ1 þ ξ Ln 2πv 00P C N T 1L g,
ð7:66Þ
Δ 3 ¼ α 00l À 1
ð
Þ Gξ Lφ þ jωξ Lφ jω þ α 00l
ð
Þ¼ξ Lφ ω
2
00L þ jω jω þ α 00l
ð
Þ
Â
Ã
¼ ξ Lφ ω
2
00L À ω
2
þ jωα 00l
Â
Á :
ð7:67Þ
We note that expressions for determinants of fluctuation equations of OEO DM
(Eq. 7.61), (Eq. 7.62) have the more complicate set of terms than expressions for
determinants of fluctuation equations for OEO MZ. Then, in the case of the opened
feedback loop, expressions for amplitude and phase fluctuations are:
m L ¼
Δ 2
Δ
¼
ξ Ln þ ξ Lφ1
À
Á
2α 00l À 1
ð
Þþjω
½
T 1L
ð Þ
2 ω 2 À ω 2
00L À jωα 00l
À
Á,
ð7:68Þ
φ ξ ¼
Δ 3
Δ
¼
ξ Lφ
jω T 1L
ð Þ
þ
ξ Lφ 2ω
2
ooL
T 1L
ð Þ
2 ω 2 À ω 2
00L À jωα 00l
À
Á
¼
ξ Lφ
jω T 1L
ð Þ
1 þ
1
T 1L
K LD jω
ð Þ
!
,
ð7:69Þ
Here for the QWLD transfer function K LD jω
ð Þ ¼ ω
2
00L = ω
2
À ω
2
00L À jωα 00L
À
Á
on
AC component of the pumping current is proportional to the EMF strength square
determined in Chap. 4.
7.6 Power Spectrum Density of Amplitude and Phase Noise in OEO DM
445
K FOS K PD R NA S NA0 sin (FT FOS ), the amplitude and phase noises of QWLD optical
oscillations and of RF oscillations in OEO DM essentially decrease. The phase
noises of OEO DM at small frequency offsets from the carrier are determined by the
quadrature component of the laser spontaneous noise ξ Lφ /( jω). At offset frequencies
close to the frequency of the photon–electron resonance ω
2
¼ ω
2
00L Á 1 À K S =G
ð
Þ ,
the value of the phase noise is inversely proportional to the laser damping decrement
α 00l . Taking into account that the transfer function K S ¼ Re K DL R NA S NA0 ¼
K FOS Á K PD R NA S NA0 contains the optical fiber with (in potential) the retarded time
T BZ , then, the laser phase noise and the RF phase noise of OEO decrease with
account of the stabilization effect on the long delay line. Amplitude noises are
defined by the carrier noise of QWLD and by the noise of the optical phase.
Now we examine the structure of OEO DM at open feedback loop, i.e., at zero
transfer function of feedback K S ¼ 0. Neglecting of small emission frequency
modulation and of the influence of amplitude variations of the laser emission
intensity upon the phase, we take into consideration that K S ¼ 0 and the determinants
for differential equations are:
Δ
jω
¼ ω
2
À α 00l À 1
ð
Þ G À jωα 00l ¼ ω
2
À ω
2
00L À jωα 00l ,
ð7:65Þ
Δ 2
jωT 1L
¼f α 00l À 1
ð
Þ ξ Ln þ ξ Lφ1
À
Á þ ξ Le jω þ α 00l
ð
Þþ2πv 00 C N T 1L
½
þ jω þ α 00l
ð
Þ ξ Lφ1 þ ξ Ln 2πv 00P C N T 1L g,
ð7:66Þ
Δ 3 ¼ α 00l À 1
ð
Þ Gξ Lφ þ jωξ Lφ jω þ α 00l
ð
Þ¼ξ Lφ ω
2
00L þ jω jω þ α 00l
ð
Þ
Â
Ã
¼ ξ Lφ ω
2
00L À ω
2
þ jωα 00l
Â
Á :
ð7:67Þ
We note that expressions for determinants of fluctuation equations of OEO DM
(Eq. 7.61), (Eq. 7.62) have the more complicate set of terms than expressions for
determinants of fluctuation equations for OEO MZ. Then, in the case of the opened
feedback loop, expressions for amplitude and phase fluctuations are:
m L ¼
Δ 2
Δ
¼
ξ Ln þ ξ Lφ1
À
Á
2α 00l À 1
ð
Þþjω
½
T 1L
ð Þ
2 ω 2 À ω 2
00L À jωα 00l
À
Á,
ð7:68Þ
φ ξ ¼
Δ 3
Δ
¼
ξ Lφ
jω T 1L
ð Þ
þ
ξ Lφ 2ω
2
ooL
T 1L
ð Þ
2 ω 2 À ω 2
00L À jωα 00l
À
Á
¼
ξ Lφ
jω T 1L
ð Þ
1 þ
1
T 1L
K LD jω
ð Þ
!
,
ð7:69Þ
Here for the QWLD transfer function K LD jω
ð Þ ¼ ω
2
00L = ω
2
À ω
2
00L À jωα 00L
À
Á
on
AC component of the pumping current is proportional to the EMF strength square
determined in Chap. 4.
7.6 Power Spectrum Density of Amplitude and Phase Noise in OEO DM
445