We make important conclusions from obtained expressions. The laser phase
noises φ ξ can be treated as noises caused by the quadrature component of its
spontaneous emission ξ sφ ,multiplied by the common transfer function [ξ Lφ /
( jωT 1L )] Á [1 + K LD ( jω)].
If the frequency is equal to the photon–electron resonance frequency of QWLD:
ω
2
¼ ω
2
00L , then the QWLD phase noise is inversely proportional to the laser
damping decrement (which is proportional to the pumping exceeding above the
threshold value) and equals: φ ξ % ξ Lφ /α 00l .
PSD of amplitude and phase noises of OEO DM with QWLD at closed and
open feedback loop. Here we obtain expressions for PSD of amplitude and phase
noises of the laser without account of frequency modulation of the optical emission
at opened feedback loop in OEO. For this case, we obtain PSD for QWLD in the
form:
1. Closed feedback loop in OEO
S AN ¼ S m ¼
α 00l À 1
ð
Þ
2 S LN1 þ S LE1 jω þ α 00l
ð
Þ
2
T 1L
ð Þ
4 ω 2 À ω 2
00L 1 À Re K S =G
ð
Þ
½
À jωα 00l
2 ,
ð7:70Þ
S PN ¼ S φ ¼
S φξ
jωT 1L
j
j
2
þ
S LE D 11
2
þ S LN D 22
2
T 1L
ð Þ
4 ω 2 À ω 2
00L 1 À Re K S =G
ð
Þ
½
À jωα 00l
2 : ð7:71Þ
2. Open feedback loop K s = 0
S AN ¼ S m ¼
α 00l À 1
ð
Þ
2 S LN þ S LE jω þ α 00l
ð
Þ
2
T 1L
ð Þ
4 ω 2 À ω 2
00L À jωα 00l
2 ,
ð7:72Þ
S PN ¼ S φ ¼
S φξ
jωT 1L
j
j
2
þ
S LE D 11
2
þ S LN D 22
2
T 1L
ð Þ
4 ω 2 À ω 2
00L À jωα 00l
2 ;
ð7:73Þ
where D 11 ¼ T 1L ρ 0L α 00l À (K S À G)2πf 00P C N T 1L + jωT 1L ρ 0L , ω is the angular
generated radio frequency, D 22 ¼ (α 00l À 1)T 1L ρ 0L À jωπf 00P C N T 1L , ν is the laser
optical generated frequency, Q pL the loaded Q-factor of the laser resonator,
S φξ ¼ S Lφ + Im (K BCFDNY S Le + K NY S FD + S NY ), α 0 is the exceed of DC current
of QWLD pumping above the threshold value, S LN ¼ S Ln + Re (K BCFDNY S Le +
K NY S FD + S NY ) K LZ0 is the transfer function of the delay line without account of
the laser transfer function, S 100 is the gain of the nonlinear amplifier.
Thus, we obtain expressions for calculation of PSD of amplitude and phase noises
of the laser not taking into account the frequency modulation of the laser emission at
closed and opened feedback loop in OEO.
Figure 7.34 shows the calculated functions (Eqs. 7.70–7.73) of phase and amplitude noises of QWLD versus the F offset in frequency from the reference
(or nominal) frequency of the subcarrier of 10 GHz in the opened feedback loop in
446
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
noises φ ξ can be treated as noises caused by the quadrature component of its
spontaneous emission ξ sφ ,multiplied by the common transfer function [ξ Lφ /
( jωT 1L )] Á [1 + K LD ( jω)].
If the frequency is equal to the photon–electron resonance frequency of QWLD:
ω
2
¼ ω
2
00L , then the QWLD phase noise is inversely proportional to the laser
damping decrement (which is proportional to the pumping exceeding above the
threshold value) and equals: φ ξ % ξ Lφ /α 00l .
PSD of amplitude and phase noises of OEO DM with QWLD at closed and
open feedback loop. Here we obtain expressions for PSD of amplitude and phase
noises of the laser without account of frequency modulation of the optical emission
at opened feedback loop in OEO. For this case, we obtain PSD for QWLD in the
form:
1. Closed feedback loop in OEO
S AN ¼ S m ¼
α 00l À 1
ð
Þ
2 S LN1 þ S LE1 jω þ α 00l
ð
Þ
2
T 1L
ð Þ
4 ω 2 À ω 2
00L 1 À Re K S =G
ð
Þ
½
À jωα 00l
2 ,
ð7:70Þ
S PN ¼ S φ ¼
S φξ
jωT 1L
j
j
2
þ
S LE D 11
2
þ S LN D 22
2
T 1L
ð Þ
4 ω 2 À ω 2
00L 1 À Re K S =G
ð
Þ
½
À jωα 00l
2 : ð7:71Þ
2. Open feedback loop K s = 0
S AN ¼ S m ¼
α 00l À 1
ð
Þ
2 S LN þ S LE jω þ α 00l
ð
Þ
2
T 1L
ð Þ
4 ω 2 À ω 2
00L À jωα 00l
2 ,
ð7:72Þ
S PN ¼ S φ ¼
S φξ
jωT 1L
j
j
2
þ
S LE D 11
2
þ S LN D 22
2
T 1L
ð Þ
4 ω 2 À ω 2
00L À jωα 00l
2 ;
ð7:73Þ
where D 11 ¼ T 1L ρ 0L α 00l À (K S À G)2πf 00P C N T 1L + jωT 1L ρ 0L , ω is the angular
generated radio frequency, D 22 ¼ (α 00l À 1)T 1L ρ 0L À jωπf 00P C N T 1L , ν is the laser
optical generated frequency, Q pL the loaded Q-factor of the laser resonator,
S φξ ¼ S Lφ + Im (K BCFDNY S Le + K NY S FD + S NY ), α 0 is the exceed of DC current
of QWLD pumping above the threshold value, S LN ¼ S Ln + Re (K BCFDNY S Le +
K NY S FD + S NY ) K LZ0 is the transfer function of the delay line without account of
the laser transfer function, S 100 is the gain of the nonlinear amplifier.
Thus, we obtain expressions for calculation of PSD of amplitude and phase noises
of the laser not taking into account the frequency modulation of the laser emission at
closed and opened feedback loop in OEO.
Figure 7.34 shows the calculated functions (Eqs. 7.70–7.73) of phase and amplitude noises of QWLD versus the F offset in frequency from the reference
(or nominal) frequency of the subcarrier of 10 GHz in the opened feedback loop in
446
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .