pillars in the manufacture process for OF containing the nitrogen. This method gives
a possibility to manufacture the ultrasmall (less than 1 cm
3 in volume) RF FODL
with the effective delay of 5–50 μs for the microwave oscillations for the frequency
of 10 GHz at optical losses in OF not more than 2–5 dB at the OF total length
1–10 km.
7.6 Power Spectrum Density of Amplitude and Phase Noise
in OEO DM
7.6.1 Fluctuation Equations of OEO DM
Differential equations of slowly changing normalized square of the strength E
2
0L , the
population N 0L and the phase φ for QWLD (for the double-level model) in the
single-frequency optical emission at absence of the positive feedback in OEO DM
with account of the Langevinian laser noises can be written as Eq. (5.100), where
ξ βAN ¼ ξ E1 , ξ βPN ¼ ξ N1 are in-phase and quadrature components of Langevinian
fluctuations of the laser field strength (which PSDs are equal, relatively, S βAN , S βPN ),
which are determined by the noise of spontaneous emission and depend on lifetime
of excited particles on the metastable level of the active medium in the laser
resonator, ξ LN is the component of Langevinian fluctuations of the inversed
population.
Taking into consideration the photoreception in the restricted band of optical
frequencies at utilization in the laser, for example, of the narrowband optical filter
(OF in Fig. 6.1), the random process of laser optical emission can be considered as
the stationary process with the zero mean value. For instance, PSD S βPN is determined by spontaneous emission in the laser mode and is equal to S βPN ¼ P sp /Δν P0 ,
where P sp is the power of the spontaneous emission in the laser mode, Δν P0 is the
half-width of the resonance curve (or AFC) of the laser optical resonator, ν 0P is the
natural frequency of the optical resonator.
The natural frequency of the optical resonator depends upon N 0L : ν 0P ¼ ν 0P (N 0L ).
Introducing the constant C N , we obtain the function f 00P ¼ ν 00P À ν at small
deviations from the average frequency ν 00P , which corresponds to the population
value N 0L ¼ N 00L , and we present the optical frequency as ν 0P ¼ ν 0P (N 0L ) ¼ ν 00P Á C N .
Here C N ¼ (ν 00P À ν 0P )/(N 00L À N 0L ).
7.6.2 The Open Feedback Loop Expression for the Laser PSD
For this process, at opened feedback loop in OEO structure (there is loop closing in
one place in OEO), where the coupler is located in Fig. 7.20, the spectral densities
S mL ν
ð Þ ¼ S βAN D A = ν À ν 0
ð
Þ
2 þ B
2
L
h
i
, and S ψL ν
ð Þ ¼ S βPN Á D F = T
2
OF Á ν À ν 0
ð
Þ
2 P L
h
i
7.6 Power Spectrum Density of Amplitude and Phase Noise in OEO DM
439
a possibility to manufacture the ultrasmall (less than 1 cm
3 in volume) RF FODL
with the effective delay of 5–50 μs for the microwave oscillations for the frequency
of 10 GHz at optical losses in OF not more than 2–5 dB at the OF total length
1–10 km.
7.6 Power Spectrum Density of Amplitude and Phase Noise
in OEO DM
7.6.1 Fluctuation Equations of OEO DM
Differential equations of slowly changing normalized square of the strength E
2
0L , the
population N 0L and the phase φ for QWLD (for the double-level model) in the
single-frequency optical emission at absence of the positive feedback in OEO DM
with account of the Langevinian laser noises can be written as Eq. (5.100), where
ξ βAN ¼ ξ E1 , ξ βPN ¼ ξ N1 are in-phase and quadrature components of Langevinian
fluctuations of the laser field strength (which PSDs are equal, relatively, S βAN , S βPN ),
which are determined by the noise of spontaneous emission and depend on lifetime
of excited particles on the metastable level of the active medium in the laser
resonator, ξ LN is the component of Langevinian fluctuations of the inversed
population.
Taking into consideration the photoreception in the restricted band of optical
frequencies at utilization in the laser, for example, of the narrowband optical filter
(OF in Fig. 6.1), the random process of laser optical emission can be considered as
the stationary process with the zero mean value. For instance, PSD S βPN is determined by spontaneous emission in the laser mode and is equal to S βPN ¼ P sp /Δν P0 ,
where P sp is the power of the spontaneous emission in the laser mode, Δν P0 is the
half-width of the resonance curve (or AFC) of the laser optical resonator, ν 0P is the
natural frequency of the optical resonator.
The natural frequency of the optical resonator depends upon N 0L : ν 0P ¼ ν 0P (N 0L ).
Introducing the constant C N , we obtain the function f 00P ¼ ν 00P À ν at small
deviations from the average frequency ν 00P , which corresponds to the population
value N 0L ¼ N 00L , and we present the optical frequency as ν 0P ¼ ν 0P (N 0L ) ¼ ν 00P Á C N .
Here C N ¼ (ν 00P À ν 0P )/(N 00L À N 0L ).
7.6.2 The Open Feedback Loop Expression for the Laser PSD
For this process, at opened feedback loop in OEO structure (there is loop closing in
one place in OEO), where the coupler is located in Fig. 7.20, the spectral densities
S mL ν
ð Þ ¼ S βAN D A = ν À ν 0
ð
Þ
2 þ B
2
L
h
i
, and S ψL ν
ð Þ ¼ S βPN Á D F = T
2
OF Á ν À ν 0
ð
Þ
2 P L
h
i
7.6 Power Spectrum Density of Amplitude and Phase Noise in OEO DM
439