As the controlling devices for the optical frequency, we can use the voltagecontrolled optical filters, Fabry–Perot cells, etc. The control of the optical frequency
of the laser diode is provided by changing of the DC bias current.
In the general case, the modulation characteristic is nonlinear; nevertheless, it can
be approximated as the straight line with the slope: S con ¼
dν
de con
: Then, the frequency
detuning Δν(t) of the laser optical emission versus the control voltage:
Δν con (e con ) ¼ ν 0 À S con e con .
In the general case, for the automatic frequency control in OEO with utilization of
the external reference oscillator (Fig. 7.37a), we write expressions for the spectral
densities of the output phase fluctuations as: S out ( f ) ¼ |K AC ( f )|
2 S in ( f ) + |K FC ( f )|
2 S ξп,
gen ( f ), where S in ( f ) is the spectral density of phase fluctuations of the signal in the
system input (or from controlled oscillator in OEO), S ξп, gen ( f ) is the spectral density
of the phase fluctuations of the reference generator. We designate the module
squares of the transfer functions of LPF included in the control chain (Fig. 7.36a),
relatively, |K AC ( f )|
2 for controlling oscillation in the input of the automatic control
system, |K FC ( f )|
2 for the reference oscillation of the oscillation of the reference
oscillator. In the structure in Fig. 7.37a the external oscillator plays a role of the
reference source of oscillation, and OEO plays a role of the controlling oscillation
source.
The control circuit included into the section of automatic control between the
phase detector and the frequency controller represents the low-pass filter, which is
used for interference suppression distorting the reference signal of the RF generator.
As PLF, we consider the simplest RC integration filter.
In this case, at utilization of the integration chain in LPF of the RC-filter type, the
appropriate equations are: L AC f
ð Þ ¼ K AC f
ð Þ
j
j
2 ¼ Ω
2
0 =½ Ω 0 À T RC 4π
2 f
2
À
Á 2 þ
4π
2 f
2
, L FC ( f ) ¼ |K FC ( f )|
2
¼ [(T RC 4π
2 f
2 )
2 + 4π
2 f
2 ]/[(Ω 0 À T RC 4π
2 f
2 )
2 + 4π
2 f
2 ],
where T RC is the time constant of the circuit, Ω 0 ¼ E F S con the system parameter
characterizing its locking range. For this system, the Ω 0 ¼ E F S con parameter is
determined as: Ω 0 ¼ R PD K PD |E 0FOS1 |
2 sin (2πν 0 T FOS1 )S con .
At regulation of OEO radio frequency (structure in Fig. 7.39): S conRF ¼ df/de con2 .
At adjustment of the laser optical frequency: S con, opt ¼ dν/de con . The Ω 0 differs from
the locking range by a multiplier equaled to the characteristic slope of the phase
detector in the operation point. Using functions L AC ( f ) and L FC ( f ), therefore, we
write expression for the spectral densities of the output phase fluctuations:
S out f
ð Þ ¼ L AC f
ð ÞS in f
ð Þ þ L FC f
ð ÞS ξn,gen f
ð Þ,
ð7:76Þ
where S in ( f ) is the spectral density of phase fluctuations of the signal in the system
input of or the controlling generator, S ξn, gen ( f ) is the spectral density of the phase
fluctuations of the reference generator.
Depending on the level of phase noises of elements, the various variants of the
structure of PLL system for frequency control are possible in OEO.
In one of variants, the laser can be the controlling element, and RF generator is
the reference one. At that, the expression (Eq. 7.76) can be written in the form:
458
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
of the laser diode is provided by changing of the DC bias current.
In the general case, the modulation characteristic is nonlinear; nevertheless, it can
be approximated as the straight line with the slope: S con ¼
dν
de con
: Then, the frequency
detuning Δν(t) of the laser optical emission versus the control voltage:
Δν con (e con ) ¼ ν 0 À S con e con .
In the general case, for the automatic frequency control in OEO with utilization of
the external reference oscillator (Fig. 7.37a), we write expressions for the spectral
densities of the output phase fluctuations as: S out ( f ) ¼ |K AC ( f )|
2 S in ( f ) + |K FC ( f )|
2 S ξп,
gen ( f ), where S in ( f ) is the spectral density of phase fluctuations of the signal in the
system input (or from controlled oscillator in OEO), S ξп, gen ( f ) is the spectral density
of the phase fluctuations of the reference generator. We designate the module
squares of the transfer functions of LPF included in the control chain (Fig. 7.36a),
relatively, |K AC ( f )|
2 for controlling oscillation in the input of the automatic control
system, |K FC ( f )|
2 for the reference oscillation of the oscillation of the reference
oscillator. In the structure in Fig. 7.37a the external oscillator plays a role of the
reference source of oscillation, and OEO plays a role of the controlling oscillation
source.
The control circuit included into the section of automatic control between the
phase detector and the frequency controller represents the low-pass filter, which is
used for interference suppression distorting the reference signal of the RF generator.
As PLF, we consider the simplest RC integration filter.
In this case, at utilization of the integration chain in LPF of the RC-filter type, the
appropriate equations are: L AC f
ð Þ ¼ K AC f
ð Þ
j
j
2 ¼ Ω
2
0 =½ Ω 0 À T RC 4π
2 f
2
À
Á 2 þ
4π
2 f
2
, L FC ( f ) ¼ |K FC ( f )|
2
¼ [(T RC 4π
2 f
2 )
2 + 4π
2 f
2 ]/[(Ω 0 À T RC 4π
2 f
2 )
2 + 4π
2 f
2 ],
where T RC is the time constant of the circuit, Ω 0 ¼ E F S con the system parameter
characterizing its locking range. For this system, the Ω 0 ¼ E F S con parameter is
determined as: Ω 0 ¼ R PD K PD |E 0FOS1 |
2 sin (2πν 0 T FOS1 )S con .
At regulation of OEO radio frequency (structure in Fig. 7.39): S conRF ¼ df/de con2 .
At adjustment of the laser optical frequency: S con, opt ¼ dν/de con . The Ω 0 differs from
the locking range by a multiplier equaled to the characteristic slope of the phase
detector in the operation point. Using functions L AC ( f ) and L FC ( f ), therefore, we
write expression for the spectral densities of the output phase fluctuations:
S out f
ð Þ ¼ L AC f
ð ÞS in f
ð Þ þ L FC f
ð ÞS ξn,gen f
ð Þ,
ð7:76Þ
where S in ( f ) is the spectral density of phase fluctuations of the signal in the system
input of or the controlling generator, S ξn, gen ( f ) is the spectral density of the phase
fluctuations of the reference generator.
Depending on the level of phase noises of elements, the various variants of the
structure of PLL system for frequency control are possible in OEO.
In one of variants, the laser can be the controlling element, and RF generator is
the reference one. At that, the expression (Eq. 7.76) can be written in the form:
458
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .