alternative structure of automatic control of frequency and phase in OEO is the
structure discussed in Sect. 7.7.1 with suppression of the RF subcarrier (Fig. 7.38).
For calculation of the relative PSD of the phase noise of OEO RF oscillations
with the operating PLL system, we deduce the main mathematical relations. We
consider the structure in Fig. 7.39a.
Let it be the field strength of the laser emission in the first optical channel of MZ
defined as: E 1L ¼ Е 0L exp [j2πν(t) À jφ 0L À jψ m1 (t)], where the optical frequency
ν(t) ¼ ν 0 + Δν(t), ν 0 is the average laser frequency, Δν(t) is the variation of the
optical frequency from its average value, φ 0L is the constant phase incursion, ψ m1 (t)
is the phase variation of the laser optical emission due to the noise of spontaneous
emission.
Electrical oscillations are applied to the electrical input of the phase detector
(Fig. 7.39a) from the output of the amplifier in the OEO structure in the steady-state
mode, and the instantaneous voltage of these oscillations is: u M (t) ¼ U M0 cos
[2πf gen (t)t + φ 0etal + Δφ m, etal (t)], where U M0 is the amplitude of OEO generation
in the steady-state mode, Δφ m, etal (t) is the etalon phase variation due to the noisy
impact.
We assume that the voltage u M (t) ¼ U M0 cos [2πf gen (t)t + φ 0etal + Δφ m, etal (t)] is
close to harmonic and we write u M (t) ¼ U M0 cos [φ m, etal (t)].
We suppose that this voltage u M (t) ¼ u gen (t) is produced by the equivalent radiofrequency generator and assume that the field strength in the first optical channel of
the MZ modulator is close to harmonic: E 1L ¼ E 0L Á cos [2πtν(t) + φ 0L + φ opt (t)] ¼
Е 0L Á cos [φ opt (t)].
We give to the current phases of laser oscillations ψ Lm1 (t) and of the RF generator
φ m, eff (t) variations Δψ L (t) and Δφ gen (t) with respect to the uniformly increasing
etalon phase of RF generator for the generality of examination.
For the phase φ opt (t) of oscillations of the laser field strength we can write:
φ opt (t) ¼ 2πν 0opt Á t + 2πf gen t + Δφ opt (t). For the phase φ m, etal (t) RF generator
oscillations, we have: φ m, etal (t) ¼ 2πf gen t + Δφ gen (t). From formulas
φ opt (t) ¼ 2πν 0opt Á t + 2πf gen t + Δφ opt (t) and φ m, etal (t) ¼ 2πf gen t + Δφ gen (t), it follows
that at detection of the RF generator phase Δφ gen (t) with the help of the traditional
electronic phase detector with RF FODL or with the help of the phase detector made
of the structure with FOS1 (Fig. 7.39b). The phase control in the first optical channel
Δφ opt (t, U 0M ) is performed by means of variation of the DC bias voltage U 0MZ of the
MZ modulator. In other words, there is the process of phase control of RF oscillations in OEO, and hence, the process of phase noises suppression of OEO RF
oscillation occurs.
Let us describe briefly the features of the phase detection in PLL system of OEO
made according to Fig. 7.39b.
456
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .
structure discussed in Sect. 7.7.1 with suppression of the RF subcarrier (Fig. 7.38).
For calculation of the relative PSD of the phase noise of OEO RF oscillations
with the operating PLL system, we deduce the main mathematical relations. We
consider the structure in Fig. 7.39a.
Let it be the field strength of the laser emission in the first optical channel of MZ
defined as: E 1L ¼ Е 0L exp [j2πν(t) À jφ 0L À jψ m1 (t)], where the optical frequency
ν(t) ¼ ν 0 + Δν(t), ν 0 is the average laser frequency, Δν(t) is the variation of the
optical frequency from its average value, φ 0L is the constant phase incursion, ψ m1 (t)
is the phase variation of the laser optical emission due to the noise of spontaneous
emission.
Electrical oscillations are applied to the electrical input of the phase detector
(Fig. 7.39a) from the output of the amplifier in the OEO structure in the steady-state
mode, and the instantaneous voltage of these oscillations is: u M (t) ¼ U M0 cos
[2πf gen (t)t + φ 0etal + Δφ m, etal (t)], where U M0 is the amplitude of OEO generation
in the steady-state mode, Δφ m, etal (t) is the etalon phase variation due to the noisy
impact.
We assume that the voltage u M (t) ¼ U M0 cos [2πf gen (t)t + φ 0etal + Δφ m, etal (t)] is
close to harmonic and we write u M (t) ¼ U M0 cos [φ m, etal (t)].
We suppose that this voltage u M (t) ¼ u gen (t) is produced by the equivalent radiofrequency generator and assume that the field strength in the first optical channel of
the MZ modulator is close to harmonic: E 1L ¼ E 0L Á cos [2πtν(t) + φ 0L + φ opt (t)] ¼
Е 0L Á cos [φ opt (t)].
We give to the current phases of laser oscillations ψ Lm1 (t) and of the RF generator
φ m, eff (t) variations Δψ L (t) and Δφ gen (t) with respect to the uniformly increasing
etalon phase of RF generator for the generality of examination.
For the phase φ opt (t) of oscillations of the laser field strength we can write:
φ opt (t) ¼ 2πν 0opt Á t + 2πf gen t + Δφ opt (t). For the phase φ m, etal (t) RF generator
oscillations, we have: φ m, etal (t) ¼ 2πf gen t + Δφ gen (t). From formulas
φ opt (t) ¼ 2πν 0opt Á t + 2πf gen t + Δφ opt (t) and φ m, etal (t) ¼ 2πf gen t + Δφ gen (t), it follows
that at detection of the RF generator phase Δφ gen (t) with the help of the traditional
electronic phase detector with RF FODL or with the help of the phase detector made
of the structure with FOS1 (Fig. 7.39b). The phase control in the first optical channel
Δφ opt (t, U 0M ) is performed by means of variation of the DC bias voltage U 0MZ of the
MZ modulator. In other words, there is the process of phase control of RF oscillations in OEO, and hence, the process of phase noises suppression of OEO RF
oscillation occurs.
Let us describe briefly the features of the phase detection in PLL system of OEO
made according to Fig. 7.39b.
456
7 Optoelectronic oscillator (OEO) as the Time and Spatial Correlator of Random. . .