Chapter 5
Optoelectronic oscillator (OEO) Differential
Equations as the Laser System
with Modulation and Positive Feedback
This chapter is devoted to main features of OEO. The optoelectronic oscillator is
considered as the oscillating system with modulation, which is spanned by the
positive feedback. We form the symbolic and abbreviated equations of OEO. The
analog model of OEO is examined taking into account the laser fluctuations.
In Sect. 5.1, we discuss the symbolic DEs of OEO DM and OEO MZ and the
analog model of OEO, which is constructed on its base. The oscillation stability of
the OEO oscillating system is investigated in Sect. 5.2, and OEO self-excitation and
oscillation existence conditions are analyzed.
In Sect. 5.3, we investigate the transient dynamics in OEO DM. On the base of
OEO abbreviated equations, we estimate the time for oscillation setting of laser
strength and oscillations of the pumping current. Solutions are considered for the
OEO DM field strength, for the population, and the pumping current in transients.
Section 5.4 is devoted to description of OEO differential equation with the
Langevinian noise sources. The main regulations of the laser fluctuation model are
described, and the Langevinian noise sources are examined for the OEO oscillating
system. On the base of laser symbolic constitutive equations with fluctuations, we
construct the analog models of OEO DM and OEO MZ with account of laser noises.
The symbolic DEs of the laser with fluctuations in the quasi-stationary mode for the
small signal are analyzed.
In Sect. 5.5, we describe the approach to calculation of the power spectral density
of the amplitude and phase noise of OEO. The influence of the spontaneous laser
emission on PSD of OEO phase noise is described. At PSD of the noise calculation,
we use the approach based on the symbolic equations of OEO. For this, the method
of abbreviated fluctuation equations of Evtianov–Kuleshov is used. The approach
for PSD of OEO noises is described at OEO representation as the correlator of
random quantities. The main correlator structures are discussed, and autocorrelation
functions for oscillations of the laser field strength and the electrical voltage in OEO
are calculated.
Main results of this chapter are summarized in Sect. 5.6.
© The Editor(s) (if applicable) and The Author(s), under exclusive license to
Springer Nature Switzerland AG 2020
A. A. Bortsov et al., Laser Optoelectronic Oscillators, Springer Series in Optical
Sciences 232, https://doi.org/10.1007/978-3-030-45700-6_5
203
Optoelectronic oscillator (OEO) Differential
Equations as the Laser System
with Modulation and Positive Feedback
This chapter is devoted to main features of OEO. The optoelectronic oscillator is
considered as the oscillating system with modulation, which is spanned by the
positive feedback. We form the symbolic and abbreviated equations of OEO. The
analog model of OEO is examined taking into account the laser fluctuations.
In Sect. 5.1, we discuss the symbolic DEs of OEO DM and OEO MZ and the
analog model of OEO, which is constructed on its base. The oscillation stability of
the OEO oscillating system is investigated in Sect. 5.2, and OEO self-excitation and
oscillation existence conditions are analyzed.
In Sect. 5.3, we investigate the transient dynamics in OEO DM. On the base of
OEO abbreviated equations, we estimate the time for oscillation setting of laser
strength and oscillations of the pumping current. Solutions are considered for the
OEO DM field strength, for the population, and the pumping current in transients.
Section 5.4 is devoted to description of OEO differential equation with the
Langevinian noise sources. The main regulations of the laser fluctuation model are
described, and the Langevinian noise sources are examined for the OEO oscillating
system. On the base of laser symbolic constitutive equations with fluctuations, we
construct the analog models of OEO DM and OEO MZ with account of laser noises.
The symbolic DEs of the laser with fluctuations in the quasi-stationary mode for the
small signal are analyzed.
In Sect. 5.5, we describe the approach to calculation of the power spectral density
of the amplitude and phase noise of OEO. The influence of the spontaneous laser
emission on PSD of OEO phase noise is described. At PSD of the noise calculation,
we use the approach based on the symbolic equations of OEO. For this, the method
of abbreviated fluctuation equations of Evtianov–Kuleshov is used. The approach
for PSD of OEO noises is described at OEO representation as the correlator of
random quantities. The main correlator structures are discussed, and autocorrelation
functions for oscillations of the laser field strength and the electrical voltage in OEO
are calculated.
Main results of this chapter are summarized in Sect. 5.6.
© The Editor(s) (if applicable) and The Author(s), under exclusive license to
Springer Nature Switzerland AG 2020
A. A. Bortsov et al., Laser Optoelectronic Oscillators, Springer Series in Optical
Sciences 232, https://doi.org/10.1007/978-3-030-45700-6_5
203