the positive feedback loop. We compose symbolic and abbreviated equations of
OEO and examine the analog model of OEO taking into consideration the laser
fluctuations. At first, we discuss the symbolic differential equations of ОЕО DM
(with direct modulation) and ОЕО MZ and construct the OEO analog model on its
base. Then we investigate the oscillation stability of ОЕО and analyze the selfoscillation conditions and oscillation existence conditions in OЕО. Then we investigate the dynamics of transients in ОЕО DM.
After that, in this chapter, we describe the differential equation of OEO with
Langevinian noise sources. The main positions of the fluctuation laser model are
discussed and Langevinian noise sources are described for OEO oscillating system.
Relying on the symbolic constitutive equations of the laser with fluctuations, we
construct the analog models of OEO DM and ОЕО MZ taking into account the laser
noises. We analyze the symbolic differential equations of the laser with fluctuations
in the quasi-stationary mode for the small signal. The approach for calculation of the
power spectral density (PSD) of the amplitude noise (AN) and the phase noise
(PN) of ОЕО is presented. We estimate the effect of the spontaneous laser emission
upon the PSD of PN in OEO. At that, at calculation of PSD noises we use the
approach basing on the symbolic equation of OEO and on the method of abbreviated
fluctuation equations of Evtianov–Kuleshov.
Then, in this chapter, we discuss the approach for calculation of PSD of noises at
representation of OEO as the correlator of random quantities. We describe the base
correlator structures and calculate the autocorrelation functions for oscillations of the
laser field strength and the electrical voltage in OEO.
In Chap. 6, we perform an analysis of the laser optoelectronic oscillator with the
fiber-optical delay line (FODL) as the system of two oscillators of optical and RF
ranges and we study the formation of the RF generation spectrum in OEO MZ taking
into account the influence of laser optical emission parameters including the laser
spectral line width and its power. Then we discuss the general statement of the
investigation task of OEO MZ and describe the structure and the operation principle
of OEO MZ.
The principles of the OEO MZ mathematical model construction and components
including in the OEO MZ structure are described. We describe characteristics and
the transfer function of the MZ modulator in OEO MZ.
After that, we examine the differential fluctuation equations of OEO MZ and
discuss results of the computer modeling of transient processes for oscillation
formation in OEO MZ.
In Chap. 7, we examine ОЕО as the time and spatial correlator of random
quantities. At first, we investigate the model of nonsymmetrical dielectric waveguide
structure of the laser and the optical waveguide. Then, we analyze the OEO DM on
the base of abbreviated differential equations and discuss the problems of the
frequency control in OEO DM by the laser pumping current.
Then we examine the schemes of the frequency control in OEO DM with
differential FODL. The problems of the parametric and long-term frequency instability of OEO with FODL are discussed. The fluctuation equations for PSD of AN
8
1 Introduction
OEO and examine the analog model of OEO taking into consideration the laser
fluctuations. At first, we discuss the symbolic differential equations of ОЕО DM
(with direct modulation) and ОЕО MZ and construct the OEO analog model on its
base. Then we investigate the oscillation stability of ОЕО and analyze the selfoscillation conditions and oscillation existence conditions in OЕО. Then we investigate the dynamics of transients in ОЕО DM.
After that, in this chapter, we describe the differential equation of OEO with
Langevinian noise sources. The main positions of the fluctuation laser model are
discussed and Langevinian noise sources are described for OEO oscillating system.
Relying on the symbolic constitutive equations of the laser with fluctuations, we
construct the analog models of OEO DM and ОЕО MZ taking into account the laser
noises. We analyze the symbolic differential equations of the laser with fluctuations
in the quasi-stationary mode for the small signal. The approach for calculation of the
power spectral density (PSD) of the amplitude noise (AN) and the phase noise
(PN) of ОЕО is presented. We estimate the effect of the spontaneous laser emission
upon the PSD of PN in OEO. At that, at calculation of PSD noises we use the
approach basing on the symbolic equation of OEO and on the method of abbreviated
fluctuation equations of Evtianov–Kuleshov.
Then, in this chapter, we discuss the approach for calculation of PSD of noises at
representation of OEO as the correlator of random quantities. We describe the base
correlator structures and calculate the autocorrelation functions for oscillations of the
laser field strength and the electrical voltage in OEO.
In Chap. 6, we perform an analysis of the laser optoelectronic oscillator with the
fiber-optical delay line (FODL) as the system of two oscillators of optical and RF
ranges and we study the formation of the RF generation spectrum in OEO MZ taking
into account the influence of laser optical emission parameters including the laser
spectral line width and its power. Then we discuss the general statement of the
investigation task of OEO MZ and describe the structure and the operation principle
of OEO MZ.
The principles of the OEO MZ mathematical model construction and components
including in the OEO MZ structure are described. We describe characteristics and
the transfer function of the MZ modulator in OEO MZ.
After that, we examine the differential fluctuation equations of OEO MZ and
discuss results of the computer modeling of transient processes for oscillation
formation in OEO MZ.
In Chap. 7, we examine ОЕО as the time and spatial correlator of random
quantities. At first, we investigate the model of nonsymmetrical dielectric waveguide
structure of the laser and the optical waveguide. Then, we analyze the OEO DM on
the base of abbreviated differential equations and discuss the problems of the
frequency control in OEO DM by the laser pumping current.
Then we examine the schemes of the frequency control in OEO DM with
differential FODL. The problems of the parametric and long-term frequency instability of OEO with FODL are discussed. The fluctuation equations for PSD of AN
8
1 Introduction