problems of achievement of extremely admissible phase noises in different OEO
structures at the specified level of the spontaneous laser emission.
The adequate OEO model with fluctuations cannot be created, to our minds,
without addressing to the fundamental laser theory with account of the carrier noise.
In classical laser model, its emission field is described with the help of classical
electrodynamics (Maxwell equations). The semiclassical theory is able to take into
consideration phase relationships, phase fluctuations of the laser emission, and then
to transform them into the OEO phase noise. This theory describes the laser with the
help of classical electrodynamics, and the atom system is described by the quantummechanical approach, the kinetic equations are analyzed, the phase and
(if necessary) frequency relationships are calculated. For spontaneous emission
description, we use the quantum theory, in which the field and the atom system
are determined from the quantum mechanics.
Authors use the different approaches of OEO mathematical modeling: on the base
of amplitude and phase balance equations, on the base of abbreviated equations, on
the base of kinetic laser equations, and on the base of semiclassical laser differential
equations taking into account the equation for optical carrier phase. At solution of
different tasks (for instance, finding of the steady-state amplitude and OEO frequency), the OEO laser is represented as the passive one-port network of the
two-port network, which is characterized by amplitude-frequency characteristic
(AFC) and phase-frequency characteristics (PFC) and its watt–ampere characteristic
(WAC). For other tasks, for example, obtaining of the OEO phase noise spectral
density or the analysis of transient dynamics, time-functions of emission intensity,
the optical emission frequency and phase, the laser should be represented by more
complicate models on the base of semiclassical description in the dipole approximation of the double-level model.
To obtain the dependence of PSD of the phase noise of OEO RF oscillations from
the laser phase noise level, we consider fluctuation differential equations for the
strength squared, the population and the phase of optical oscillations, and equations
for the positive feedback network.
We hope that the autonomous delayed oscillator theory is well known to the
reader, because it is discussed in many books and papers. The features of OEO
modulation methods and methods of the noise suppression are studied in lesser
degree. Therefore, in our OEO analysis we begin from description of structures with
direct and external modulation of laser emission taking into consideration the phase
fluctuations of the laser emission.
3.1.2 Variants with Direct and External Modulations
Following the approach described in [1–3] for the OEO noise analysis, we consider
the system (Fig. 3.1), in which two different oscillating processes are developed: in
the laser with oscillation frequency about 200 THz and in a closed into a loop RF
76 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
structures at the specified level of the spontaneous laser emission.
The adequate OEO model with fluctuations cannot be created, to our minds,
without addressing to the fundamental laser theory with account of the carrier noise.
In classical laser model, its emission field is described with the help of classical
electrodynamics (Maxwell equations). The semiclassical theory is able to take into
consideration phase relationships, phase fluctuations of the laser emission, and then
to transform them into the OEO phase noise. This theory describes the laser with the
help of classical electrodynamics, and the atom system is described by the quantummechanical approach, the kinetic equations are analyzed, the phase and
(if necessary) frequency relationships are calculated. For spontaneous emission
description, we use the quantum theory, in which the field and the atom system
are determined from the quantum mechanics.
Authors use the different approaches of OEO mathematical modeling: on the base
of amplitude and phase balance equations, on the base of abbreviated equations, on
the base of kinetic laser equations, and on the base of semiclassical laser differential
equations taking into account the equation for optical carrier phase. At solution of
different tasks (for instance, finding of the steady-state amplitude and OEO frequency), the OEO laser is represented as the passive one-port network of the
two-port network, which is characterized by amplitude-frequency characteristic
(AFC) and phase-frequency characteristics (PFC) and its watt–ampere characteristic
(WAC). For other tasks, for example, obtaining of the OEO phase noise spectral
density or the analysis of transient dynamics, time-functions of emission intensity,
the optical emission frequency and phase, the laser should be represented by more
complicate models on the base of semiclassical description in the dipole approximation of the double-level model.
To obtain the dependence of PSD of the phase noise of OEO RF oscillations from
the laser phase noise level, we consider fluctuation differential equations for the
strength squared, the population and the phase of optical oscillations, and equations
for the positive feedback network.
We hope that the autonomous delayed oscillator theory is well known to the
reader, because it is discussed in many books and papers. The features of OEO
modulation methods and methods of the noise suppression are studied in lesser
degree. Therefore, in our OEO analysis we begin from description of structures with
direct and external modulation of laser emission taking into consideration the phase
fluctuations of the laser emission.
3.1.2 Variants with Direct and External Modulations
Following the approach described in [1–3] for the OEO noise analysis, we consider
the system (Fig. 3.1), in which two different oscillating processes are developed: in
the laser with oscillation frequency about 200 THz and in a closed into a loop RF
76 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .