the transfer function of PD, S NY is the nonlinear function of RF first harmonic of
collector current of the RF amplifier: S NY ¼ i C =u B ¼ αu B À βu
3
B at u B ¼ u PD .
The connection of the current first harmonic with the normalized strength E
2
1L is
evident: i 1L ¼
p
2 þ 1=T EF
ð
Þ pþ 2πf 0e
ð
Þ
2
½
exp ÀpT OF
ð
Þ
1=T EF
ð
Þ pK OF K PD S NY
E
2
1L . With the purpose to substantiate the
great attention to investigation of the quantum generator in Chap. 3, Fig. 4.1 shows
the other OEO structures, in which the laser is covered by the positive FB loop. The
OEO structure (Fig. 4.1a) with the external synchronizing radio-frequency oscillator
(RFO) can be attributed to these structures (without which the representation of OEO
cannot be complete). The OEO structure (Fig. 4.1b) with the reference “Laser 2,”
which synchronizes the first laser spanned by positive FB, can be also attributed to
these structures. Operation of structures in Fig. 4.1 cannot be understood and
investigated without the deep knowledge of processes, which takes place in the
laser, taking into consideration the fluctuations. Fundamentals of the theory
presented in the present chapter allow determination of the complete DE system
and its analysis not only for OEO DM and OEO MZ (Fig. 3.2), but from the point of
view of standard approaches of nonlinear oscillation theory, which is approved in
radio electronics and the communication theory. Developed laser theory on the base
of symbolic equations is relevant for many laser systems, in which the laser
synchronization from the external laser (Fig. 4.1b) and the modulation of the laser
optical frequency by variation of the OF Q-factor are used. The laser spanned by
delayed FB, the laser with the set of optical filters including the optical disks with the
high Q-factor, and also with the set of inertial optical components, the laser with
control system for optical frequency, the laser with the PLL system, etc. can be
attributed to these systems.
4.1.2 Quasi-Classical Laser Theory
In spite of literature plenty, the transition from the electromagnetic field equations in
the laser to dynamical DEs for the separate longitudinal mode often causes many
problems, therefore, we discuss it in detail. The relative simplicity of our approach is
explained by the fact that we consider the laser operating in the single-mode regime
with generation of the single optical frequency. At that, the laser spectral line width
in OEO we consider as narrow and close to the Lorentzian curve. This is true, for
example, for single-mode single-frequency semiconductor QWLDs with the Bragg
optical filter, which has the spectral line width of less than 50–300 MHz, and the
oscillation frequency is about 150–250 THz. Such a condition is satisfied in the
fiber-optical lasers (FOL) with the active medium on erbium, ytterbium,
neodymium, etc.
4.1 Semiclassical Laser Equations and OEO Differential Equations
137
collector current of the RF amplifier: S NY ¼ i C =u B ¼ αu B À βu
3
B at u B ¼ u PD .
The connection of the current first harmonic with the normalized strength E
2
1L is
evident: i 1L ¼
p
2 þ 1=T EF
ð
Þ pþ 2πf 0e
ð
Þ
2
½
exp ÀpT OF
ð
Þ
1=T EF
ð
Þ pK OF K PD S NY
E
2
1L . With the purpose to substantiate the
great attention to investigation of the quantum generator in Chap. 3, Fig. 4.1 shows
the other OEO structures, in which the laser is covered by the positive FB loop. The
OEO structure (Fig. 4.1a) with the external synchronizing radio-frequency oscillator
(RFO) can be attributed to these structures (without which the representation of OEO
cannot be complete). The OEO structure (Fig. 4.1b) with the reference “Laser 2,”
which synchronizes the first laser spanned by positive FB, can be also attributed to
these structures. Operation of structures in Fig. 4.1 cannot be understood and
investigated without the deep knowledge of processes, which takes place in the
laser, taking into consideration the fluctuations. Fundamentals of the theory
presented in the present chapter allow determination of the complete DE system
and its analysis not only for OEO DM and OEO MZ (Fig. 3.2), but from the point of
view of standard approaches of nonlinear oscillation theory, which is approved in
radio electronics and the communication theory. Developed laser theory on the base
of symbolic equations is relevant for many laser systems, in which the laser
synchronization from the external laser (Fig. 4.1b) and the modulation of the laser
optical frequency by variation of the OF Q-factor are used. The laser spanned by
delayed FB, the laser with the set of optical filters including the optical disks with the
high Q-factor, and also with the set of inertial optical components, the laser with
control system for optical frequency, the laser with the PLL system, etc. can be
attributed to these systems.
4.1.2 Quasi-Classical Laser Theory
In spite of literature plenty, the transition from the electromagnetic field equations in
the laser to dynamical DEs for the separate longitudinal mode often causes many
problems, therefore, we discuss it in detail. The relative simplicity of our approach is
explained by the fact that we consider the laser operating in the single-mode regime
with generation of the single optical frequency. At that, the laser spectral line width
in OEO we consider as narrow and close to the Lorentzian curve. This is true, for
example, for single-mode single-frequency semiconductor QWLDs with the Bragg
optical filter, which has the spectral line width of less than 50–300 MHz, and the
oscillation frequency is about 150–250 THz. Such a condition is satisfied in the
fiber-optical lasers (FOL) with the active medium on erbium, ytterbium,
neodymium, etc.
4.1 Semiclassical Laser Equations and OEO Differential Equations
137