We must emphasize that the main aim of our research in this part is an analysis of
laser characteristic influence (the optical power of stimulated emission, the spontaneous emission level, the laser phase noise, the Q-factor or the time constant of the
laser optical cavity, the photon lifetime in the QWLD optical cavity, the carrier
lifetime in QWLD) and the fiber-optical path (the geometric length of the fiber, the
optical losses of emission in the fiber, etc.) on OEO characteristics as a whole.
Therefore, the laser or QWLD is marked during analysis as the main element. The
laser is the optical quantum generator, which generates oscillations using the forced
transitions of the active substance between energy levels. The laser differs from
traditional electronic oscillators by the nature of generation. It has features, one of
which is the quantum nature of the laser emission noise. At that, noises of
spontaneous output laser emission, which are determined by the lifetime of particles
in excited state, essentially exceed thermal noises in the optical range.
In options of direct and external laser modulation, the low-noise OEO is built
using the phase and amplitude principles of the laser emission modulation. In this
case, the laser phase noise determines the total OEO phase noise level, taking into
account a smallness of all remaining noises of the nonlinear amplifier and the phase
detector.
2.1.4 Semiclassical Laser Approximation
The semiclassical approach to the laser theory (in particular, to QWLD) forms the
one of the main methodic fundamentals of the present book. This means that for laser
description (in Chaps. 6 and 7), which is a part of OEO with RF FODL, we use the
classical Maxwell equations, but substance properties and properties of the active
element material are described by polarization vectors. A peculiarity of this approach
in semiclassical approximation is the fact that for specific laser type with narrowband
QWLD cavity, we can express the substance polarization through the vector of the
field strength. This allows reduction of three equations for the laser field strength, the
active substance polarization, and the population difference of energy levels to the
system of two equations for the field strength and the population difference
(Chap. 3). The complete differential equations of the system obtained for this
approach, permit so-called abbreviation (reduction of equation order) under assumption of band limitation or the high effective Q-factor. Abbreviation of our system of
complete differential equations enables us to obtain a system from three equations
for amplitude and phase of the optical oscillations strength and the equation for
carrier population of active material. Such an approach is true for processes with the
time constant of the optical cavity of 10
À11 to 10
À6 s, which is more than the time
constant of longitudinal relaxation (substance polarization) 10
À12 s. At that, for
narrowband semiconductor QWLD (with the line width less than 1–1000 MHz),
the time constant of the optical cavity is 10
À9 to 10
À6 s. The population settling
process in the active substance plays an important role in the phase noise formation
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2 Nanostructural Optoelectronic Oscillators with the Fiber-Optical Delay Line
laser characteristic influence (the optical power of stimulated emission, the spontaneous emission level, the laser phase noise, the Q-factor or the time constant of the
laser optical cavity, the photon lifetime in the QWLD optical cavity, the carrier
lifetime in QWLD) and the fiber-optical path (the geometric length of the fiber, the
optical losses of emission in the fiber, etc.) on OEO characteristics as a whole.
Therefore, the laser or QWLD is marked during analysis as the main element. The
laser is the optical quantum generator, which generates oscillations using the forced
transitions of the active substance between energy levels. The laser differs from
traditional electronic oscillators by the nature of generation. It has features, one of
which is the quantum nature of the laser emission noise. At that, noises of
spontaneous output laser emission, which are determined by the lifetime of particles
in excited state, essentially exceed thermal noises in the optical range.
In options of direct and external laser modulation, the low-noise OEO is built
using the phase and amplitude principles of the laser emission modulation. In this
case, the laser phase noise determines the total OEO phase noise level, taking into
account a smallness of all remaining noises of the nonlinear amplifier and the phase
detector.
2.1.4 Semiclassical Laser Approximation
The semiclassical approach to the laser theory (in particular, to QWLD) forms the
one of the main methodic fundamentals of the present book. This means that for laser
description (in Chaps. 6 and 7), which is a part of OEO with RF FODL, we use the
classical Maxwell equations, but substance properties and properties of the active
element material are described by polarization vectors. A peculiarity of this approach
in semiclassical approximation is the fact that for specific laser type with narrowband
QWLD cavity, we can express the substance polarization through the vector of the
field strength. This allows reduction of three equations for the laser field strength, the
active substance polarization, and the population difference of energy levels to the
system of two equations for the field strength and the population difference
(Chap. 3). The complete differential equations of the system obtained for this
approach, permit so-called abbreviation (reduction of equation order) under assumption of band limitation or the high effective Q-factor. Abbreviation of our system of
complete differential equations enables us to obtain a system from three equations
for amplitude and phase of the optical oscillations strength and the equation for
carrier population of active material. Such an approach is true for processes with the
time constant of the optical cavity of 10
À11 to 10
À6 s, which is more than the time
constant of longitudinal relaxation (substance polarization) 10
À12 s. At that, for
narrowband semiconductor QWLD (with the line width less than 1–1000 MHz),
the time constant of the optical cavity is 10
À9 to 10
À6 s. The population settling
process in the active substance plays an important role in the phase noise formation
22
2 Nanostructural Optoelectronic Oscillators with the Fiber-Optical Delay Line