S η f
ð Þ ¼ S ξ f
ð Þ Á
1
N
2
Á
sin
2 T FOS Á N Á f =2
ð
Þ
T FOS Á N Á f =2
ð
Þ
2
:
ð3:12Þ
This formula shows that the larger a number of delay lines N, the more effectively
the input noise impact will be suppressed.
Our analysis is directed to the determination of the laser phase fluctuation
connection with the OEO phase fluctuations. The laser phase fluctuations are defined
by the quantum nature of spontaneous emission. Let us devote the next section to this
physical phenomenon.
3.1.4 Quantum Nature of Laser Noises in OEO
Usually, the quantum-well semiconductor lasers are used in OEO as the optical
source. In the quantum-well lasers, the special conditions have been created for the
charge carriers, and at these conditions, the moving charge demonstrates the quantum properties. At that, the carrier moving in the electrostatic field can be characterized by the de Broglie wavelength, which has the order in tens nanometers. In the
volumetric semiconductor crystal, the quantum wells or spatial resonators are
created by means of evaporation of special layers with thickness from one nanometer
to several tens nanometers. An electron, which falls in these “nano-resonators,”
acquires properties of the particle with the sharply defined energy states. In other
words, the energy spectrum of carriers is quantizing.
The calculation of the laser spontaneous emission, which plays the important role
in formation of OEO phase noises, is performed with the help of quantum-mechanic
Schrodinger equations (SE). The energy of the charge carriers and eigenfunctions are
obtained by the electric field operator supplement in SE. The particle lifetime at
specified energy level and the energy level width are determined. The calculation of
the lifetime in the quantum well is similar the same calculation for the particle in the
single atom, which is located in the electrical field. In the stationary SE with the
potential energy V(z), which defines the quantum-well shape, the term ÀqFz is
added, which takes into consideration the electric field influence:
À
2π
ð Þ
2 h
2
2m
d
2
ψ
d
2 z
þ V z
ð Þ À qFz
ð
Þ ψ ¼ Eψ,
ð3:13Þ
where ψ is the eigenfunction, z is the spatial coordinate, q is the carrier charge, F is
the electrostatic Coulomb force, m is the charge carrier mass, ħ is the Planck
constant. Eigenfunctions for the single-dimension task are defined by Airy functions.
Specifying the shape of the potential well V(z) and the Coulomb force of the
electrical field F, which affects the charged particle, we determine from SE the
positions of the energy levels, coefficient of well passage by the particle, the energy
level widths, the particle lifetime at each level, and the probability of the photon
88 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .
ð Þ ¼ S ξ f
ð Þ Á
1
N
2
Á
sin
2 T FOS Á N Á f =2
ð
Þ
T FOS Á N Á f =2
ð
Þ
2
:
ð3:12Þ
This formula shows that the larger a number of delay lines N, the more effectively
the input noise impact will be suppressed.
Our analysis is directed to the determination of the laser phase fluctuation
connection with the OEO phase fluctuations. The laser phase fluctuations are defined
by the quantum nature of spontaneous emission. Let us devote the next section to this
physical phenomenon.
3.1.4 Quantum Nature of Laser Noises in OEO
Usually, the quantum-well semiconductor lasers are used in OEO as the optical
source. In the quantum-well lasers, the special conditions have been created for the
charge carriers, and at these conditions, the moving charge demonstrates the quantum properties. At that, the carrier moving in the electrostatic field can be characterized by the de Broglie wavelength, which has the order in tens nanometers. In the
volumetric semiconductor crystal, the quantum wells or spatial resonators are
created by means of evaporation of special layers with thickness from one nanometer
to several tens nanometers. An electron, which falls in these “nano-resonators,”
acquires properties of the particle with the sharply defined energy states. In other
words, the energy spectrum of carriers is quantizing.
The calculation of the laser spontaneous emission, which plays the important role
in formation of OEO phase noises, is performed with the help of quantum-mechanic
Schrodinger equations (SE). The energy of the charge carriers and eigenfunctions are
obtained by the electric field operator supplement in SE. The particle lifetime at
specified energy level and the energy level width are determined. The calculation of
the lifetime in the quantum well is similar the same calculation for the particle in the
single atom, which is located in the electrical field. In the stationary SE with the
potential energy V(z), which defines the quantum-well shape, the term ÀqFz is
added, which takes into consideration the electric field influence:
À
2π
ð Þ
2 h
2
2m
d
2
ψ
d
2 z
þ V z
ð Þ À qFz
ð
Þ ψ ¼ Eψ,
ð3:13Þ
where ψ is the eigenfunction, z is the spatial coordinate, q is the carrier charge, F is
the electrostatic Coulomb force, m is the charge carrier mass, ħ is the Planck
constant. Eigenfunctions for the single-dimension task are defined by Airy functions.
Specifying the shape of the potential well V(z) and the Coulomb force of the
electrical field F, which affects the charged particle, we determine from SE the
positions of the energy levels, coefficient of well passage by the particle, the energy
level widths, the particle lifetime at each level, and the probability of the photon
88 3 Modulation Methods of Laser Emission in Optoelectronic oscillator (OEO) and OEO. . .