discussed for determination of resonance characteristics in the steady-state mode.
Results of nonlinear DE equations and resonance characteristics at high power
density in the optical resonator are described in Sect. 4.7. Section 4.8 contains the
main conclusions on this chapter.
4.1 Semiclassical Laser Equations and OEO Differential
Equations
In this chapter, we continue to develop the main idea of this book: in OEO, the laser
is the main element defining the dynamic and noise properties of OEO (Fig. 3.2а–с).
We address for the analysis of the quantum generator, which plays a role in OEO
of the main energy source, to the semiclassical laser theory based on the dipole
representation in the double-level approximation. The classical theory uses the
Maxwell equations connecting the polarization of the laser active medium and the
oscillation field strength for description of the electromagnetic field of laser emission. At that, the model of complete nonlinear DEs is traditionally considered
consisting of three equations, which connect the medium polarization, the field
strength and the particle population difference in upper and lower levels. This system
of nonlinear DEs of fourth order with inertial oscillation control allows formation of
the laser analog model.
In the classical model, the laser emission field is described with the help of the
classical electrodynamics (Maxwell equations). In kinetic equations, which are
constructed on the base of constitutive law (on the phenomenological approach),
the emission field is characterized by the average number of photons, and the atom
system is represented on the language of mathematical expectation of level
populations.
Although the method of kinetic equations permits to analyze of dynamics and to
find out the intensity and thresholds of emission, this method does not allow
calculation of phase relationships. The semiclassical theory is able to take into
consideration phase relationships, phase fluctuations of laser emission and then to
transform it into the phase noise of OEO. This quasi-classical theory describes the
laser with the help of the classical electrodynamics, and the atom system is described
in the quantum mechanics manner, kinetic equations are analyzed and specified, the
phase relations are calculated and (if necessary) the frequency relations. To describe
the spontaneous emission, we can use the quantum theory, in which the field and the
atom system are determined from the quantum mechanics manner.
Here we deal not only with description (available for students and engineers) of
known positions developed in the 1960s–1980s by Haken [1–3], Haug [4], Lamb
[5], and others, but we analyze of the laser system from positions of the nonlinear
oscillation theory for QWLD.
At our analysis, as will be shown in further sections of this chapter, we sequentially perform the following:
134
4 Semiclassical Theory and Laser Differential Equations for Optoelectronic. . .
Results of nonlinear DE equations and resonance characteristics at high power
density in the optical resonator are described in Sect. 4.7. Section 4.8 contains the
main conclusions on this chapter.
4.1 Semiclassical Laser Equations and OEO Differential
Equations
In this chapter, we continue to develop the main idea of this book: in OEO, the laser
is the main element defining the dynamic and noise properties of OEO (Fig. 3.2а–с).
We address for the analysis of the quantum generator, which plays a role in OEO
of the main energy source, to the semiclassical laser theory based on the dipole
representation in the double-level approximation. The classical theory uses the
Maxwell equations connecting the polarization of the laser active medium and the
oscillation field strength for description of the electromagnetic field of laser emission. At that, the model of complete nonlinear DEs is traditionally considered
consisting of three equations, which connect the medium polarization, the field
strength and the particle population difference in upper and lower levels. This system
of nonlinear DEs of fourth order with inertial oscillation control allows formation of
the laser analog model.
In the classical model, the laser emission field is described with the help of the
classical electrodynamics (Maxwell equations). In kinetic equations, which are
constructed on the base of constitutive law (on the phenomenological approach),
the emission field is characterized by the average number of photons, and the atom
system is represented on the language of mathematical expectation of level
populations.
Although the method of kinetic equations permits to analyze of dynamics and to
find out the intensity and thresholds of emission, this method does not allow
calculation of phase relationships. The semiclassical theory is able to take into
consideration phase relationships, phase fluctuations of laser emission and then to
transform it into the phase noise of OEO. This quasi-classical theory describes the
laser with the help of the classical electrodynamics, and the atom system is described
in the quantum mechanics manner, kinetic equations are analyzed and specified, the
phase relations are calculated and (if necessary) the frequency relations. To describe
the spontaneous emission, we can use the quantum theory, in which the field and the
atom system are determined from the quantum mechanics manner.
Here we deal not only with description (available for students and engineers) of
known positions developed in the 1960s–1980s by Haken [1–3], Haug [4], Lamb
[5], and others, but we analyze of the laser system from positions of the nonlinear
oscillation theory for QWLD.
At our analysis, as will be shown in further sections of this chapter, we sequentially perform the following:
134
4 Semiclassical Theory and Laser Differential Equations for Optoelectronic. . .