Energy Exchange Between the Field and the Active Medium of the Waveguide

Abstract

The work based on a semiclassical description, presents the results of studying the processes of absorption and radiation of a field in the form of a standing wave in a waveguide filled with a two-level active medium. Under conditions of spatial inhomogeneity of the field intensity, interference of quasi-periodic oscillations of population inversion occurs in different local regions of the waveguide. A quasiperiodic change in population inversion is determined by the Rabi frequency, which is known to be associated with the probability of induced radiation with a positive population inversion, or induced absorption with its negative value. Since the population inversion change is accompanied by absorption or emission of field quanta, this leads to the exchange of energy between the field and the active medium located in the waveguide. It is shown that the attenuation of a large-amplitude field to a waveguide filled with an unexcited active medium is nonlinear. In the developed mode, this process has the character of energy exchange between the field and the active medium. In this case, the wave attenuation is replaced by its growth, just as it happens in the well-known case of Landau kinetic damping. Competition of the processes of radiation and absorption leads to the fact that the nature of the oscillations (nutations) of the population inversion at different points of the waveguide space is different. The interference of nonsynchronous spatially localized oscillations of the population inversion in the volume of the waveguide leads to changes in the field amplitude. The paper also discusses the process of field excitation in a waveguide with a pre-inverted two-level active medium, taking into account external mechanisms for the absorption of wave energy. Consideration of these problems is important for understanding the processes of generation of induced radiation, which, as noted by C. Towns, is to a large extent coherent radiation.

On the Attenuation of a Wave Packet in Limited Systems Filled With an Active Medium and Plasma

“…The behavior of the relative number of quanta (bold line) and relative population inversion (thin line) over time with a negligible line width 12 0 Γ = .The population inversion oscillation frequency corresponds to the Rabi frequency and is proportional to the electric field in this local region. From the equations of a simple model presented in[4] for the same initial conditions it follows turns out in our case with different line widths over time 0M → . With an increase in the width of the oscillation line of the field intensity (the number of quanta) and population inversions weaken(Fig.…”

“…1.). This phenomenon is discussed in detail in [4]. With a sufficiently large line width, the mode of changing the field intensity (number of quanta) and population inversion becomes monotonic ( Fig.…”

“…The generation cases described by equations (10) - (12), when the natural line width is much less than the Rabi frequency 12 1 Γ << , under the conditions of the formation of a standing electromagnetic wave due to reflections from its boundaries, were considered in [4]. If the conditions 12 1 Γ >> are satisfied, the oscillatory character (nutations) of the population inversions can be neglected and equations (7-9) can be written in the form…”

“…( 1 6 )Note that the time scale in this description is related to the scale of a simple model [4], as follows S τ τ → . A remarkable circumstance is the quality identity of the calculation results for the case of a simple model [4] and the more complicated description given below for the case of a narrow spectral line ( 12 0 Γ = ), which indicates a rather simple mechanism of energy exchange between the wave and the active medium. It demonstrates the importance of interference of oscillations (nutations) population inversions to describe changes in the amplitude of the field of a steady form in a waveguide.…”

“…In this approach, the Rabi frequency plays an important role, which determines the probabilities of induced radiation or absorption of field quanta [2,3] ). In this case, one should expect noticeable nutations of population inversions with different frequencies corresponding to the local Rabi frequency Ω in different regions of the waveguide, the interference of which determines the behavior of the wave field [4]. If the opposite inequality holds 12 γ > Ω , this case corresponds to rather low levels of electric field intensity or small values of population inversion, which describes the behavior of a two-level system, first formulated in [5].…”