Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

East European Journal of Physics

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

Volodymyr M. Kuklin, Eugen V. Poklonskiy, S. M. Sevidov

Published Jan 1, 2020• 1 citation
Publisher

Abstract

In the article, for limited system conditions that form the spatial structure of the field, the attenuation processes of wave packets of finite amplitude are considered. The line width of the wave field may be the result of the dissipative processes (in a quantum system it is inverse of the lifetime of energy levels) or the result of reactive processes (in classical waveguide systems this is the spectral width of the packet). In the case of filling the waveguide with an active two-level medium, a description is possible using a quasiclassical model of the interaction of the field and particles. In this case, the quantum-mechanical description of the medium is combined with the classical representation of the field. Here, the Rabi frequency plays an important role, which determines the probabilities of induced radiation or absorption of field quanta and the oscillatory change in population inversion (nutation). Depending on the relationship between the Rabi frequency and the line width of the wave packet, the process can change the nature of the field behavior. In strong fields or with a significant population inversion, the line width can be neglected, while the field energy density is quite high. In this case, one should expect noticeable nutations of population inversions with different frequencies corresponding to the local Rabi frequency in different regions of the waveguide, the interference of which will determine the oscillatory behavior of the wave field. At a low level of electric field intensity or a slight population inversion, the mode of changing the field amplitude becomes monotonic. Plasma field damping (Landau damping) is considered. The role of population inversion is assumed by a quantity proportional to the derivative with respect to velocity of the electron distribution function. If the spectral width of the packet is small, the process of wave attenuation acquires a characteristic oscillatory form due to the exchange of energy between the wave and the plasma electrons captured by its field. The attenuation of wide packets is almost monotonic with the formation of a characteristic “plateau” in the vicinity of the phase velocity of the wave on the electron velocity distribution function.

DOI
10.26565/2312-4334-2020-1-02

Related papers

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

Volodymyr M. Kuklin, Eugen V. Poklonskiy

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.

East European Journal of Physics•Jan 1, 2019•5 citations

ON GENERATION OF A WAVE PACKAGE IN A WAVEGUIDE, FILLED ACTIVE MEDIUM

V.V. Kostenko, Volodymyr M. Kuklin, Eugen V. Poklonskiy

Excitation of electromagnetic waves in a waveguide with a medium, which is a two-level system, is considered. To describe the processes, both classical electrodynamics methods and quantum mechanics methods are used. The nature of the processes under study turns out to depend on the relationship between the Rabi frequency and the line width of the excited wave packet. It is shown that if the field energy density is high, then spatially inhomogeneous Rabi frequencies arise, which leads to oscillatory behavior of the wave field amplitudes. If the levels of the excited field are small, then the dynamics of the two-level quantum system becomes monotonic and the population inversion tends to zero.

•Jun 1, 2020•2 citations

Semiclassic Models of the Dissipative Regime of Instability and Superradiation of a Quantum Radiator System

Volodymyr M. Kuklin, В.Т. Лазурик, Eugen V. Poklonskiy

The paper discusses the similarity between dissipative generation and superradiance regimes for systems of excited quantum emitters placed in an open cavity. In the case of the existence of a resonator field due to reflections from the ends of the system, a dissipative generation regime is usually realized. In this case, the decrement of oscillations in the waveguide in the absence of radiators turns out to be greater than the increment of the arising instability of the system of radiators placed in the resonator. When describing this mode, the influence of the emitters on each other and the sum of their own fields is neglected. The resonator field forces the oscillators to emit or absorb quanta synchronously with it, depending on the local value of the population inversion. Lasing takes on a weakly oscillatory character due to an asynchronous change in the population inversion of the system of emitting dipoles (nutations), which have a ground and excited energy levels. To describe the process, the equations of the semiclassical theory based on the use of the density matrix are quite sufficient. In the case when there is no resonator or waveguide field, taking into account the eigenfields of the oscillators becomes essential. To simulate the superradiance process, large emitting particles are used, to describe which one should use the equations for the density matrix. It is shown that the interaction of quantum emitters in this case is due to electromagnetic fields under conditions when the overlap of their wave functions is insignificant. Equations are obtained that allow considering the process of interaction of emitters. When the emitters interact, an integral field is formed in the resonator, an increase in the intensity of which leads to synchronization of the emitters. It is shown that the characteristic times of the development of the process, as well as the attainable amplitudes of the excited fields for dissipative regimes of generation and regimes of superradiance of emitters filling an open resonator, are comparable.

East European Journal of Physics•Jan 1, 2021•4 citations

ON THE NATURE OF COHERENTS IN THE SYSTEM OF OSCILLATORS

Volodymyr M. Kuklin

The paper presents the transition to the regime of induced radiation of a system of oscillators in the classical and the quantum cases. This transition occurs due to synchronization by the integral field of the phases of a small part of oscillator-emitters. In the quantum analogue of this model, it is shown that the formation of an induced (and, therefore, coherent, as noted by Ch. Towns) pulse of the field is due to the interference of nutation of population inversion in different regions of the system of oscillators. The law of spatial variation of the field intensity is deter-mined by the dispersion characteristics of the system and the level of absorption or output of the radiation energy. Only a small fraction of oscillators provide induced radiation: 8% in the classical case and half as much in the case of a quantum system, where a change in the sign of population inversion in the regions of the highest field values significantly affects the limitation of the radiation intensity.

•Aug 15, 2019•6 citations

Spectroscopy of a resonance medium based on the use of nonlinear absorption of strong polychromatic radiation with equidistant spectrum

G. I. Toptygina, Evald E. Fradkin

Let us consider preliminary two situations. In the first of them the monochromatic radiation is absorbing. The increase of its intensity leads to the diminution of an absorption down to zero in a limiting case, i.e. to the effect of saturated absorption. In the second case an absorption of test radiation with a small intensity is observing, while two—level atom is strongly interacting with a perturbing field. This case is characterized by asymmetric dependence of absorption on the frequency difference w- w = A, where w and w are the frequencies of two light waves. As it was shown by Rautian and Sobelman in 19611, the amplification of test radiation arises in a certain range of frequency offsets A instead of the absorption, and the energy transfers from a strong wave to a weak one. In this paper we study the problem which appears from the above situation, when the intensity of test radiation increases. Such an increase leads to new maxima in absorption spectra of test radiation at frequencies A = i n = 2, 3 4 . . . which are additional to the main maxima at n R A = where R the Rabi frequency. These new resonances were observed by Bonch-Bruevich, Vartanyan, and Chigir in 19792 and cal led the subradiat ive structure. We have the following simple approximate expression for R obtained in the case of interaction with two fields: Q =d(?+E2)1"2/h. (1) R 0 1 There are two essential effects in the described situation: the saturation of absorption and the nonlinear interference effect. The last causes the redistribution of an absorbed energy between radiation components, the negative absorption (amplification) without population inversion, and the multiphoton parametric resonances at difference frequencies. The laser generation on the base7of the negative absorption without population inversion was obtained in 1989. The following problems arise from the facts reviewed above: 1. The calculation of absorption coefficients for individual components of a strong polychromatic radiation with an equidistant spectrum. 2. Determining of a generalized Rabi frequency and verification of the simple formula A = In for maxima of resonances. n R The aim of this paper is to solve these problems.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 1, 1992•1 citation

Nonstationary parametric amplification of polychromatic radiation propagating in an extended absorbing resonant medium

Sergei N Bagaev, V. S. Egorov, Igor B. Mekhov +4 more

An experimental and theoretical study of the two-wave interaction (of a probe wave and a pumping wave) of wide-band multimode laser pulses with an optically dense extended resonant medium (metastable neon atoms in a positive glow-discharge column) is presented. Depending on the pumping power and characteristics of the medium, various regimes of interaction between the field and the matter, leading to qualitatively different types of amplification spectra, are realized: a cooperative interaction regime at low pumping powers corresponds to amplification spectra consisting of two peaks, which lie on both sides of the absorption line; in the regime of nonstationary Rabi oscillations (Rabi flopping), the amplification appears in the form of an isolated peak at a frequency close to the resonance in the substance; under certain interaction conditions, a dispersive shape of amplification spectra is observed. A significant gain in the probe field (by several times at a length of 10 cm) is obtained as a result of a nonstationary population inversion upon rotation of the Bloch vector of the resonant medium under the action of a strong pumping field in the course of propagation of the two waves.

Optics and Spectroscopy•Jan 1, 2003•6 citations
In the article, for limited system conditions that form the spatial structure of the field, the attenuation processes of wave packets of finite amplitude are considered. The line width of the wave field may be the result of the dissipative processes (in a quantum system it is inverse of the lifetime of energy levels) or the result of reactive processes (in classical waveguide systems this is the spectral width of the packet). In the case of filling the waveguide with an active two-level medium, a description is possible using a quasiclassical model of the interaction of the field and particles. In this case, the quantum-mechanical description of the medium is combined with the classical representation of the field. Here, the Rabi frequency plays an important role, which determines the probabilities of induced radiation or absorption of field quanta and the oscillatory change in population inversion (nutation). Depending on the relationship between the Rabi frequency and the line width of the wave packet, the process can change the nature of the field behavior. In strong fields or with a significant population inversion, the line width can be neglected, while the field energy density is quite high. In this case, one should expect noticeable nutations of population inversions with different frequencies corresponding to the local Rabi frequency in different regions of the waveguide, the interference of which will determine the oscillatory behavior of the wave field. At a low level of electric field intensity or a slight population inversion, the mode of changing the field amplitude becomes monotonic. Plasma field damping (Landau damping) is considered. The role of population inversion is assumed by a quantity proportional to the derivative with respect to velocity of the electron distribution function. If the spectral width of the packet is small, the process of wave attenuation acquires a characteristic oscillatory form due to the exchange of energy between the wave and the plasma electrons captured by its field. The attenuation of wide packets is almost monotonic with the formation of a characteristic “plateau” in the vicinity of the phase velocity of the wave on the electron velocity distribution function.
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.
Excitation of electromagnetic waves in a waveguide with a medium, which is a two-level system, is considered. To describe the processes, both classical electrodynamics methods and quantum mechanics methods are used. The nature of the processes under study turns out to depend on the relationship between the Rabi frequency and the line width of the excited wave packet. It is shown that if the field energy density is high, then spatially inhomogeneous Rabi frequencies arise, which leads to oscillatory behavior of the wave field amplitudes. If the levels of the excited field are small, then the dynamics of the two-level quantum system becomes monotonic and the population inversion tends to zero.
The paper discusses the similarity between dissipative generation and superradiance regimes for systems of excited quantum emitters placed in an open cavity. In the case of the existence of a resonator field due to reflections from the ends of the system, a dissipative generation regime is usually realized. In this case, the decrement of oscillations in the waveguide in the absence of radiators turns out to be greater than the increment of the arising instability of the system of radiators placed in the resonator. When describing this mode, the influence of the emitters on each other and the sum of their own fields is neglected. The resonator field forces the oscillators to emit or absorb quanta synchronously with it, depending on the local value of the population inversion. Lasing takes on a weakly oscillatory character due to an asynchronous change in the population inversion of the system of emitting dipoles (nutations), which have a ground and excited energy levels. To describe the process, the equations of the semiclassical theory based on the use of the density matrix are quite sufficient. In the case when there is no resonator or waveguide field, taking into account the eigenfields of the oscillators becomes essential. To simulate the superradiance process, large emitting particles are used, to describe which one should use the equations for the density matrix. It is shown that the interaction of quantum emitters in this case is due to electromagnetic fields under conditions when the overlap of their wave functions is insignificant. Equations are obtained that allow considering the process of interaction of emitters. When the emitters interact, an integral field is formed in the resonator, an increase in the intensity of which leads to synchronization of the emitters. It is shown that the characteristic times of the development of the process, as well as the attainable amplitudes of the excited fields for dissipative regimes of generation and regimes of superradiance of emitters filling an open resonator, are comparable.
The paper presents the transition to the regime of induced radiation of a system of oscillators in the classical and the quantum cases. This transition occurs due to synchronization by the integral field of the phases of a small part of oscillator-emitters. In the quantum analogue of this model, it is shown that the formation of an induced (and, therefore, coherent, as noted by Ch. Towns) pulse of the field is due to the interference of nutation of population inversion in different regions of the system of oscillators. The law of spatial variation of the field intensity is deter-mined by the dispersion characteristics of the system and the level of absorption or output of the radiation energy. Only a small fraction of oscillators provide induced radiation: 8% in the classical case and half as much in the case of a quantum system, where a change in the sign of population inversion in the regions of the highest field values significantly affects the limitation of the radiation intensity.
Let us consider preliminary two situations. In the first of them the monochromatic radiation is absorbing. The increase of its intensity leads to the diminution of an absorption down to zero in a limiting case, i.e. to the effect of saturated absorption. In the second case an absorption of test radiation with a small intensity is observing, while two—level atom is strongly interacting with a perturbing field. This case is characterized by asymmetric dependence of absorption on the frequency difference w- w = A, where w and w are the frequencies of two light waves. As it was shown by Rautian and Sobelman in 19611, the amplification of test radiation arises in a certain range of frequency offsets A instead of the absorption, and the energy transfers from a strong wave to a weak one. In this paper we study the problem which appears from the above situation, when the intensity of test radiation increases. Such an increase leads to new maxima in absorption spectra of test radiation at frequencies A = i n = 2, 3 4 . . . which are additional to the main maxima at n R A = where R the Rabi frequency. These new resonances were observed by Bonch-Bruevich, Vartanyan, and Chigir in 19792 and cal led the subradiat ive structure. We have the following simple approximate expression for R obtained in the case of interaction with two fields: Q =d(?+E2)1"2/h. (1) R 0 1 There are two essential effects in the described situation: the saturation of absorption and the nonlinear interference effect. The last causes the redistribution of an absorbed energy between radiation components, the negative absorption (amplification) without population inversion, and the multiphoton parametric resonances at difference frequencies. The laser generation on the base7of the negative absorption without population inversion was obtained in 1989. The following problems arise from the facts reviewed above: 1. The calculation of absorption coefficients for individual components of a strong polychromatic radiation with an equidistant spectrum. 2. Determining of a generalized Rabi frequency and verification of the simple formula A = In for maxima of resonances. n R The aim of this paper is to solve these problems.
An experimental and theoretical study of the two-wave interaction (of a probe wave and a pumping wave) of wide-band multimode laser pulses with an optically dense extended resonant medium (metastable neon atoms in a positive glow-discharge column) is presented. Depending on the pumping power and characteristics of the medium, various regimes of interaction between the field and the matter, leading to qualitatively different types of amplification spectra, are realized: a cooperative interaction regime at low pumping powers corresponds to amplification spectra consisting of two peaks, which lie on both sides of the absorption line; in the regime of nonstationary Rabi oscillations (Rabi flopping), the amplification appears in the form of an isolated peak at a frequency close to the resonance in the substance; under certain interaction conditions, a dispersive shape of amplification spectra is observed. A significant gain in the probe field (by several times at a length of 10 cm) is obtained as a result of a nonstationary population inversion upon rotation of the Bloch vector of the resonant medium under the action of a strong pumping field in the course of propagation of the two waves.