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

Soviet Journal of Quantum Electronics

Instabilities and chaos in a bistable thin layer of two-level atoms

Yu. A. Logvin, A. M. Samson, Sergei I. Turovets

Published Nov 30, 1990• 12 citations
Publisher

Abstract

A theoretical analysis is made of the interaction between a bistable thin layer and an electromagnetic wave of modulated amplitude. It is shown that complex (including random) regimes appear in the reflection and transmission of light by a thin layer. The model equations are presented in a form correpsonding to the motion of a classical nonlinear oscillator with parametric and external force excitation. The behavior of the system is analyzed in terms of the dynamics of this oscillator.

DOI
10.1070/qe1990v020n11abeh007568

Related papers

Mirrorless Optical Bistability of Thin Layer with Resonant Two-Level Atoms in Ultrashort Light Pulse Field

Viktor A. Malyshev, Evgenii Dmitrievich Trifonov, А. И. Зайцев +1 more

We investigate the problem of resonant re flection and transmission of an ultrashort light pulse passing through a medium consisting of two-level atoms. We show that for a thin layer it is important to take into account the difference between the external macroscopic field and the field acting on the individual atoms within the medium. The local field correction leads to an inversion dependent resonant frequency. In thin layers this generates a new mechanism of nonlinear transparency induced by the dynamical frequency shift. When the excitation frequency is larger than the original resonant frequency, then the transmission of the layer exhibits bistable behavior.

Nonlinear Dynamics in Optical Systems•Jan 1, 1990•0 citations

Phase of an optical wave as an additional degree of freedom in optical information processing systems based on optical bistability

Askhat M Basharov

It is shown theoretically that additional illumination by a squeezed field of a thin layer of two-level atoms, which interact with a resonant coherent electromagnetic wave, results in bistable transmission/reflection of this wave. This bistability depends strongly on the difference between the phases of the coherent and squeezed fields.

Quantum Electronics•Oct 31, 1995•0 citations

Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local-field effects

M. G. Benedict, Victor A Malyshev, Evgenii Dmitrievich Trifonov +1 more

We investigate the problem of resonant reflection and transmission of an ultrashort light pulse passing through a thin layer consisting of two-level atoms. The local-field correction that leads to an inversion-dependent resonance frequency generates a new mechanism of nonlinear transparency. When the excitation frequency is somewhat larger than the original resonant frequency, then the transmission of the layer exhibits a transient bistable behavior on the time scale of superradiation, which can be much shorter than the relaxation times. This type of bistability is essentially different from the ordinary stationary intrinsic bistability investigated earlier by other authors.

Physical Review A•Apr 1, 1991•124 citations

Delay effects in a system formed by a bistable thin film and a mirror

Natalia A. Loiko, Yu. A. Logvin, A. M. Samson

A theoretical investigation is made of the dynamics of the interaction of light with a bistable system formed by a thin film and a feedback mirror. The dependence of the dynamics on the ratio of the relaxation time of a two-level medium to the delay associated with the transmission of light from the film to the mirror and back again is determined. The reasons and conditions for the appearance of regular pulsations and of more complex dynamics are found.

Quantum Electronics•Apr 30, 1995•3 citations

Instabilities of counterpropagating beams in a nonlinear medium

Railing Chang, Pierre Meystre

The dynamical behavior of counterpropagating light beams interacting with a nonlinear medium is studied numerically. When the incident intensities are increased, this system becomes unstable and exhibits oscillations undergoing complex behavior, including quasiperiodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are calculated. A physical interpretation of the quasiperiodic motion is also given by an exact calculation of the absorption spectrum of a two-level atom.

Physical Review A•Sep 1, 1991•7 citations

Instability and chaos of counterpropagating beams in a nonlinear medium.

Railing Chang

The dynamical behavior of counterpropagating light waves interacting with a nonlinear medium is studied numerically. It is found that the wave and the medium form a system that becomes unstable under certain conditions and exhibits self-oscillation. Because the interacting medium is modeled by an ensemble of two-level systems, we recognize the self-oscillation frequency as the Rabi-frequency of the constituent systems. The physical mechanisms responsible for this self-oscillation are the gain and the distributed feedback of the combined lightwave-medium system. When the environment changes, in particular when the intensity is increased, this system becomes more unstable and we find that the oscillation exhibits more complex behavior, including quasi-periodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are also calculated. A physical interpretation of the quasiperiodic motion is given by an exact calculation of the absorption spectrum of our two-level medium. The negative absorption (gain) peaks are found at the frequencies of the quasi-periodic motions, thus implying that the gain of the combined light-medium system is responsible at least in part for the observed complex behavior. In addition, we investigate the stability of the propagating plane wave when a transverse wave is added to the system as a perturbation. Instabilities are analyzed by linearizing the nonlinear equations which model the lightwave-medium system. The results show that the instability is highly-correlated with the four-wave mixing phase conjugation.

•Jan 1, 1991•0 citations
A theoretical analysis is made of the interaction between a bistable thin layer and an electromagnetic wave of modulated amplitude. It is shown that complex (including random) regimes appear in the reflection and transmission of light by a thin layer. The model equations are presented in a form correpsonding to the motion of a classical nonlinear oscillator with parametric and external force excitation. The behavior of the system is analyzed in terms of the dynamics of this oscillator.
We investigate the problem of resonant re flection and transmission of an ultrashort light pulse passing through a medium consisting of two-level atoms. We show that for a thin layer it is important to take into account the difference between the external macroscopic field and the field acting on the individual atoms within the medium. The local field correction leads to an inversion dependent resonant frequency. In thin layers this generates a new mechanism of nonlinear transparency induced by the dynamical frequency shift. When the excitation frequency is larger than the original resonant frequency, then the transmission of the layer exhibits bistable behavior.
We investigate the problem of resonant reflection and transmission of an ultrashort light pulse passing through a thin layer consisting of two-level atoms. The local-field correction that leads to an inversion-dependent resonance frequency generates a new mechanism of nonlinear transparency. When the excitation frequency is somewhat larger than the original resonant frequency, then the transmission of the layer exhibits a transient bistable behavior on the time scale of superradiation, which can be much shorter than the relaxation times. This type of bistability is essentially different from the ordinary stationary intrinsic bistability investigated earlier by other authors.
The dynamical behavior of counterpropagating light beams interacting with a nonlinear medium is studied numerically. When the incident intensities are increased, this system becomes unstable and exhibits oscillations undergoing complex behavior, including quasiperiodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are calculated. A physical interpretation of the quasiperiodic motion is also given by an exact calculation of the absorption spectrum of a two-level atom.
The dynamical behavior of counterpropagating light waves interacting with a nonlinear medium is studied numerically. It is found that the wave and the medium form a system that becomes unstable under certain conditions and exhibits self-oscillation. Because the interacting medium is modeled by an ensemble of two-level systems, we recognize the self-oscillation frequency as the Rabi-frequency of the constituent systems. The physical mechanisms responsible for this self-oscillation are the gain and the distributed feedback of the combined lightwave-medium system. When the environment changes, in particular when the intensity is increased, this system becomes more unstable and we find that the oscillation exhibits more complex behavior, including quasi-periodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are also calculated. A physical interpretation of the quasiperiodic motion is given by an exact calculation of the absorption spectrum of our two-level medium. The negative absorption (gain) peaks are found at the frequencies of the quasi-periodic motions, thus implying that the gain of the combined light-medium system is responsible at least in part for the observed complex behavior. In addition, we investigate the stability of the propagating plane wave when a transverse wave is added to the system as a perturbation. Instabilities are analyzed by linearizing the nonlinear equations which model the lightwave-medium system. The results show that the instability is highly-correlated with the four-wave mixing phase conjugation.