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

Physical Review A

Localized structures in chaotic patterns: From disorder to ordering

Martine Le Berre, A. S. Patrascu, Elisabeth Ressayre, Andree A. Tallet

Published Oct 1, 1997• 28 citations
Publisher

Abstract

Two-dimensional (2D) ``chaotic'' localized structures are observed in the transverse profile of light with a delay model of a ring cavity with strongly dispersive two-level atoms. Near nascent optical bistability, the 2D homogeneous solution undergoes a subcritical transition to a spatiotemporal chaos. The inhomogeneous pattern coexisting with the homogeneous solution is filled with large-intensity peaks, oscillating with time. In the subcritical domain, localized structures are observed, with isolated peaks more stable and more coherent than the ones in the filled structure. The order is easily recovered by a filtering procedure that reduces the wave-vector bandwidth.

DOI
10.1103/physreva.56.3150

Related papers

Scaling laws for localized pattern formation in optical bistability

Mustapha Tlidi, Paul Mandel

We study the kinetics of transverse pattern formation in a passive ring cavity containing two-level atoms. Parameters are chosen such that the Turing instabilities are on the upper and lower branches of a bistable domain and close to the limit points, so that the interaction between the long-wavelength modes includes the homogeneous mode. This leads to the formation of a localized structure which connects the two stable branches of the homogeneous bistable solution. The kinetics of this pattern formation is described by simple scaling laws.

Europhysics Letters (EPL)•Nov 15, 1998•11 citations

Hexagonal patterns in optical bistability

W. J. Firth, Andrew J. Scroggie, Graham S. McDonald +1 more

The mean-field model of optical bistability in a ring cavity is extended to include diffraction in two transverse dimensions. Nonlinear analysis in the neighborhood of the instability of the homogeneous solution indicates the formation of stable hexagonal patterns, and this is confirmed by numerical simulation, with reasonable quantitative agreement. Simulations with higher excitation show defect structures and complex dynamical patterns.

Physical Review A•Oct 1, 1992•105 citations

2 Dimensional Transverse Patterns in Optical Bistability

W. J. Firth, Graham S. McDonald, Andrew J. Scroggie +2 more

Pioneered by Moloney and collaborators [1], transverse effects of nonlinear passive systems in a ring cavity have been the object of extensive study. Analytical investigations with diffractive coupling in one transverse dimension have demonstrated [1] that static and dynamic transverse structures occur in this system. Extension of the mean-field dispersive model developed from optical bistability to include diffraction [2] independently demonstrated qualitatively similar features, again in one transverse dimension. Investigations in two transverse dimensions have been largely confined to numerical studies by the Moloney group [1], showing for gaussian beam illumination ring structures which develop through azimuthal instability to a pattern of spots which typically execute a slow chaotic motion with a progressive loss of symmetries.

Nonlinear Dynamics in Optical Systems•Jan 1, 1992•0 citations

Complex spatiotemporal dynamics in lasers

Jorge R. Tredicce, C. Green, E. J. D’Angelo +1 more

It is well known that transverse intensity profiles of lasers may show a nontrivial spatial structure. Usually, depending on the degree of symmetry, the spatial patterns have been associated with modes of a passive resonator or combinations of them which cause oscillations in the laser intensity (mode beating).1 It was recently shown2 that the fluctuations may be due, instead, to the nonlinear coupling between atoms and the field. Here we show that a spontaneous symmetry-breaking process is also at the origin of the formation of complex spatiotemporal dynamics in which oscillations at a single frequency, quasiperiodicity, and chaos may coexist within in the same spatial structure. We compare our experimental results with those obtained from bifurcation theory and numerical integration of the Maxwell–Bloch equations. The transition from a simple (Gaussian) profile to a complex (turbulent) profile is studied by means of the average intensity patterns, frequencies, and phases of the local intensity and cross-correlation functions.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Switching Behavior of Bistable Resonators Filled with Two-Level Atoms

E. Chang, Gene D. Cooperman, M. Dagenais +1 more

A comprehensive numerical and analytical study of the switching dynamics of bistable optical devices is reported. The intracavity medium is modelled as an ensemble of two-level atoms which may be either homogeneously or inhomogeneously broadened. By allowing for arbitrary atomic detunings and cavity mistunings, both the absorptive and dispersive contributions to optical bistability are included. Standing waves are fully taken into account in the usual way through Fourier expansions.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1983•0 citations

Bistable dynamics beyond rotating wave approximation

Yasser Amoun Sharaby, Stephen Lynch, Amitabh Joshi +1 more

In this paper, we investigate the nonlinear dynamical behavior of dispersive optical bistability (OB) for a homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity without invoking the rotating wave approximation (RWA). The periodic oscillations (self-pulsing) and chaos of the unstable state of the OB curve is affected by the counter rotating terms through the appearance of spikes during its periods. Further, the bifurcation with atomic detuning, within and outside the RWA, shows that the OB system can be converted from a chaotic system to self-pulsing system and vice-versa.

Journal of Nonlinear Optical Physics & Materials•Jun 1, 2014•3 citations
Two-dimensional (2D) ``chaotic'' localized structures are observed in the transverse profile of light with a delay model of a ring cavity with strongly dispersive two-level atoms. Near nascent optical bistability, the 2D homogeneous solution undergoes a subcritical transition to a spatiotemporal chaos. The inhomogeneous pattern coexisting with the homogeneous solution is filled with large-intensity peaks, oscillating with time. In the subcritical domain, localized structures are observed, with isolated peaks more stable and more coherent than the ones in the filled structure. The order is easily recovered by a filtering procedure that reduces the wave-vector bandwidth.
We study the kinetics of transverse pattern formation in a passive ring cavity containing two-level atoms. Parameters are chosen such that the Turing instabilities are on the upper and lower branches of a bistable domain and close to the limit points, so that the interaction between the long-wavelength modes includes the homogeneous mode. This leads to the formation of a localized structure which connects the two stable branches of the homogeneous bistable solution. The kinetics of this pattern formation is described by simple scaling laws.
Pioneered by Moloney and collaborators [1], transverse effects of nonlinear passive systems in a ring cavity have been the object of extensive study. Analytical investigations with diffractive coupling in one transverse dimension have demonstrated [1] that static and dynamic transverse structures occur in this system. Extension of the mean-field dispersive model developed from optical bistability to include diffraction [2] independently demonstrated qualitatively similar features, again in one transverse dimension. Investigations in two transverse dimensions have been largely confined to numerical studies by the Moloney group [1], showing for gaussian beam illumination ring structures which develop through azimuthal instability to a pattern of spots which typically execute a slow chaotic motion with a progressive loss of symmetries.
It is well known that transverse intensity profiles of lasers may show a nontrivial spatial structure. Usually, depending on the degree of symmetry, the spatial patterns have been associated with modes of a passive resonator or combinations of them which cause oscillations in the laser intensity (mode beating).1 It was recently shown2 that the fluctuations may be due, instead, to the nonlinear coupling between atoms and the field. Here we show that a spontaneous symmetry-breaking process is also at the origin of the formation of complex spatiotemporal dynamics in which oscillations at a single frequency, quasiperiodicity, and chaos may coexist within in the same spatial structure. We compare our experimental results with those obtained from bifurcation theory and numerical integration of the Maxwell–Bloch equations. The transition from a simple (Gaussian) profile to a complex (turbulent) profile is studied by means of the average intensity patterns, frequencies, and phases of the local intensity and cross-correlation functions.
In this paper, we investigate the nonlinear dynamical behavior of dispersive optical bistability (OB) for a homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity without invoking the rotating wave approximation (RWA). The periodic oscillations (self-pulsing) and chaos of the unstable state of the OB curve is affected by the counter rotating terms through the appearance of spikes during its periods. Further, the bifurcation with atomic detuning, within and outside the RWA, shows that the OB system can be converted from a chaotic system to self-pulsing system and vice-versa.