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

Europhysics Letters (EPL)

Spontaneous Pattern Formation in an Absorptive System

W. J. Firth, Andrew J. Scroggie

Published Jun 1, 1994• 106 citations
Publisher

Abstract

Spontaneous pattern formation occurs in a ring cavity containing a resonant two-level medium. Non-linear analysis, confirmed by simulations, indicates that both positive and negative hexagonal patterns, as well as rolls, can be stable. Patterns exist because of, and are scaled by, a tilted-wave mechanism.
DOI
10.1209/0295-5075/26/7/008

Related papers

Spontaneous pattern formation in an absorptive system

W. J. Firth, Andrew J. Scroggie

We present analytical and numerical results indicating pattern formation in a purely absorptive medium, namely a resonantly-excited two-level system in a ring cavity. Pattern formation occurs when the cavity is mistuned such that the optical wavelength exceeds that of the nearby cavity mode. But then off-axis or "tilted" waves can exactly fit the cavity, and this determines the dominant transverse wave vector of the pattern.>

Nonlinear Optics•Dec 17, 2002•0 citations

Spontaneous pattern formation in an absorptive system

W. J. Firth, Andrew J. Scroggie

We present analytical and numerical results indicating pattern formation in a purely absorptive medium, namely a resonantly-excited two-level system in a ring cavity. Pattern formation occurs when the cavity is mistuned such that the optical wavelength exceeds that of the nearby cavity mode. But then off-axis or tilted waves can exactly fit the cavity, and this determines the dominant transverse wave vector of the pattern. >

European Quantum Electronics Conference (EQEC)•Aug 24, 2005•0 citations

Non-linear stability analyses of optical pattern formation in an atomic sodium vapour ring cavity

David J. Wollkind, Francisco Alvarado, Dean Emmanuel Edmeade

The development of spontaneous stationary equilibrium patterns induced by the injection of a laser pump field into a purely absorptive two-level atomic sodium vapour ring cavity is investigated by means of various weakly non-linear stability analyses applied to the appropriate governing evolution equation for this optical phenomenon. In the quasi-equilibrium limit for its atomic variables, the mathematical system modelling that phenomenon can be reduced to a single modified Swift–Hohenberg non-linear partial differential time-evolution equation describing the intracavity field on an unbounded 2D spatial domain. Diffraction of radiation can induce transverse patterns consisting of stripes, squares and hexagonal arrays of bright spots or honeycombs in an initially uniform plane-wave configuration. Then, these theoretical predictions are compared with both relevant experimental evidence and existing numerical simulations from some recent non-linear optical pattern formation studies.

IMA Journal of Applied Mathematics•Oct 24, 2008•3 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

Transverse patterns in nascent optical bistability

Mustapha Tlidi, Miltos Georgiou, Paul Mandel

We study the Swift-Hohenberg equation describing a passive optical cavity driven by an external coherent field, valid close to the onset of optical bistability. A linear analysis shows that the system can sustain nontrivial stationary structures for small positive detunings. A weakly nonlinear analysis in the vicinity of the instability points reveals the existence of stable hexagonal structures which eventually give way to rolls. Numerical simulations support such a bifurcation scenario.

Physical Review A•Dec 1, 1993•92 citations

Polarization patterns in a passive ring-cavity

J.B. Geddes, Jerome V. Moloney, Ewan M. Wright +1 more

A ring-cavity system, filled with an isotropic nonlinear medium and driven by a linearly polarized coherent input field, has been the subject of intense study over the last decade. This system can show a number of non-equilibrium phase transitions, including optical bistability (OB), and transverse pattern formation. The instability responsible for pattern formation then simply serves to drive the system from the unstable lower branch to the stable upper branch. This conclusion, however, is based on the assumption that the internal field in the nonlinear ring-cavity preserves its polarization state as that of the input field. Here we extend the mean field model to include polarization effects.>

Nonlinear Optics•Dec 17, 2002•0 citations
The development of spontaneous stationary equilibrium patterns induced by the injection of a laser pump field into a purely absorptive two-level atomic sodium vapour ring cavity is investigated by means of various weakly non-linear stability analyses applied to the appropriate governing evolution equation for this optical phenomenon. In the quasi-equilibrium limit for its atomic variables, the mathematical system modelling that phenomenon can be reduced to a single modified Swift–Hohenberg non-linear partial differential time-evolution equation describing the intracavity field on an unbounded 2D spatial domain. Diffraction of radiation can induce transverse patterns consisting of stripes, squares and hexagonal arrays of bright spots or honeycombs in an initially uniform plane-wave configuration. Then, these theoretical predictions are compared with both relevant experimental evidence and existing numerical simulations from some recent non-linear optical pattern formation studies.
A ring-cavity system, filled with an isotropic nonlinear medium and driven by a linearly polarized coherent input field, has been the subject of intense study over the last decade. This system can show a number of non-equilibrium phase transitions, including optical bistability (OB), and transverse pattern formation. The instability responsible for pattern formation then simply serves to drive the system from the unstable lower branch to the stable upper branch. This conclusion, however, is based on the assumption that the internal field in the nonlinear ring-cavity preserves its polarization state as that of the input field. Here we extend the mean field model to include polarization effects.>