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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Pattern selection in optical bistability

Mustapha Tlidi, R. Leféver, Paul Mandel

Published Aug 1, 1996• 34 citations
Publisher

Abstract

Using the weakly nonlinear theory, we analyse the stability and relative stability of transverse patterns appearing in a passive Kerr cavity. We show that the hexagonal H0 structures are stable in the vicinity of the Turing bifurcation point. Numerical simulations confirm the analytical predictions.
DOI
10.1088/1355-5111/8/4/014

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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.
Summary form only given. Transverse optical patterns are capable of allowing noteworthy aspects linked to quantum fluctuations. These issues have been mainly studied in stripe patterns, which present only two modes in the far-field. We address the study of the fluctuations and correlations in a hexagonal pattern in a ring cavity filled with a self-focusing Kerr medium. The dynamics of the electric field is described, in the mean-field approximation, by a Langevin equation for the scaled slowly varying amplitude of the field. We show that the pattern fluctuations can be understood in terms of the neutral modes of the pattern and modes with small damping. These modes are obtained from a stability analysis of the hexagonal pattern. We find strong correlations between the intensity fluctuations of the modes of the pattern, not only among the fundamental harmonics, but also with the higher order ones. We also find strong anticorrelations between the intensity fluctuations of the modes of the pattern and the homogeneous mode which are related to energy conservation.