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Physical Review Letters

Curvature Instability in Passive Diffractive Resonators

Mustapha Tlidi, A. G. Vladimirov, Paul Mandel

Published Nov 18, 2002• 16 citations
Publisher

Abstract

We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.

DOI
10.1103/physrevlett.89.233901

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 28, 1992•0 citations
We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.
Summary form only given. Stationary localized structures (LS) and localized patterns have been predicted in passive resonators in regimes where the homogeneous steady states exhibit a subcritical Turing (or modulational) instability. These solutions consist of bright or dark spots in the transverse profile of the intracavity field amplitude. They can be either spatially independent and randomly distributed or clusters forming well-defined spatial patterns in the transverse plane orthogonal to the propagation axis. We consider an optical cavity with plane mirrors filled with resonant two-level atoms and driven by a coherent plane-wave injected signal. We focus on the purely absorptive limit where the two-level atoms are in resonance with the injected field. In this system, two type of LS may be generated, depending on the magnitude of the critical wave number associated with the modulational instability: circular localized bright spots or a stationary localized single stripe. Both types of LS can form for the same value of parameters.
In this paper, the general ring cavity model of passive and active optical systems is presented. In the mean field and the Gaussian one transverse mode approximations, the steady state and stability properties of the systems are analyzed for mixed absorptive and dispersive cases. It is found that when the transmissivity ratio M (equals T1/T2) varies, the bistable loop changes its size and even the systematic behavior varies from the bistability mode into the amplification mode, and the instability domain on the steady state curve varies obviously. The mode-pulling formula and bistable threshold with varying values of M are also discussed.