The absorptive ring cavity: Dynamics & patterns beyond the mean-field limit

An optical ring cavity filled with an absorptive material is a fundamental spontaneous pattern-forming system [1]. Analyses of Turing bifurcations in these (uni-directional) cavity configurations [see Fig. 1(a)] can be simplified by deploying the thin-slice limit, wherein the host nonlinear medium (typically of the Maxwell-Bloch type) has a near-negligible thickness [2]. Our most recent research has investigated the emergence of spontaneous simple [see Fig. 1(b)] and fractal patterns (which are defined by the presence of a single dominant scale length and multiple scale lengths of proportional amplitude, respectively) in absorptive thin-slice cavities [3]. Extensive simulations have demonstrated that the plane-wave limit of our model (where transverse effects are neglected) tends to be stable and well behaved: the cavity dynamics lack the Ikeda-type instabilities that can dominate purely-dispersive systems [4]. We have also started to generalize earlier analyses [3] by accommodating a finite light-medium interaction length. Such considerations will, potentially, facilitate the description of fully-nonparaxial fractal light patterns in bulk-medium geometries [5]. References [1] A. S. Patrascu, C. Nath, M. Le Berre, E. Ressayre, and A. Tallet, Opt. Commun. 91, 433 (1992). [2] M. Le Berre, A. S. Patrascu, E. Ressayre, and A. Tallet, Opt. Commun. 123, 810 (1996). [3] J. G. Huang, J. M. Christian, and G. S. McDonald, J. Nonlin. Opt. Mat. Phys. 21, 1250018 (2012). [4] K. Ikeda, H. Daido, and O. Akimoto, Phys. Rev. Lett. 45, 709 (1980). [5] M. Brambilla, L. Columbo, and T. Maggipinto, J. Phys. B: Quantum Semiclass. Opt. 6, S197 (2004)