Excitability Mediated by Localized Structures in Kerr Cavities

Abstract

We characterize a scenario where localized structures in nonlinear optical cavities display an oscillatory behavior which becomes unstable leading to an excitable regime. Ex- citability emerges from spatial dependence since the system locally is not excitable. We show the existence of difierent mechanisms leading to excitability depending on the proflle of the pump fleld. DOI: 10.2529/PIERS060907134206 Localized structures (LS) in dissipative optical cavities arise as a consequence of the interplay between difiraction, nonlinearity, driving, and dissipation (1). These structures, also known as cavity solitons, are unique once the parameters of the system have been flxed. This fact makes this structures potentially useful in optical storage and processing of information (2,3). LS may develop a number of instabilities, for instance their amplitude can oscillate in time while remaining static in space. Here we report on a novel regime of excitability associated to the existence of localized structures in a nonlinear optical system (4,5). Excitability has been found in a variety of systems (6), including optical systems (7), and is characterized by a nonlinear response under applied external perturbation. Perturbations exceeding a certain threshold are able to elicit in the system a full and well deflned response. Furthermore after one perturbation the system cannot be excited again within a refractory period of time. Excitability is behind excitation waves in heart tissue and the existence of action potentials in neurons, and, so, may confer new computational capabilities to optical systems beyond information storage. In this paper we show the existence of difierent mechanisms leading to excitability depending on the proflle of the pump fleld. For a homogeneous pump the mechanism leading to excitable behavior is a saddle-loop bifurcation through which an stable oscillating LS collides with an unstable LS (4). For a system pumped by a localized Gaussian beam on top of homogeneous background the scenario is richer and one flnds two difierent mechanisms leading to excitability. One is based on a saddle- loop bifurcation as above while the other takes place through a saddle-node in the invariant circle (SNIC) bifurcation. This second mechanism has excitability threshold which can be much lower. We consider a ring cavity fllled with a nonlinear self-focusing Kerr medium pumped by an external fleld. In the mean fleld approximation, the dynamics of the electric fleld inside the cavity can be described by a single partial difierential equation for the scaled slowly varying amplitude E(~) (8) @tE = i(1 + iµ)E + ir 2 E + E0 + ijEj 2 E;