Excitability is observed in many natural and artificial systems, from spiking neurons to cardiac cells and semiconductor lasers. It corresponds to the all-or-none pulse-shaped response of a system to an external perturbation, depending whether or not the perturbation amplitude exceeds the so-called excitable threshold. When subject to delayed feedback, an excitable system can regenerate its own excitable response when it is reinjected after a delay time τ. As the process repeats, this results in sustained pulsing regimes, which can be of interest for many applications, from data transmission to all-optical signal processing or neuromorphic photonic networks.

 

Here we investigate the short-term and long-term dynamics of an excitable microlaser subject to delayed optical feedback. This is done both experimentally and numerically through a bifurcation analysis of a suitable model written in the form of three delay-differential equations (DDEs) with one fast and two slow variables. We show that almost any pulse sequence can be excited and regenerated by the system over short periods of time. In the long-term, on the other hand, the system settles down to one of the coexisting, slowly-attracting periodic orbits. These correspond to different numbers of pulses in the feedback cavity, which are demonstrated to be either 

equidistant (i.e. with equalized pulse intervals) or non-equidistant in the feedback cavity depending on the ratio between the internal timescales of the excitable system. We demonstrate that non-equidistant pulsing patterns originate in resonance phenomena and that they are observed in very large locking regions in the parameter space. The mechanism for the emergence of such large locking regions is investigated through a numerical bifurcation analysis.