Large period spiking andburstingin anexcitable system with memory

Abstract

Excitability in dynamical systems refers to the ability to transition from a resting stationary state to a spiking state when a parameter is varied. It is the mechanism behind spike generation in neurons. Optical non-linear resonators can be excitable systems, but they usually present a fast response compared to neuronal systems, and they prove difficult to observe experimentally. We propose investigating optical resonators with delayed Kerr effects, specifically in two different geometries: an oil-filled single-mode cavity with thermo-optical nonlinearity, and two coupled, symmetrically driven cavities. When the Kerr effect is delayed, even a single cavity exhibits excitability. However, we show that it suffers from limitations on the thermo-optical relaxation time in order to be realized experimentally. We overcome these limitations using the geometry with coupled cavities, where the thermo-optical relaxation time acts as a memory. This slow variable enables to tailor the spiking frequency and it mimics neuronal behaviours by enabling large-period spiking.