Thermo-optical dynamics in injected Kerr micro-cavities with strong time-delayed feedback

Koch, E. R.; Greve, D.; Javaloyes, J.; Gurevich, S. V.

Abstract

We investigate the impact of slow thermal effects on the dynamics of vertically emitting Kerr micro-cavities under detuned optical injection. Our model incorporates thermal detuning caused by refractive index shifts due to heating. Through numerical and analytical approaches, we uncover a rich spectrum of dynamical phenomena, including excitable thermo-optical pulses, mixed-mode oscillations, and chaotic spiking, governed by a higher-dimensional canard scenario. Introducing a long external feedback loop with time delay comparable to the micro-cavity photon lifetime but shorter than thermal relaxation time-scales, we demonstrate how temporal localized states are subjected to slanted snaking in the presence of thermal effects. A multiple time-scale analysis performed in the mean field limit shows that the slow evolution of the system is captured by a Lugiato–Lefever equation with third-order dispersion coupled to a non-local heat equation, responsible for the slanting.