Oscillatory dynamics in nanocavities with noninstantaneous Kerr response

TL;DR

This paper explores how the finite response time of Kerr nonlinearities influences spontaneous oscillations in nanocavities, revealing critical thresholds and regimes where oscillations transition to chaos or coexist with bistability.

Contribution

It provides a comprehensive analysis of the Hopf bifurcation in nanocavities considering noninstantaneous Kerr response, highlighting the conditions for oscillation, bistability, and chaos.

Findings

Existence of a critical response time for oscillations.

Transition to chaos occurs only far off-resonance.

Oscillatory regimes are mutually exclusive with bistability regions.

Abstract

We investigate the impact of a finite response time of Kerr nonlinearities over the onset of spontaneous oscillations (self-pulsing) occurring in a nanocavity. The complete characterization of the underlying Hopf bifurcation in the full parameter space allows us to show the existence of a critical value of the response time and to envisage different regimes of competition with bistability. The transition from a stable oscillatory state to chaos is found to occur only in cavities which are detuned far off-resonance, which turns out to be mutually exclusive with the region where the cavity can operate as a bistable switch.