Parametric control of self-sustained and self-modulated optomechanical oscillations

TL;DR

This paper systematically analyzes the parameter space of optomechanical oscillators to identify regions supporting stable, controllable oscillations, aiding their application in technology through bifurcation analysis and numerical methods.

Contribution

It introduces a comprehensive bifurcation analysis of optomechanical oscillators, mapping parameter regions for stable oscillations and their accessibility, which was not previously detailed.

Findings

Identification of parameter regions with stable self-sustained oscillations.

Mapping of basins of attraction for bistable oscillatory states.

Guidelines for tuning optomechanical systems for specific oscillatory behaviors.

Abstract

Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization of optomechanical systems in technological applications, in most cases necessitates a complex, yet predictable and controllable, oscillatory response. In fact, the various types of robust oscillations supported by optomechanical systems are nested in either the same or neighboring regions of the parameter space, where chaos exists. In this work we systematically dissect the parameter space of the fundamental optomechanical oscillator in order to identify regions where stable self-sustained and self-modulated oscillations exist, by utilizing bifurcation analysis and advanced numerical continuation techniques. Moreover,in cases where bistability occurs, we study the accessibility of these oscillatory states in terms of initial conditions and their location with respect to well-defined basins of attraction. The results provide specific knowledge for the parameter sets enabling the appropriate oscillatory response for different types of applications.