Nonlinear dynamics and chaos in an optomechanical beam

TLDR

Optical nonlinearities such as thermo‑optic effects and free‑carrier dispersion are typically considered undesirable in silicon resonators and optomechanical cavities because they alter the detuning between the optical resonance and the excitation laser. The study aims to exploit these nonlinearities and their coupling with mechanical modes in a silicon optomechanical nanobeam to reveal diverse complex dynamics. The authors use the nonlinear thermo‑optic and free‑carrier effects coupled to mechanical degrees of freedom in the nanobeam to generate and control limit cycles and chaotic behavior. By tuning the laser parameters, they can precisely activate two‑ and four‑dimensional limit cycles, induce a period‑doubling route to six‑dimensional chaos, and observe bistability and hysteresis between these states, underscoring the potential of silicon optomechanical photonic crystals for neurocomputational networks and chaos‑based applications.

Abstract

Abstract Optical nonlinearities, such as thermo-optic mechanisms and free-carrier dispersion, are often considered unwelcome effects in silicon-based resonators and, more specifically, optomechanical cavities, since they affect, for instance, the relative detuning between an optical resonance and the excitation laser. Here, we exploit these nonlinearities and their intercoupling with the mechanical degrees of freedom of a silicon optomechanical nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser we demonstrate accurate control to activate two- and four-dimensional limit cycles, a period-doubling route and a six-dimensional chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between two- and four-dimensional limit cycles, between different coherent mechanical states and between four-dimensional limit cycles and chaos. Our findings open new routes towards exploiting silicon-based optomechanical photonic crystals as a versatile building block to be used in neurocomputational networks and for chaos-based applications.