A scaling law in optomechanically induced nonlinear oscillation

TL;DR

This paper discovers a universal scaling law in nonlinear optomechanical oscillations, linking system parameters to the resulting mechanical limit cycle, aiding experimental design and understanding of complex dynamical behaviors.

Contribution

The paper introduces a quantitative scaling law for nonlinear optomechanical oscillations, derived from numerical simulations, which was previously unestablished.

Findings

Existence of a universal scaling law in optomechanical limit cycles

The scaling law relates system parameters to oscillation characteristics

Facilitates experimental parameter selection for desired dynamical outcomes

Abstract

Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear whether there exists a quantitative law to relate an evolved mechanical oscillation (the limit cycle of the dynamical process) to the given parameters of the fabricated system. Here, by means of the numerical simulations based on nonlinear dynamics, we demonstrate the existence of such quantitative relations that are generally valid to the nonlinear optomechanical processes. These quantitative relations can be summarized to a scaling law that is seemingly similar to those in phase transitions of many-body systems but has very different properties. Such a quantitative law enables one to find the more feasible system parameters for realizing the same or a similar dynamical evolution result, so it will be useful to the relevant experimental researches.