Optomechanical response of a non-linear mechanical resonator

TL;DR

This paper theoretically analyzes the nonlinear optomechanical response of a cavity coupled to a Duffing resonator, revealing how nonlinearities influence reflection and absorption phenomena under different driving conditions.

Contribution

It provides a detailed theoretical investigation of nonlinear effects in optomechanical responses, extending understanding beyond linear models and considering higher-order nonlinearities.

Findings

Red-sideband drive can lead to OMIA or OMIR depending on drive strength.

Blue-sideband drive predominantly results in OMIR.

Nonlinearities beyond Duffing have minimal impact on OMIA dip size, but affect its width.

Abstract

We investigate theoretically in detail the non-linear effects in the response of an optical/microwave cavity coupled to a Duffing mechanical resonator. The cavity is driven by a laser at a red or blue mechanical subband, and a probe laser measures the reflection close to the cavity resonance. Under these conditions, we find that the cavity exhibits optomechanically induced reflection (OMIR) or absorption (OMIA) and investigate the optomechanical response in the limit of non-linear driving of the mechanics. Similar to linear mechanical drive, an overcoupled cavity the red-sideband drive may lead to both OMIA and OMIR depending on the strength of the drive, whereas the blue-sideband drive only leads to OMIR. The dynamics of the phase of the mechanical resonator leads to the difference between the shapes of the response of the cavity and the amplitude response of the driven Duffing oscillator, for example, at weak red-sideband drive the OMIA dip has no inflection point. We also verify that mechanical non-linearities beyond Duffing model have little effect on the size of the OMIA dip though they affect the width of the dip.