Spatial localization and pattern formation in discrete optomechanical cavities and arrays

TL;DR

This paper explores how nonlinear dissipative structures and pattern formation can occur in discrete optomechanical arrays, bridging continuous and discrete models, and demonstrating observable effects even with few mechanical elements.

Contribution

It introduces a theoretical framework connecting continuous and discrete optomechanical models, showing pattern formation persists in small arrays.

Findings

Pattern formation occurs in small arrays despite finite-size effects.

Discrete models can replicate continuous optomechanical behaviors.

Spatial localization is achievable with few mechanical resonators.

Abstract

We investigate theoretically the generation of nonlinear dissipative structures in optomechanical (OM) systems containing discrete arrays of mechanical resonators. We consider both hybrid models in which the optical system is a continuous multimode field, as it would happen in an OM cavity containing an array of micro-mirrors, and also fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig & Marquardt [Phys. Rev. Lett. 101, 073603 (2013)]. Also, we study the connections between both types of models and continuous OM models. While all three types of models merge naturally in the limit of a large number of densely distributed mechanical resonators, we show that the spatial localization and the pattern formation found in continuous OM models can be still observed for a small number of mechanical elements, even in the presence of finite-size effects, which we discuss. This opens new venues for experimental approaches to the subject.