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 and Marquardt (2013 Phys. Rev. Lett. 101, 073603). 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 still be 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.

Highlights

  • The emergence of patterns that spontaneously break some spatial symmetry is widespread in nonlinear optical systems, especially in large aspect-ratio cavities

  • 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 fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig and Marquardt

  • 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 still be observed for a small number of mechanical elements, even in the presence of finite-size effects, which we discuss

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Summary

10 September 2020

J Ruiz-Rivas, G Patera, C Navarrete-Benlloch3,4,5,∗ , E Roldan1,∗ and G J de Valcarcel1,∗. China 5 Shanghai Research Center for Quantum Sciences, Shanghai 201315, People’s Republic of China ∗ Authors to whom any correspondence should be addressed

Introduction
Continuous limit
Numerical simulations
Connection with the standard OM array theory
Conclusions
Full Text
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