# Mechanical bound states in the continuum for macroscopic optomechanics

## TL;DR

This paper demonstrates the existence of symmetry-protected mechanical bound states in the continuum within slab-on-substrate optomechanical crystals, revealing their potential for macroscopic quantum physics and practical applications.

## Contribution

It introduces the concept of mechanical BICs in optomechanical crystals with specific symmetries and analyzes their coupling with optical modes using group theory and simulations.

## Key findings

- Mechanical BICs identified at the $$ point in crystals with $C_{4v}$ and $C_{6v}$ symmetries.
- Strong optomechanical interactions between mechanical BICs and optical resonances verified.
- High-$Q$, large-size mechanical BICs enable potential applications in sensing and beam steering.

## Abstract

Bound states in the continuum (BICs), an emerging type of long-lived resonances different from the cavity-based ones, have been explored in several classical systems, including photonic crystals and surface acoustic waves. Here, we reveal symmetry-protected mechanical BICs in the structure of slab-on-substrate optomechanical crystals. Using a group theory approach, we identified all the mechanical BICs at the $\Gamma$ point in optomechanical crystals with $C_{4v}$ and $C_{6v}$ symmetries as examples, and analyzed their coupling with the co-localized optical BICs and guided resonances due to both moving boundary and photo-elastic effects. We verified the theoretical analysis with numerical simulations of specific optomechanical crystals which support substantial optomechanical interactions between the mechanical BICs and optical resonances. Due to the unique features of high-$Q$, large-size mechanical BICs and substrate-enabled thermal dissipation, this architecture of slab-on-substrate optomechanical crystals might be useful for exploring macroscopic quantum mechanical physics and enabling new applications such as high-throughput sensing and free-space beam steering.