# Bragg's reflection for walking droplets in 1D crystals

## TL;DR

This paper explores how a periodic pattern beneath a liquid-air interface influences the behavior of walking droplets in an annular cavity, revealing effects analogous to photonic crystals that could enable new macroscopic waveguiding and reflection devices.

## Contribution

It demonstrates the impact of periodic patterns on droplet dynamics, drawing an analogy with photonic crystals, and suggests potential for designing droplet-based metamaterials.

## Key findings

- Droplet speed nearly vanishes at certain pattern wavelengths.
- Periodic patterns influence droplet trajectories and motion.
- Analogies with photonic crystal behavior are established.

## Abstract

A walking droplet possesses fascinating properties due to its peculiar wave/particle interaction. The self-propelling motion of such a droplet is driven by the Faraday instability triggered around the droplet at each impact. We studied in this article how such a droplet behaves in an annular cavity where a periodic pattern is placed underneath the liquid-air interface, altering the Faraday instability. We show that, while the annulus ensures a circular motion of the droplet, the periodic pattern affects the global droplet motion. Similarly to electromagnetic waves in photonic crystals, the average droplet speed nearly vanishes when the pattern has a characteristic length close to half the Faraday wavelength. This effect opens ways to design guides, reflectors, lattices and metamaterials for such macroscopic particles.