# Edge waves and localisation in lattices containing tilted resonators

## TL;DR

This paper investigates wave phenomena in chiral lattices with tilted resonators, revealing Dirac-like dispersion, edge waves, and localisation effects, supported by theoretical analysis and numerical simulations.

## Contribution

It introduces a detailed analysis of Bloch-Floquet waves in chiral lattices with tilted resonators, highlighting Dirac-like dispersion and edge wave phenomena.

## Key findings

- Identification of Dirac-like dispersion in the structure
- Observation of wave localisation and edge waves
- Numerical validation of theoretical models

## Abstract

The paper presents the study of waves in a structured geometrically chiral solid. A special attention is given to the analysis of the Bloch-Floquet waves in a doubly periodic high-contrast lattice containing tilted resonators. Dirac-like dispersion of Bloch waves in the structure is identified, studied and applied to wave-guiding and wave-defect interaction problems. The work is extended to the transmission problems and models of fracture, where localisation and edge waves occur. The theoretical derivations are accompanied with numerical simulations and illustrations.