Symmetry-induced quasicrystalline waveguides

TL;DR

This paper develops a general theory for reflection-induced localized edge modes in quasicrystals, enabling the design of robust waveguides with potential advantages over periodic structures.

Contribution

It introduces a unified theoretical framework for reflection-induced localized modes in quasicrystalline and periodic materials, including analysis of Fibonacci-based quasicrystals.

Findings

Localized edge modes can be created within spectral gaps of quasicrystals.

Quasicrystalline waveguides can be more robust than periodic ones in certain scenarios.

The benefits of quasicrystals depend on specific decay rates and application contexts.

Abstract

Introducing an axis of reflectional symmetry in a quasicrystal leads to the creation of localised edge modes that can be used to build waveguides. We develop theory that characterises reflection-induced localised modes in materials that are formed by recursive tiling rules. This general theory treats a one-dimensional continuous differential model and describes a broad class of both quasicrystalline and periodic materials. We present an analysis of a material based on the Fibonacci sequence, which has previously been shown to have exotic, Cantor-like spectra with very wide spectral gaps. Our approach provides a way to create localised edge modes at frequencies within these spectral gaps, giving strong and stable wave localisation. We also use our general framework to make a comparison with reflection-induced modes in periodic materials. These comparisons show that while quasicrystalline waveguides enjoy enhanced robustness over periodic materials in certain settings, the benefits are less clear if the decay rates are matched. This shows the need to carefully consider equivalent structures when making robustness comparisons and to draw conclusions on a case-by-case basis, depending on the specific application.