Symmetry-induced quasicrystalline waveguides
File(s)
Published version
Author(s)
Davies, Bryn
Craster, Richard V
Type
Journal Article
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.
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.
Date Issued
2022-11
Date Acceptance
2022-10-11
Citation
Wave Motion, 2022, 115, pp.1-16
ISSN
0165-2125
Publisher
Elsevier
Start Page
1
End Page
16
Journal / Book Title
Wave Motion
Volume
115
Copyright Statement
© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
http://arxiv.org/abs/2208.14906v1
Subjects
math-ph
math-ph
math.CA
math.MP
physics.optics
Publication Status
Published
Date Publish Online
2022-10-21