Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers
File(s)
Accepted version
OA Location
Author(s)
Wiltshaw, Richard
Craster, Richard
Makwana, Mehul
Type
Journal Article
Abstract
We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet-Bloch waves through an infinite array of scatterers. The approach also lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on some topical examples from topological wave physics.
Date Issued
2020-12-01
Date Acceptance
2020-09-23
Citation
Wave Motion, 2020, 99
ISSN
0165-2125
Publisher
Elsevier
Journal / Book Title
Wave Motion
Volume
99
Copyright Statement
© 2020 Elsevier B.V. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Commission of the European Communities
Grant Number
EP/L024926/1
RF-2017-017/9
863179
Subjects
physics.comp-ph
physics.comp-ph
Applied Mathematics
0102 Applied Mathematics
0203 Classical Physics
Publication Status
Published
Article Number
ARTN 102662
Date Publish Online
2020-10-02