Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers
- 1. Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
Description
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 lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on topical examples from topological wave physics.
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- Preprint: arXiv:2003.10876 (arXiv)
Funding
- BOHEME – Bio-Inspired Hierarchical MetaMaterials 863179
- European Commission
- Mathematical fundamentals of Metamaterials for multiscale Physics and Mechanics EP/L024926/1
- UK Research and Innovation
- EPSRC Centre for Doctoral Training in Fluid Dynamics across Scales EP/L016230/1
- UK Research and Innovation
- Biological metamaterials for enhanced noise control technology EP/T002654/1
- UK Research and Innovation