Abstract
This paper studies wave localisation in chains of finitely many resonators. There is an extensive theory predicting the existence of localised modes induced by defects in infinitely periodic systems. This work extends these principles to finite-sized systems. We consider finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analogue of the Su-Schrieffer-Heeger model. We prove the existence of a spectral gap for defectless finite dimer structures and then show the existence of an eigenvalue in the gap of the defect structure. We find a direct relationship between an eigenvalue being within the spectral gap and the localisation of its associated eigenmode, which we show is exponentially localised. To the best of our knowledge, our method, based on Chebyshev polynomials, is the first to characterise quantitatively the localised interface modes in systems of finitely many resonators. Show more
Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Finite Hermitian systems; Subwavelength resonators; Capacitance matrix; Topological protection; Chebyshev polynomials; Wave localisationOrganisational unit
09504 - Ammari, Habib / Ammari, Habib
Funding
200307 - Mathematics of dielectric artificial media (SNF)
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