Functional analytic methods for discrete approximations of subwavelength resonator systems

Ammari, Habib; Davies, Bryn; Orvehed Hiltunen, Erik

doi:10.2140/paa.2024.6.873

Pure Appl. Analysis

2024

DOI: 10.2140/paa.2024.6.873

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Functional analytic methods for discrete approximations of subwavelength resonator systems

Habib Ammari,

Bryn Davies,

Erik Orvehed Hiltunen

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2024

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Cited by 1 publication

References 105 publications

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Exponentially localized interface eigenmodes in finite chains of resonators

Ammari,

Barandun,

Davies

et al. 2024

Stud Appl Math

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This paper studies wave localization in chains of finitely many resonators. There is an extensive theory predicting the existence of localized modes induced by defects in infinitely periodic systems. This work extends these principles to finite‐sized systems. We consider one‐dimensional, finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analog of the Su–Schrieffer–Heeger model. We prove the existence of a spectral gap for defectless finite dimer structures and find a direct relationship between eigenvalues being within the spectral gap and the localization of their associated eigenmode. Then, for sufficiently large‐size systems, we show the existence and uniqueness of an eigenvalue in the gap in the defect structure, proving the existence of a unique localized interface mode. To the best of our knowledge, our method, based on Chebyshev polynomials, is the first to characterize quantitatively the localized interface modes in systems of finitely many resonators.

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Exponentially localized interface eigenmodes in finite chains of resonators

Ammari,

Barandun,

Davies

et al. 2024

Stud Appl Math

View full text Add to dashboard Cite

show abstract

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Functional analytic methods for discrete approximations of subwavelength resonator systems

Cited by 1 publication

References 105 publications

Exponentially localized interface eigenmodes in finite chains of resonators

Exponentially localized interface eigenmodes in finite chains of resonators

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