Double-negative acoustic metamaterials

Davies

2019

Proc. R. Soc. A.

Self Cite

The aim of this paper is to understand the behaviour of a large number of coupled subwavelength resonators. We use layer potential techniques in combination with numerical computations to study the acoustic pressure field due to scattering by a graded array of subwavelength resonators. Using this method, we study a graded-resonance model for the cochlea. We compute the resonant modes of the system and explore the model's ability to decompose incoming signals. We are able to offer mathematical explanations for the cochlea's so-called "travelling wave" behaviour and tonotopic frequency map. Mathematics subject classification: 35R30, 35C20

Section: Hair Cells Tectorial Membranementioning

confidence: 95%

Section: Hair Cells Tectorial Membranementioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Resonant Modesmentioning

confidence: 99%

See 2 more Smart Citations

A fully coupled subwavelength resonance approach to filtering auditory signals

Davies

2019

Proc. R. Soc. A.

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“…Our methodology in this paper follows the one introduced recently for achieving double-negative acoustic media using bubbles [4]. In acoustics, it is known that the air bubbles are subwavelength resonators [24].…”

Section: Introductionmentioning

confidence: 99%

Double-negative electromagnetic metamaterials due to chirality

2018

Quart. Appl. Math.

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The aim of this paper is to provide a mathematical theory for understanding the mechanism behind the double-negative refractive index phenomenon in chiral materials. The design of double-negative metamaterials generally requires the use of two different kinds of subwavelength resonators, which may limit the applicability of double-negative metamaterials. Herein, we rely on media that consist of only a single type of dielectric resonant element, and show how the chirality of the background medium induces double-negative refractive index metamaterial, which refracts waves negatively, hence acting as a superlens. Using plasmonic dielectric particles, it is proved that both the effective electric permittivity and the magnetic permeability can be negative near some resonant frequencies. A justification of the approximation of a plasmonic particle in a chiral medium by the sum of a resonant electric dipole and a resonant magnetic dipole, is provided. Moreover, the set of resonant frequencies is characterized. For an appropriate volume fraction of plasmonic particles with certain conditions on their configuration, a double-negative effective medium can be obtained when the frequency is near one of the resonant frequencies.Mathematics Subject Classification (MSC2000). 35R30, 35C20.

Subwavelength resonant dielectric nanoparticles with high refractive indices

Math Methods in App Sciences

Dabrowski

Fitzpatrick³

et al. 2019

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This paper aims at understanding the nature of the subwavelength resonant frequencies of dielectric particles with high refractive indices. It is proved that for an arbitrary shaped particle, these subwavelength resonant frequencies can be expressed in terms of the eigenvalues of the Newtonian potential associated with its shape. The enhancement of the scattered field at the resonant frequencies is shown. The hybridization of the subwavelength resonant frequencies of a dimer consisting of high refractive index dielectric nanoparticles is also characterized. KEYWORDS asymptotic expansions, dielectric nanoparticles, high refractive index, subwavelength resonances MSC CLASSIFICATION 35R30, 35C20