arXiv subjects

Bryn Davies

Publications and source records attributed to Bryn Davies.

47 records · Page 3Linked to original sources

arXiv2022

Asymptotic analysis of subwavelength halide perovskite resonators

Halide perovskites are promising materials with many significant applications in photovoltaics and optoelectronics. In this paper, we use integral methods to quantify the resonant properties of halide perovskite nano-particles. We prove that, for arbitrarily small particles, the subwavelength resonant frequencies can be expressed in terms of the eigenvalues of the Newtonian potential associated with its shape. We also characterize the hybridized subwavelength resonant frequencies of a dimer of two halide perovskite particles. Finally, we examine the specific case of spherical resonators and demonstrate that our new results are consistent with previous works.

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arXiv2021

Robust edge modes in dislocated systems of subwavelength resonators

Robustly manipulating waves on subwavelength scales can be achieved by, firstly, designing a structure with a subwavelength band gap and, secondly, introducing a defect so that eigenfrequencies fall within the band gap. Such frequencies are well known to correspond to localized modes. We study a one-dimensional array of subwavelength resonators, proving that there is a subwavelength band gap, and showing that by introducing a dislocation we can place localized modes at any point within the band gap. We complement this analysis by studying the stability properties of the corresponding finite array of resonators, demonstrating the value of being able to customize the position of eigenvalues within the band gap.

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arXiv2021

Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors

The aim of this work is to derive precise formulas which describe how the properties of subwavelength devices are changed by the introduction of errors and imperfections. As a demonstrative example, we study a class of cochlea-inspired rainbow sensors. These are devices based on a graded array of subwavelength resonators which have been designed to mimic the frequency separation performed by the cochlea. We show that the device's properties (including its role as a signal filtering device) are stable with respect to small imperfections in the positions and sizes of the resonators. Additionally, if the number of resonators is sufficiently large, then the device's properties are stable under the removal of a resonator.

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arXiv2021

Bound states in the continuum and Fano resonances in subwavelength resonator arrays

When wave scattering systems are subject to certain symmetries, resonant states may decouple from the far-field continuum; they remain localized to the structure and cannot be excited by incident waves from the far field. In this work, we use layer-potential techniques to prove the existence of such states, known as bound states in the continuum, in systems of subwavelength resonators. When the symmetry is slightly broken, this resonant state can be excited from the far field. Remarkably, this may create asymmetric (Fano-type) scattering behaviour where the transmission is fundamentally different for frequencies on either side of the resonant frequency. Using asymptotic analysis, we compute the scattering matrix of the system explicitly, thereby characterizing this Fano-type transmission anomaly.

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arXiv2021

Exceptional points in parity-time-symmetric subwavelength metamaterials

When sources of energy gain and loss are introduced to a wave-scattering system, the underlying mathematical formulation will be non-Hermitian. This paves the way for the existence of exceptional points, where eigenmodes are linearly dependent. The primary goal of this work is to study the existence of exceptional points in high-contrast subwavelength metamaterials. We begin by studying a parity-time-symmetric pair of subwavelength resonators and prove that this system supports asymptotic exceptional points. These are points at which the subwavelength eigenvalues and eigenvectors coincide at leading order in the asymptotic parameters. We then investigate further properties of parity-time-symmetric subwavelength metamaterials. First, we study the exotic scattering behaviour of a metascreen composed of repeating parity-time-symmetric pairs of subwavelength resonators. We prove that the non-Hermitian nature of this structure means that it exhibits asymptotic unidirectional reflectionless transmission at certain frequencies and demonstrate extraordinary transmission close to these frequencies. Thereafter, we consider cavities containing many small resonators and use homogenization theory to show that non-Hermitian behaviour can be replicated at the macroscale.

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arXiv2020

Wave interaction with subwavelength resonators

The aim of this review is to cover recent developments in the mathematical analysis of subwavelength resonators. The use of sophisticated mathematics in the field of metamaterials is reported, which provides a mathematical framework for focusing, trapping, and guiding of waves at subwavelength scales. Throughout this review, the power of layer potential techniques combined with asymptotic analysis for solving challenging wave propagation problems at subwavelength scales is demonstrated.

math.AP↗

arXiv2020

High-order exceptional points and enhanced sensing in subwavelength resonator arrays

Systems exhibiting degeneracies known as exceptional points have remarkable properties with powerful applications, particularly in sensor design. These degeneracies are formed when eigenstates coincide, and the remarkable effects are exaggerated by increasing the order of the exceptional point (that is, the number of coinciding eigenstates). In this work, we use asymptotic techniques to study PT-symmetric arrays of many subwavelength resonators and search for high-order asymptotic exceptional points. This analysis reveals the range of different configurations that can give rise to high-order exceptional points and provides efficient techniques to compute them. We also show how systems exhibiting high-order exceptional points can be used for sensitivity enhancement.

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arXiv2020

Close-to-touching acoustic subwavelength resonators: eigenfrequency separation and gradient blow-up

In this paper, we study the behaviour of the coupled subwavelength resonant modes when two high-contrast acoustic resonators are brought close together. We consider the case of spherical resonators and use bispherical coordinates to derive explicit representations for the capacitance coefficients which, we show, capture the system's resonant behaviour at leading order. We prove that the pair of resonators has two subwavelength resonant modes whose frequencies have different leading-order asymptotic behaviour. We, also, derive estimates for the rate at which the gradient of the scattered pressure wave blows up as the resonators are brought together.

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arXiv2020

Topologically protected edge modes in one-dimensional chains of subwavelength resonators

The goal of this paper is to advance the development of wave-guiding subwavelength crystals by developing designs whose properties are stable with respect to imperfections in their construction. In particular, we make use of a locally resonant subwavelength structure, composed of a chain of high-contrast resonators, to trap waves at deep subwavelength scales. We first study an infinite chain of subwavelength resonator dimers and define topological quantities that capture the structure's wave transmission properties. Using this for guidance, we design a finite crystal that is shown to have wave localization properties, at subwavelength scales, that are robust with respect to random imperfections.

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arXiv2019

Mimicking the active cochlea with a fluid-coupled array of subwavelength Hopf resonators

We present a design for an acoustic metamaterial that mimics the behaviour of the active cochlea. This material is composed of a size-graded array of cylindrical subwavelength resonators, has similar dimensions to the cochlea and is able to reproduce the frequency separation of audible frequencies. Non-linear amplification is introduced to the model in order to replicate the behaviour of the cochlear amplifier. This formulation takes the form of a fluid-coupled array of Hopf resonators. We seek solutions based on a modal decomposition, so as to retain the physically-derived coupling between resonators.

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arXiv2019

A fully-coupled subwavelength resonance approach to modelling the passive cochlea

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.

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