Exceptional points in parity-time-symmetric subwavelength metamaterials

Ammari, Habib; Davies, Bryn; Hiltunen, Erik Orvehed; Lee, Hyundae; Yu, Sanghyeon

doi:10.48550/arxiv.2003.07796

Cited by 12 publications

(39 citation statements)

References 26 publications

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“…Our results in this paper can be of immense importance for the mathematical foundation of other non-reciprocal guiding phenomena such as the valley Hall effect [16,23,25,26,32,48] and the skin effect [33,44,49]. The valley Hall effect may occur in truncated honeycomb lattices of time-modulated subwavelength resonators by opening non-reciprocal band gaps at Dirac points [6,12] while the skin effect may be obtained by opening non-reciprocal band gaps at exceptional points associated with the unmodulated structure [3,4,14]. These two challenging topics will be the subject of forthcoming publications.…”

Section: Discussionmentioning

confidence: 75%

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Non-reciprocal wave propagation in space-time modulated media

Ammari¹,

Jinghao²,

Hiltunen³

2021

Preprint

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We prove the possibility of achieving non-reciprocal wave propagation in space-time modulated media and give an asymptotic analysis of the non-reciprocity property in terms of the amplitude of the time-modulation. Such modulation causes a folding of the band structure of the material, which may induce degenerate points. By breaking time-reversal symmetry, we show that these degeneracies may open into non-symmetric, unidirectional band gaps. Finally, we illustrate our results by several numerical simulations.

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Section: Discussionmentioning

confidence: 75%

“…Here, the subwavelength nature stems from a high material contrast between the constituting materials of the structure. Such structures can be used to achieve a variety of effects [1,[3][4][5][6][7][8][9]12]. Of particular importance for us are systems of time dependent high-contrast resonators.…”

Section: Introductionmentioning

confidence: 99%

Non-reciprocal wave propagation in space-time modulated media

Ammari¹,

Jinghao²,

Hiltunen³

2021

Preprint

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“…We study a metascreen consisting of periodically repeated pairs of resonators, which are inclusions of a contrasting material surrounded by some background medium, as depicted in Figure 2. We will begin by presenting a capacitance matrix characterization of the band structure, similar to previous works [3,4]. Thereafter, we will restrict our attention to the band structure in a neighbourhood of the origin and will compute the corresponding resonant frequencies explicitly.…”

Section: Metascreensmentioning

confidence: 99%

“…We refer to, e.g. [12,13,3] for the definitions of the radiation conditions. We seek solutions u which are α-quasiperiodic in (x 1 , x 2 ) for some α in the sense that…”

Section: Please Cite This Article As Doi:101063/50051292mentioning

confidence: 99%

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

Ammari

Davies

Hiltunen

et al. 2021

Journal of Mathematical Physics

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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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Edge modes in active systems of subwavelength resonators

Ammari¹,

Hiltunen²

2020

Preprint

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Wave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states in acoustic systems with gain and loss. We demonstrate that localized edge modes appear in a periodic structure of subwavelength resonators with a defect in the gain/loss distribution, and explicitly compute the corresponding frequency and decay length. Similarly to the Hermitian case, these edge modes can be attributed to the winding of the eigenmodes. In the non-Hermitian case, the topological invariants fail to be quantized, but can nevertheless predict the existence of localized edge modes.

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Exceptional points in parity-time-symmetric subwavelength metamaterials

Cited by 12 publications

References 26 publications

Non-reciprocal wave propagation in space-time modulated media

Non-reciprocal wave propagation in space-time modulated media

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

Edge modes in active systems of subwavelength resonators

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