Asymptotic behavior of spectral of Neumann‐Poincaré operator in Helmholtz system

Given the flexibility of choosing negative elastic parameters, we construct material structures that can induce two resonance phenomena, referred to as the elastodynamical resonances. They mimic the emerging plasmon/polariton resonance and anomalous localized resonance in optics for subwavelength particles. However, we study the peculiar resonance phenomena for linear elasticity beyond the subwavelength regime. It is shown that the resonance behaviors possess distinct characters, with some similar to the subwavelength resonances, but some sharply different due to the frequency effect. It is particularly noted that we construct a core–shell material structure that can induce anomalous localized resonance as well as cloaking phenomena beyond the quasistatic limit. The study is boiled down to analyzing the so‐called elastic Neumann–Poincaré (N‐P) operator in the frequency regime. We provide an in‐depth analysis of the spectral properties of the N‐P operator on a circular domain beyond the quasistatic approximation, and these results are of independent interest to the spectral theory of layer potential operators.

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“…Ref. 38):

\begin{equation} H_{0}(k|\mathbf {x}-\mathbf {y}|)=\sum _{n \in \mathbb {Z}} H_{n}(k|\mathbf {x}|) e^{\mathrm{i} n \theta \mathbf {x}} J_{n}(k|\mathbf {y}|) e^{-\mathrm{i} n \theta \mathbf {y}}. \end{equation}

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Section: Auxiliary Resultsmentioning

confidence: 99%

Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Liu

Zou

2023

Stud Appl Math

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“…Core‐shell structures are widely used for analysis of cloaking due to anomalous localized resonance [1–3, 6, 8, 14]. Plasmon resonance for spherical structure with normal scale has been studied in these years [10, 15]. It is noted that the above structures are all isotropic material structures.…”

Section: Introductionmentioning

confidence: 99%

On plasmon modes in multi‐layer structures

Fang

Deng

2023

Math Methods in App Sciences

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In this paper, we consider the plasmon resonance in multi‐layer structures. We show that the plasmon mode is equivalent to the eigenvalue problem of a matrix, whose order is the same to the number of layers. For any number of layers, the exact characteristic polynomial is derived by a conjecture and is verified by using induction. It is shown that all the roots to the characteristic polynomial are real and exist in the span , when the background field is uniform in . Numerical examples are presented for finding all the plasmon modes, and it is surprisingly to find out that such multi‐layer structures may induce so called surface‐plasmon‐resonance‐like band.

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“…Core-shell structures are widely used for analysis of cloaking due to anomalous localized resonance [1-3, 9, 11, 23]. Plasmon resonance for spherical structure with normal scale has been studied in these years [14,17]. It is noted that the above structures are all isotropic material structures.…”

Section: Introductionmentioning

confidence: 99%

On plasmon modes in multi-layer structures

Deng¹,

Fang²

2022

Preprint

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In this paper, we consider the plasmon resonance in multi-layer structures. The conductivity problem associated with uniformly distributed background field is considered. We show that the plasmon mode is equivalent to the eigenvalue problem of a matrix, whose order is the same to the number of layers. For any number of layers, the exact characteristic polynomial is derived by a conjecture and is verified by using induction. It is shown that all the roots to the characteristic polynomial are real and exist in the span [−1, 2]. Numerical examples are presented for finding all the plasmon modes, and it is surprisingly to find out that such multi-layer structures may induce so called surface-plasmon-resonance-like band.

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Asymptotic behavior of spectral of Neumann‐Poincaré operator in Helmholtz system

Cited by 9 publications

References 29 publications

Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

On plasmon modes in multi‐layer structures

On plasmon modes in multi-layer structures

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