Localization and geometrization in plasmon resonances and geometric structures of Neumann-Poincaré eigenfunctions

Blåsten, Emilia; Li, Hongjie; Liu, Hongyu; Wang, Yuliang

doi:10.1051/m2an/2019091

Cited by 22 publications

(19 citation statements)

References 46 publications

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“…We refer to [10,11,36,47,50,53] and the references cited therein for many striking optical, phononic, biomedical, diagnostic and therapeutic applications in the physical literature. Recent studies have revealed the deep and intriguing connection between the plasmon resonance and the spectral study of the Neumann-Poincaré operator [2,3,5,12,22,23,31,42,45]. In addition, there are many theoretical understandings and conceptual proposals about plasmonic devices.…”

Section: Introductionmentioning

confidence: 99%

“…In [8], by analyzing the imaginary part of the Green function, it is shown that one can achieve super-resolution and super-focusing by using plasmonic nanoparticles. In [2,3,12], it is shown that the plasmon resonance concentrates and localises at high-curvature places, which can provide potential application in super-resolution imaging of plasmon particles. We would also like to mention in passing some related studies on plasmonic cloaking [5, 9, 16, 22, 25, 38-41, 46, 56].…”

Section: Introductionmentioning

confidence: 99%

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Shape reconstructions by using plasmon resonances

2022

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We study the shape reconstruction of an inclusion from the faraway measurement of the associated electric field. This is an inverse problem of practical importance in biomedical imaging and is known to be notoriously ill-posed. By incorporating Drude’s model of the permittivity parameter, we propose a novel reconstruction scheme by using the plasmon resonance with a significantly enhanced resonant field. We conduct a delicate sensitivity analysis to establish a sharp relationship between the sensitivity of the reconstruction and the plasmon resonance. It is shown that when plasmon resonance occurs, the sensitivity functional blows up and hence ensures a more robust and effective construction. Then we combine the Tikhonov regularization with the Laplace approximation to solve the inverse problem, which is an organic hybridization of the deterministic and stochastic methods and can quickly calculate the minimizer while capture the uncertainty of the solution. We conduct extensive numerical experiments to illustrate the promising features of the proposed reconstruction scheme.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shape reconstructions by using plasmon resonances

2022

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“…Due to their connection to the SPR discussed above, the quantitative properties of the NP eigenvalues have been extensively studied in recent years; see e.g. [3,16,17,30,36,43,44] and the references cited therein. As is mentioned earlier that the SPR mainly oscillates around the material interface ∂D, which is rigorously justified in [12].…”

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confidence: 99%

Quantum integrable systems and concentration of plasmon resonance

Ammari¹,

Chow²,

Liu³

et al. 2021

Preprint

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We are concerned with the quantitative mathematical understanding of surface plasmon resonance (SPR). SPR is the resonant oscillation of conducting electrons at the interface between negative and positive permittivity materials and forms the fundamental basis of many cutting-edge applications of metamaterials. It is recently found that the SPR concentrates due to curvature effect. In this paper, we derive sharper and more explicit characterisations of the SPR concentration at high-curvature places in both the static and quasi-static regimes. The study can be boiled down to analyzing the geometries of the so-called Neumann-Poincaré (NP) operators, which are certain pseudo-differential operators sitting on the interfacial boundary. We propose to study the joint Hamiltonian flow of an integral system given by a moment map defined by the NP operator. Via considering the Heisenberg picture and lifting the joint flow to a joint wave propagator, we establish a more general version of quantum ergodicity on each leaf of the foliation of this integrable system, which can then be used to establish the desired SPR concentration results. The mathematical framework developed in this paper leverages the Heisenberg picture of quantization and extends some results of quantum integrable system via generalising the concept of quantum ergodicity, which can be of independent interest to the spectral theory and the potential theory.

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“…The CALR has been extensively investigated. We refer to [4,6,9,11,15,20,21,29] for the relevant study in acoustics, [8,10,17,18,19,27,28,24] for elastic system and [3,2,1,7,13,14,15,25,26,31,32,33,34,36,37,38] for the Maxwell system.…”

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confidence: 99%

Recent progress on the mathematical study of anomalous localized resonance in elasticity

2020

era

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We consider the anomalous localized resonance induced by negative elastic metamaterials and its application in invisibility cloaking. We survey the recent mathematical developments in the literature and discuss two mathematical strategies that have been developed for tackling this peculiar resonance phenomenon. The first one is the spectral method, which explores the anomalous localized resonance through investigating the spectral system of the associated Neumann-Poincaré operator. The other one is the variational method, which considers the anomalous localized resonance via calculating the nontrivial kernels of a non-elliptic partial differential operator. The advantages and the relationship between the two methods are discussed. Finally, we propose some open problems for the future study.

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Localization and geometrization in plasmon resonances and geometric structures of Neumann-Poincaré eigenfunctions

Cited by 22 publications

References 46 publications

Shape reconstructions by using plasmon resonances

Shape reconstructions by using plasmon resonances

Quantum integrable systems and concentration of plasmon resonance

Recent progress on the mathematical study of anomalous localized resonance in elasticity

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