High-Order Perturbation of Surfaces Algorithms for the Simulation of Localized Surface Plasmon Resonances in Two Dimensions

Nicholls, David P.; Tong, Xin

doi:10.1007/s10915-018-0665-2

Cited by 4 publications

(2 citation statements)

References 47 publications

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“…If λ j = 0, from the plasmon resonance condition (2.8) and the fact that γ is sufficiently small in (2.6), we nearly get Re(ε D (ω)) = −ε m . This relationship is called the Fröhlich condition (see [48]). Furthermore, by Drude's model (2.6), we can obtain the resonance frequency ω = 2 , which is called the Fröhlich frequency (see [51]).…”

Section: Plasmon Resonancementioning

confidence: 99%

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: Plasmon Resonancementioning

confidence: 99%

Shape reconstructions by using plasmon resonances

2022

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show abstract

“…If λ j = 0, from the plasmon resonance condition (2.8) and the fact that γ is sufficiently small in (2.6), we nearly get Re(ε D (ω)) = −ε m . This relationship is called the Fröhlich condition (see [31]). Furthermore, by Drude's model (2.6), we can obtain the resonance frequency ω =…”

Section: Dielectric Plasmon Resonancementioning

confidence: 99%

Shape reconstructions by using plasmon resonances

Ding¹,

Liu²,

Zheng³

2021

Preprint

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We study the shape reconstruction of a dielectric 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 dielectric 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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High–order perturbation of surfaces algorithms for the simulation of localized surface plasmon resonances in graphene nanotubes

Nicholls

Tong

2020

Applied Numerical Mathematics

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High-Order Perturbation of Surfaces Algorithms for the Simulation of Localized Surface Plasmon Resonances in Two Dimensions

Cited by 4 publications

References 47 publications

Shape reconstructions by using plasmon resonances

Shape reconstructions by using plasmon resonances

Shape reconstructions by using plasmon resonances

High–order perturbation of surfaces algorithms for the simulation of localized surface plasmon resonances in graphene nanotubes

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