Plasmon resonance with finite frequencies: A validation of the quasi-static approximation for diametrically small inclusions

Kazunori Ando; Hyeonbae Kang; Hongyu Liu

doi:10.1137/15M1025943

Plasmon resonance with finite frequencies: A validation of the quasi-static approximation for diametrically small inclusions

Kazunori Ando, Hyeonbae Kang^*, Hongyu Liu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

51 Citations (Scopus)

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Abstract

We study resonance for the Helmholtz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of an inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann{Poincare operator associated with the inclusion.

Original language	English
Pages (from-to)	731-749
Number of pages	19
Journal	SIAM Journal on Applied Mathematics
Volume	76
Issue number	2
DOIs	https://doi.org/10.1137/15M1025943
Publication status	Published - 31 Mar 2016

Scopus Subject Areas

Applied Mathematics

User-Defined Keywords

Eigenvalues
Finite frequency
Helmholtz equation
Neumann-Poincaré operator
Plasmon resonance
Quasi-static limit

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title = "Plasmon resonance with finite frequencies: A validation of the quasi-static approximation for diametrically small inclusions",

abstract = "We study resonance for the Helmholtz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of an inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann{Poincare operator associated with the inclusion.",

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AU - Kang, Hyeonbae

AU - Liu, Hongyu

N1 - Funding Information: This author's work supported by the FRG grants of Hong Kong Baptist University, Hong Kong RGC General Research Funds, 12302415 and 405513, and NSF of China grant 11371115. Publisher copyright: © 2016, Society for Industrial and Applied Mathematics

PY - 2016/3/31

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N2 - We study resonance for the Helmholtz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of an inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann{Poincare operator associated with the inclusion.

AB - We study resonance for the Helmholtz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of an inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann{Poincare operator associated with the inclusion.

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Plasmon resonance with finite frequencies: A validation of the quasi-static approximation for diametrically small inclusions

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