General properties of two-dimensional conformal transformations in electrostatics

Yong Zeng; Jinjie Liu; Douglas H. Werner

doi:10.1364/OE.19.020035

General properties of two-dimensional conformal transformations in electrostatics

Yong Zeng, Jinjie Liu, Douglas H. Werner

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Abstract

Electrostatic properties of two-dimensional nanosystems can be completely described by their non-trivial geometry modes. In this paper we prove that these modes as well as the corresponding eigenvalues are invariant under any conformal transformation. This invariance suggests a new way to study electrostatic conformal transformations, while also providing an in-depth interpretation of the behavior exhibited by singular plasmonic nanoparticles.

Original language	English (US)
Pages (from-to)	20035-20047
Number of pages	13
Journal	Optics Express
Volume	19
Issue number	21
DOIs	https://doi.org/10.1364/OE.19.020035
State	Published - Oct 10 2011

All Science Journal Classification (ASJC) codes

Atomic and Molecular Physics, and Optics

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title = "General properties of two-dimensional conformal transformations in electrostatics",

abstract = "Electrostatic properties of two-dimensional nanosystems can be completely described by their non-trivial geometry modes. In this paper we prove that these modes as well as the corresponding eigenvalues are invariant under any conformal transformation. This invariance suggests a new way to study electrostatic conformal transformations, while also providing an in-depth interpretation of the behavior exhibited by singular plasmonic nanoparticles.",

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N2 - Electrostatic properties of two-dimensional nanosystems can be completely described by their non-trivial geometry modes. In this paper we prove that these modes as well as the corresponding eigenvalues are invariant under any conformal transformation. This invariance suggests a new way to study electrostatic conformal transformations, while also providing an in-depth interpretation of the behavior exhibited by singular plasmonic nanoparticles.

AB - Electrostatic properties of two-dimensional nanosystems can be completely described by their non-trivial geometry modes. In this paper we prove that these modes as well as the corresponding eigenvalues are invariant under any conformal transformation. This invariance suggests a new way to study electrostatic conformal transformations, while also providing an in-depth interpretation of the behavior exhibited by singular plasmonic nanoparticles.

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General properties of two-dimensional conformal transformations in electrostatics

Abstract

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