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A new model of geometric chirality for two-dimensional continuous media and planar meta-materials

A new model of geometric chirality for two-dimensional continuous media and planar meta-materials
A new model of geometric chirality for two-dimensional continuous media and planar meta-materials
We have, for the first time, identified ten tenets of two-dimensional (2D) chirality that define and encapsulate the symmetry and scaling behaviour of planar objects and have used them to develop three new measures of geometric 2D chirality. All three models are based on the principle of overlap integrals and can be expressed as simple analytical functions of the two-dimensional surface density, rho(r). In this paper we will compare the predicted behaviour of these models and show that two of them are fully integrable and scalable and can therefore be applied to both discrete and continuous 2D systems of any finite size, or any degree of complexity. The only significant difference in these two models appears in their behaviour at infinite length scales. Such differences could, however, have profound implications for the analysis of chirality in new generations of planar meta-materials, such as chiral arrays, fractals, quasi-periodic 2D crystals and Penrose tiled structures.
chiral, planar geometry, optical activity, overlap integral, 2D topology
1741-3567
193-203
Potts, A.
60d57f4c-abcf-4b6b-8247-28711e6fd4d4
Bagnall, D.M.
5d84abc8-77e5-43f7-97cb-e28533f25ef1
Zheludev, N.I.
32fb6af7-97e4-4d11-bca6-805745e40cc6
Potts, A.
60d57f4c-abcf-4b6b-8247-28711e6fd4d4
Bagnall, D.M.
5d84abc8-77e5-43f7-97cb-e28533f25ef1
Zheludev, N.I.
32fb6af7-97e4-4d11-bca6-805745e40cc6

Potts, A., Bagnall, D.M. and Zheludev, N.I. (2004) A new model of geometric chirality for two-dimensional continuous media and planar meta-materials. Journal of Optics A: Pure and Applied Optics, 6 (2), 193-203. (doi:10.1088/1464-4258/6/2/007)).

Record type: Article

Abstract

We have, for the first time, identified ten tenets of two-dimensional (2D) chirality that define and encapsulate the symmetry and scaling behaviour of planar objects and have used them to develop three new measures of geometric 2D chirality. All three models are based on the principle of overlap integrals and can be expressed as simple analytical functions of the two-dimensional surface density, rho(r). In this paper we will compare the predicted behaviour of these models and show that two of them are fully integrable and scalable and can therefore be applied to both discrete and continuous 2D systems of any finite size, or any degree of complexity. The only significant difference in these two models appears in their behaviour at infinite length scales. Such differences could, however, have profound implications for the analysis of chirality in new generations of planar meta-materials, such as chiral arrays, fractals, quasi-periodic 2D crystals and Penrose tiled structures.

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Published date: 2004
Keywords: chiral, planar geometry, optical activity, overlap integral, 2D topology
Organisations: Nanoelectronics and Nanotechnology

Identifiers

Local EPrints ID: 259024
URI: https://eprints.soton.ac.uk/id/eprint/259024
ISSN: 1741-3567
PURE UUID: 6730ca0d-a47e-4f63-8220-fcaa5e487ad2
ORCID for N.I. Zheludev: ORCID iD orcid.org/0000-0002-1013-6636

Catalogue record

Date deposited: 08 Mar 2004
Last modified: 29 Oct 2019 02:07

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Contributors

Author: A. Potts
Author: D.M. Bagnall
Author: N.I. Zheludev ORCID iD

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