## Abstract

The aim of this paper is to provide a mathematical theory for understanding the mechanism behind the double-negative refractive index phenomenon in chiral materials. The design of double-negative metamaterials generally requires the use of two different kinds of sub-wavelength resonators, which may limit the applicability of doublenegative metamaterials. Herein, we rely on media that consist of only a single-type of dielectric resonant element, and show how the chirality of the background medium induces double-negative refractive index metamaterial, which refracts waves negatively, hence acting as a superlens. Using plasmonic dielectric particles, it is proved that both the effective electric permittivity and the magnetic permeability can be negative near some resonant frequencies. A justification of the approximation of a plasmonic particle in a chiral medium by the sum of a resonant electric dipole and a resonant magnetic dipole is provided. Moreover, the set of resonant frequencies is characterized. For an appropriate volume fraction of plasmonic particles with certain conditions on their configuration, a double-negative effective medium can be obtained when the frequency is near one of the resonant frequencies.

Original language | English |
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Pages (from-to) | 105-130 |

Number of pages | 26 |

Journal | Quarterly of Applied Mathematics |

Volume | 77 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2018 Brown University.

## Keywords

- Chiral materials
- Double-negative metamaterials
- Effective medium theory
- Electric and magnetic resonant dipoles
- Plasmonic nanoparticles
- Sub-wavelength resonance

## ASJC Scopus subject areas

- Applied Mathematics