  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 subwavelength resonators, which may limit the
applicability of double-negative 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.
