Mixing Rules for Left-Handed Disordered Metamaterials: Effective-Medium and Dispersion Properties

Left-handed materials are known to exhibit exotic properties in controlling electromagnetic fields, with direct applications in negative reflection and refraction, conformal optical mapping, and electromagnetic cloaking. While typical left-handed materials are constructed periodic metal-dielectric structures, the same effect can be obtained in composite guest-host systems with no periodicity or structural order. Such systems are typically described by the effective-medium approach, in which the components of the electric permittivity tensor are determined as a function of individual material properties and doping concentration. In this paper, we extend the discussion on the mixing rules to include left-handed composite systems and highlight the exotic properties arising from the effective-medium approach in this framework in terms of effective values and dispersion properties.