Negative refractive index arises typically in metamaterials via multiple routes. One such avenue is the condition where the Poynting vector of the electromagnetic wave is in opposition to the group velocity in the material. An earlier work along this route in a chiral material led to the well-known result of requiring very large (non-realizable) chirality.

Thereafter, a combination of chirality together with first-order dispersion was examined using plane wave electromagnetic analysis. To arrive at the conclusions in that approach, the three wave velocities (energy, group and phase) were derived under first-order dispersion in permittivity, permeability and chirality. Negative index in this approach was established under the condition of contra-propagating group and phase velocities. Regions of negative index were found analytically by assuming standard dispersive models (such as Condon).

In this paper, we will re-visit the negative index problem under higher-order dispersion. In addition, we will re-examine the plane wave propagation model under parametric dispersion where each material parameter (ε, μ, κ) is dispersively expanded up to the second order in frequency. Such a physical effect may be traced to group velocity dispersion (GVD) in the material. Field solutions are then obtained under the GVD effect, and extended to the evaluation of the energy, phase and group velocities.