Negative Refraction in isotropic achiral and chiral materials

We show that negative refraction in materials can occur at frequencies $\omega$ where the real part of the permittivity $\veps(\omega)$ and the real part of the permeability $\mu(\omega)$ are of different sign, and that light with such frequencies can propagate just as well as light with frequencies where they are of equal sign. Therefore, in order to have negative refraction one does not need to be in the "double negative" regime. We consider negative refractive index achiral materials using the Drude model, and chiral materials using the Drude-Born-Fedorov model. We find that the time-averaged Poynting vector always points along the wave vector, the time-averaged energy flux density is always positive, and the time-averaged energy density is positive (negative) when the refractive index is positive (negative). The phase velocity is negative when the real part of the refractive index is negative, and the group velocity generally changes sign several times as a function of frequency near resonance.