On resolving the refractive index and the wave vector

The identification of the refractive index and wave vector for general (possibly active) linear, isotropic, homogeneous, and non-spatially dispersive media is discussed. Correct conditions for negative refraction necessarily include the global properties of the permittivity and permeability functions $\epsilon=\epsilon(\omega)$ and $\mu=\mu(\omega)$. On the other hand, a necessary and sufficient condition for left-handedness can be identified at a single frequency ($\re\epsilon/|\epsilon|+\re\mu/|\mu|<0$). At oblique incidence to semi-infinite, active media it is explained that the wave vector generally loses its usual interpretation for real frequencies.