  The planewave response of a linear passive material generally cannot be
characterized by a single scalar refractive index, as directionality of energy
flow and multiple wavevectors may need to be considered. This is especially
significant for materials which support negative refraction, negative phase
velocity, and counterposition. By means of a numerical example based on a
commonly studied bianisotropic material, our theoretical investigation revealed
that: (i) negative (positive) refraction can arise even though the phase
velocity is positive (negative); (ii) counterposition can arise in instances of
positive and negative refraction; (iii) the phase velocity and time-averaged
Poynting vectors can be mutually orthogonal; and (iv) whether or not negative
refraction occurs can depend upon the state of polarization and angle of
incidence. A further numerical example revealed that negative phase velocity
and positive refraction can co-exist even in a simple isotropic dielectric
material.
