  Reflection and refraction of electromagnetic waves by artificial periodic
composites (metamaterials) can be accurately modeled by an effective medium
theory only if the boundary of the medium is explicitly taken into account and
the two effective parameters of the medium -- the index of refraction and the
impedance -- are correctly determined. Theories that consider infinite periodic
composites do not satisfy the above condition. As a result, they cannot model
reflection and transmission by finite samples with the desired accuracy and are
not useful for design of metamaterial-based devices. As an instructive case in
point, we consider the "current-driven" homogenization theory, which has
recently gained popularity. We apply this theory to the case of one-dimensional
periodic medium wherein both exact and homogenization results can be obtained
analytically in closed form. We show that, beyond the well-understood zero-cell
limit, the current-driven homogenization result is inconsistent with the exact
reflection and transmission characteristics of the slab.
