  The scattering parameter extraction method of metamaterial homogenization is
reviewed to show that the only ambiguity is the one related to the choice of
the branch of the complex logarithmic function (or the complex inverse cosine
function), whereas it has no ambiguity for the sign of the wave number and
intrinsic impedance. While the method indeed yields two signs of the intrinsic
impedance, and thus the wave number, the signs are dependent, and moreover,
both sign combinations lead to the same permittivity and permeability, and are
thus permissible. This observation is in distinct contrast to a number of
statements in the literature where the correct sign of the intrinsic impedance
and wave number, resulting from the scattering parameter method, is chosen by
imposing additional physical requirements such as passivity. The scattering
parameter method is reviewed through an investigation of a uniform plane wave
normally incident on a planar slab in free-space, and the severity of the
branch ambiguity is illustrated through simulations of a known metamaterial
realization. Several approaches for proper branch selection are reviewed and
their suitability to metamaterial samples is discussed.
