A review of the scattering parameter extraction method with   clarification of ambiguity issues in relation to metamaterial homogenization
  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. 
S. Arslanagi\'c, T. V. Hansen, N. A. Mortensen, A. H. Gregersen, O.   Sigmund, R. W. Ziolkowski, and O. Breinbjerg
physics.optics cond-mat.mes-hall physics.comp-ph