Homogenization of periodic metamaterials by field averaging over unit cell boundaries: use and limitations

Abstract

We revise the method of periodic metamaterials homogenization initially proposed by Pendry, Holden, Robbins and Stewart (PHRS). The shortcomings of the PHRS derivation of the basic formulae of their method are outlined, subtleties of the method implementation are discussed and the range of validity of both the PHRS method and its later modifications are analyzed. We then give a rigorous derivation of the PHRS averaging formulae in the static approximation and modify the PHRS method to account for the phase advance of an incident wave across the unit cells of metamaterials beyond the quasistatic regime. The advantages of our proposed method are illustrated by numerical calculations of the effective parameters of some periodic metamaterials.