Causal homogenization of metamaterials

We propose a homogenization scheme for metamaterials that utilizes causality to determine their effective parameters. By requiring the Kramers-Kronig causality condition in the homogenization of metamaterials, we show that the effective parameters can be chosen uniquely, in contrast to the conventional parameter retrieval method which has unavoidable phase ambiguity arising from the multivalued logarithm function. We demonstrate that the effective thickness of metamaterials can also be determined to a specific value by saturating the minimum-error condition for the causality restriction. Our causal homogenization provides a robust and accurate characterization method for metamaterials.