Transition from thin-film to bulk properties of metamaterials
Carsten Rockstuhl, Thomas Paul, Falk Lederer, Thomas Pertsch, Thomas Zentgraf, Todd P. Meyrath, and Harald Giessen

Effective material parameters for metamaterials are usually extracted for a single thin layer only. We show that in general these parameters can not directly be assigned to a multi-layered (bulk) metamaterial. The principal issue is the presence of higher-order Bloch modes. These modes are usually negligible for a single layer, but can have considerable influence on the results for a periodically stacked structure. In particular we show examples where a stack of single-layer negative refractive index metamaterials exhibits a positive index. Furthermore, on the basis of the dispersion relation of the respective Bloch modes, we derive criteria for the validity of the effective parameter approach.

© 2008 The American Physical Society.