Effective parameters for periodic photonic structures of resonant elements.

We report on the effective electromagnetic parameters of metamaterials consisting of resonant building units, through systematic full-electrodynamic calculations by the layer-multiple-scattering method on a model system: a photonic crystal of metallic nanoshells. The results obtained by the S-matrix retrieval procedure for single- and multi-layer slabs of ordered arrays of such nanoshells are analysed in conjunction with the complex band structure of the corresponding infinite crystal and the Maxwell-Garnett effective-medium approximation. We discuss conditions that must be fulfilled in order for an effective-medium description of a metamaterial to be valid and explain artefacts which often occur in numerical calculations of the effective parameters. In particular, we propose a method to resolve ambiguities in the determination of the effective refractive index, which become prominent for thick slabs, based on the complex band structure of the infinite crystal.