Abstract
We report on the effective electromagnetic parameters of metamaterialsconsisting of resonant building units, through systematic full-electrodynamiccalculations by the layer-multiple-scattering method on a model system:a photonic crystal of metallic nanoshells. The results obtained by theS-matrix retrieval procedure for single- and multi-layer slabs of ordered arrays of suchnanoshells are analysed in conjunction with the complex band structure of thecorresponding infinite crystal and the Maxwell–Garnett effective-medium approximation.We discuss conditions that must be fulfilled in order for an effective-medium description ofa metamaterial to be valid and explain artefacts which often occur in numericalcalculations of the effective parameters. In particular, we propose a method to resolveambiguities in the determination of the effective refractive index, which becomeprominent for thick slabs, based on the complex band structure of the infinite crystal.
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