Investigation of the Lower Limit of the Applicability of Effective Medium Approximation for Hyperbolic Metamaterials

Hyperbolic metamaterials (HMMs) are hailed as one of the main advances in nano-optics in general and metamaterials in particular. Generally, HMMs are multi-layered structures where it is assumed that, due to geometric reasons, one can describe them as a uniform material with effective properties [1]. Their extraordinary characteristics come precisely from the extremely different values of their effective parameters. While the assumption of assigning material properties to these structures may be valid for a very large number of layers, it will start to fail when the number of layers diminishes. In practice, the number of periods these structures have is generally below 10, thus the investigation of the lower limit of such assumption is necessary.