Interface conditions for a metamaterial with strong spatial dispersion

TL;DR

This paper derives interface conditions for metamaterials exhibiting strong spatial dispersion, extending the effective medium theory to accurately describe their behavior at boundaries.

Contribution

It introduces a general method to determine interface conditions for nonlocal metamaterials with strong spatial dispersion, advancing the modeling of functional devices.

Findings

Derived explicit interface conditions for nonlocal metamaterials.

Extended effective medium theory to include boundary effects.

Facilitated accurate modeling of devices using nonlocal metamaterials.

Abstract

Local constitutive relations, i.e. a weak spatial dispersion, are usually considered in the effective description of metamaterials. However, they are often insufficient and effects due to a nonlocality, i.e. a strong spatial dispersion, are encountered. Recently (K.~Mnasri et al., arXiv:1705.10969), a generic form for a nonlocal constitutive relation has been introduced that could accurately describe the bulk properties of a metamaterial in terms of a dispersion relation. However, the description of functional devices made from such nonlocal metamaterials also requires the identification of suitable interface conditions. In this contribution, we derive the interface conditions for such nonlocal metamaterials.