Effective properties of metamaterials

Abstract

Properties of metamaterials are usually discussed in terms of biaxial anisotropic material parameters. To consider the underlying constitutive relations as valid, it is required that only weak spatial dispersion occurs. At operational frequencies of optical metamaterials this assumption often ceases to be valid. A description using effective material properties tends to be inadequate and new approaches are required. We outline here our latest achievements along this direction and discuss two approaches. The first one assumes that if it is not possible to introduce useful effective properties, a more primary source of information should be used to quantify metamaterials, leading to a characterization of metamaterials in terms of Jones matrices. We discuss the implications of this description and show that all metamaterials can be categorized into five classes, each with distinct properties. The second approach resorts to an effective description but restricts its considerations to a dispersion relation, characterizing the propagation of light in bulk metamaterials, and an impedance, characterizing the coupling between metamaterials and their surroundings. Definitions of both properties linked to a single Bloch mode are discussed and metamaterials are introduced which can be homogenized while considering only this single mode.