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.
We present the results of rigorous numerical calculations of the dependence of the reflection coefficient of a semi-infinite two-dimensional photonic crystal on the angle of incidence of the incoming plane wave. We show that,
contrary to some results published earlier, this coefficient is not strictly real even outside the crystal bandgaps.
We also propose a definition of the effective permittivity and permeability μ of a truncated photonic crystal
and specify the symmetry conditions to be satisfied by the truncation plane and the dominant crystal eigenmode
to assure continuity of ε and μ when the mode character changes from propagating to evanescent. The value of
the reflection coefficient obtained by treating the crystal as a homogeneous medium with ε and μ defined in the
proposed way is shown to be a good approximation to the rigorous value in a wide range of angles of incidence,
extending beyond that corresponding to propagating crystal modes.