On electromagnetic characterization and homogenization of nanostructured metamaterials

In this overview paper the trends in the modern literature concerning the characterization of linear electromagnetic properties of nanostructured metamaterials are briefly discussed. Electromagnetic characterization of bulk and surface metamaterials is discussed. The problem of characterization of metamaterials with spatial dispersion effects is addressed. It is shown that for bulk metamaterials formed as orthorhombic dipole lattices experimental electromagnetic characterization (retrieval of material parameters) becomes possible. However, standard schemes of material parameter retrieval contain pitfalls even for this kind of material. To clarify these pitfalls the concept of characteristic material parameters is suggested which is clearer and more restrictive that the concept of effective material parameters. For a special but important class of metamaterials (called Bloch lattices by the author) bulk material parameters are obtained which probably fit the concept of electromagnetic characterization because they satisfy basic physical limitations. Further, the problem of the violation of Maxwell boundary conditions for a macroscopic field at the physical boundary of the metamaterial lattice is discussed. The role of transition layers (perhaps transition sheets) in the characterization of metamaterials is explained. Finally, a relevant numerical example is presented as an illustration of the theory.