Over the past several years, metamaterials have been introduced and rapidly been adopted as a means of achieving unique electromagnetic material response. In metamaterials, artificially structured—often periodically positioned—inclusions replace the atoms and molecules of conventional materials. The scale of these inclusions is smaller than that of the electromagnetic wavelength of interest, so that a homogenized description applies. We present a homogenization technique in which macroscopic fields are determined via averaging the local fields obtained from a full-wave electromagnetic simulation or analytical calculation. The field-averaging method can be applied to homogenize any periodic structure with unit cells having inclusions of arbitrary geometry and material. By analyzing the dispersion diagrams and retrieved parameters found by field averaging, we review the properties of several basic metamaterial structures.
© 2006 Optical Society of America
Original Manuscript: July 19, 2005
Manuscript Accepted: August 21, 2005
Vol. 1, Iss. 4 Virtual Journal for Biomedical Optics
David R. Smith and John B. Pendry, "Homogenization of metamaterials by field averaging (invited paper)," J. Opt. Soc. Am. B 23, 391-403 (2006)