Modern Analytical Electromagnetic Homogenization

Electromagnetic homogenization is the process of estimating the effective electromagnetic properties of composite materials in the long-wavelength regime, wherein the length scales of nonhomogeneities are much smaller than the wavelengths involved. This is a bird’s-eye view of currently available homogenization formalisms for particulate composite materials. It presents analytical methods only, with focus on the general settings of anisotropy and bianisotropy.The authors largely concentrate on ‘effective’ materials as opposed to ‘equivalent’ materials, and emphasize the fundamental (but sometimes overlooked) differences between these two categories of homogenized composite materials. The properties of an ‘effective’ material represents those of its composite material, regardless of the geometry and dimensions of the bulk materials and regardless of the orientations and polarization states of the illuminating electromagnetic fields. In contrast, the properties of ‘equivalent’ materials only represent those of their corresponding composite materials under certain restrictive circumstances.

Tom G Mackay graduated from the universities of Edinburgh, Glasgow and Strathclyde. His university education was supported, in part, by The Carnegie Trust for The Universities of Scotland. He is a reader in the School of Mathematics at the University of Edinburgh, and also an adjunct professor in the Department of Engineering Science and Mechanics at the Pennsylvania State University. In 2006/07 he held a Royal Society of Edinburgh/Scottish Executive Support Research Fellowship and in 2009/2010, a Royal Academy of Engineering/Leverhulme Trust Senior Research Fellowship. He is a Fellow of the Institute of Physics (UK) and SPIE. He has been carrying out research on the electromagnetic theory of complex mediums, including homogenized composite materials, for the past 17 years.

Akhlesh Lakhtakia is the Charles Godfrey Binder (Endowed) Professor of Engineering Science and Mechanics at the Pennsylvania State University. He received his BTech (1979) and DSc (2006) degrees in Electronics Engineering from the Institute of Technology, Banaras Hindu University, and his MS (1981) and PhD (1983) degrees in Electrical Engineering from the University of Utah. He was the Editor-in-Chief of the Journal of Nanophotonics from its inception in 2007 through to 2013. He is a Fellow of the American Association for the Advancement of Sciences, American Physical Society, Institute of Physics (UK), Optical Society of America, and SPIE. His current research interests relate to electromagnetic fields in complex mediums, sculptured thin films, surface multiplasmonics and electromagnetic surface waves, bioreplication, bone nanoresurfacing, forensic science, and engineered biomimicry.