Effective-medium theory for multilayer metamaterials: Role of near-field corrections

Although many effective-medium theories have been proposed for studying metamaterials, most of them do not work well for multilayer metamaterials with small interlayer distances. Based on rigorous mode-expansion analyses on a model system consisting of multiple layers of subwavelength gratings, we identify that the failures of conventional effective-medium theories are caused by neglecting strong near-field couplings in homogenizing such systems. These understandings motive us to propose an alternative homogenization approach for strongly coupled multilayer metamaterials, in which predominant near-field corrections have been considered automatically. Our effective-medium theory can well describe multilayer metamaterials with arbitrary interlayer distances including particularly those systems for which conventional effective-medium theories fail. We finally extend our theory to multilayer metamaterials with complicated microstructures and validate the theory by full-wave simulations as well as microwave experiments. Our theory not only well complements the available effective-medium theory formalisms, but also provides a powerful tool to study the properties of strongly coupled metamaterials, which may find many applications in practice.