Homogenization of 3-D-connected and nonconnected wire metamaterials

The homogenization of composite structures made of long thin metallic wires is an important problem in electromagnetics because they are one of the basic components of the double-negative medium. In this paper, we propose a new analytical model to characterize the effective permittivity of the three-dimensional-wire medium in the long wavelength limit. We study two different topologies for the wire medium. The first structure consists of a lattice of connected wires, whereas the second one consists of a lattice in which the wires are not connected. Our results show that the propagation of electromagnetic waves in the two metamaterials is very different. While one of the structures exhibits strong spatial dispersion, the other one seems to be a good candidate for important metamaterial applications. We also found that, for extremely low frequencies, one of the structures supports modes with hyperbolic wave normal contours, originating negative refraction at an interface with air. We validated our theoretical results with numerical simulations.