Modeling of spatially-dispersive wire media: transport representation, comparison with natural materials, and additional boundary conditions

Abstract—Natural and artificial wire materials exhibiting spa-tial dispersion are considered using a transport (drift-diffusion) model. The connection between drift-diffusion and electron trans-port in naturalmaterials is highlighted, and then applied to various forms of wire media, leading to the definition of effective conduc-tivity and diffusion parameters that characterize the material. It is shown that the effective material parameters lead to a Debye length that provides a quantitative measure of the strength of spa-tial dispersion for wire mediums. Further, it is shown that Pekar’s additional boundary condition applies in many instances to nat-ural materials as well as artificial wire media, and can be derived from elementary electromagnetics. Index Terms—Diffusion, metamaterial, plasma, wire medium. I