Effective Local Permittivity Model for Non-Local Wire Media

A local permittivity model is proposed to accurately characterize spatial dispersion in non-local wire-medium (WM) structures with arbitrary terminations. A closed-form expression for the local thickness-dependent permittivity is derived for a general case of a bounded WM with lumped impedance insertions and terminated with impedance surfaces, which takes into account the effects of spatial dispersion and loads/terminations in the averaged sense per length of the wire medium. The proposed approach results in a local model formalism and accurately predicts the response of WM structures for near-field and far-field excitation. It is also shown that a traditional transmission network and circuit model can be effectively used to quantify the interaction of propagating and evanescent waves with WM structures. In addition, the derived analytical expression for the local thickness-dependent permittivity has been used in the full-wave numerical solver (CST Microwave Studio) demonstrating a drastic reduction in the computation time and memory in the solution of near-field and far-field problems involving wire media.