Homogenization and applications of the Fakirs bed of nails substrate

In this paper, we propose a homogenization approach to describe the reflection of plane waves by a periodic arrangement of thin metallic pins attached to a conducting ground plane: the "Fakir\´s bed of nails" substrate. To this end, the propagation in the metamaterial substrate is described using an effective permittivity model. It is shown that an additional boundary condition, besides the continuity of the tangential components of the fields, is necessary to compute the scattering parameters, consistently with the results recently derived in M. Silveirinha (http://arxiv.org/abs/cond-mat/0509612). It is proved that the proposed homogenization model correctly predicts the dispersion characteristic of TM surface waves in the metamaterial substrate. Possible applications of the "Fakir\´s bed of nails", such as the synthesis of a surface reactance, are discussed