Electromagnetic characterization of textured surfaces formed by metallic pins

We develop a homogenization model to characterize textured surfaces formed by a periodic arrangement of thin metallic pins attached to a conducting ground plane: the Fakir's bed of nails substrate. It is demonstrated that the textured surface can be accurately modeled using a dielectric function, provided spatial dispersion effects are considered as well as additional boundary conditions. We derive closed analytical formulas for the reflection coefficient, and for the dispersion characteristic of the surfaces waves. In addition, it is demonstrated that the artificial substrate may mimic almost exactly the behavior of an ideal impedance surface boundary, and that the only physical factor that may limit this remarkable property is the skin depth of the metal. The reported results are supported by full wave simulations as well as by experimental data.