Abstract-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.

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In this work, we demonstrate that the interaction of electromagnetic waves with a microstructured material formed by metallic wires connected to a metallic surface can be described using homogenization methods provided an additional boundary condition is considered. The additional boundary condition is derived by taking into account the specific microstructure of the wire medium. To illustrate the application of the result, we characterize a substrate formed by an array of tilted metallic wires connected to a ground plane, demonstrating that in such configuration the wire medium behaves essentially as a material with extreme optical anisotropy and that in some circumstances the substrate can be seen as an impedance surface.