Electromagnetic properties of three-dimensional wire arrays: photons, plasmons, and equivalent circuits

It has been known for some time (Rothman, 1962) that meta-materials consisting of a network of metal wires share a number of electromagnetic properties with plasma. For example, both have a cutoff frequency below which there is no wave propagation. These ideas have recently been re-discovered (Pendry, 1996) and applied to designing electromagnetic structures that have negative dielectric permittivity and magnetic permeability. The extent to which the electromagnetic properties of wire arrays actually mimics the properties of the plasma is still open to debate. We demonstrate that two-dimensional wire arrays are essentially different from plasmas in all aspects except having a cut-off for a particular wave polarization. On the other hand, three-dimensional wire arrays support the same classes of waves as the plasma: longitudinally polarized plasmons and transversely polarized photons. Electromagnetic properties of two and three-dimensional wire arrays are also explained using equivalent lumped circuits.