Electrodynamics of metal-dielectric composites and electromagnetic crystals

A theory that takes into account effects of retardation is developed for calculating the effective dielectric constant and magnetic permeability of metal-dielectric composites and photonic crystals containing a metallic component. The effective parameters depend, in general, on the local microgeometry of composites and electromagnetic crystals. For example, in metal-wire crystals the effective dielectric constant becomes negative at frequencies below the cutoff frequency, which, in the case of a strong skin effect, is determined by the crystal structure only. It is also shown that the effective high-frequency magnetic permeability, which originates from the eddy currents in metal grains or wires, does not vanish, even in systems with no intrinsic magnetism. In metal-dielectric composites, it is shown that the effective dielectric constant has a positive maximum and a negative minimum in the vicinity of the percolation threshold. A new class of photonic crystals is proposed, where both dielectric permittivity and magnetic permeability are negative in optical spectral range.