Tunable double negative band structure from non-magnetic coated rods

A system of periodic poly-disperse-coated nano-rods is considered. Both the coated nano-rods and the host material are non-magnetic. The exterior nano-coating has a frequency-dependent dielectric constant and the rod has a high dielectric constant. A negative effective magnetic permeability is generated near the Mie resonances of the rods, while the coating generates a negative permittivity through a field resonance controlled by the plasma frequency of the coating and the geometry of the crystal. The explicit band structure for the system is calculated in the subwavelength limit. Tunable pass bands exhibiting negative group velocity are generated and correspond to simultaneously negative effective dielectric permittivity and magnetic permeability. These can be explicitly controlled by adjusting the distance between the rods, the coating thickness and the rod diameters.