Dispersion and negative refraction in photonic crystals without negative index

It is reported that certain photonic crystals posses negative refraction without relying on negative index. The findings show that both the intrinsic permittivity ɛ(f) and μ(f) must be strongly dispersive and having negative values over a limited frequency range. To meet that requirement, the band structure of the photonic crystal is performed. The photonic crystal consists of dielectric cylinders with metallic cores of ɛ(f) and μ(f) and a varying radius. The outer cylinders coated with a dielectric of radius 0.45a. The expanded plane wave method is developed and used to determine the band structure.