Effective permittivity and permeability of one-dimensional dielectric photonic crystal within a band gap

We take a finite dielectric photonic crystal as a homogeneous slab and have extracted the effective parameters. Our systematic study shows that the effective permittivity or permeability of dielectric photonic crystal is negative within a band gap region. This means that the band gap might act as in-negative materials (ENMs) with in < 0 and μ > 0, or μ-negative materials (MNMs) with in > 0 and μ < 0. Moreover the effective parameters sensitively rely on size, surface termination, symmetry, etc. The effective parameters can be used to design full transmission tunnelling modes and amplify evanescent wave. Several cases are studied and the results show that dielectric photonic band gap can indeed mimic a single negative material (ENM or MNM) under some restrictions. (classical areas of phenomenology)