__Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals__

We consider layered heterostructures combining ordinary positive index materials and dispersive metamaterials. We show that these structures can exhibit a new type of photonic gap around frequencies where either the magnetic permeability ? or the electric permittivity e of the metamaterial is zero. Although the interface of a semi-infinite medium with zero refractive index (a condition attained either when ? = 0 or when e = 0) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to ? = 0 occurs only for TE polarized waves, whereas a gap corresponding to e = 0 occurs only for TM polarized waves. These band gaps are scale-length invariant and very robust against disorder, although they may disappear for the particular case of propagation along the stratification direction.