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 \mu or the electric permittivity \epsilon of the metamaterial is zero. Although the interface of a semi-infinite medium with zero refractive index (a condition attained either when \mu= 0 or when \epsilon= 0) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to \mu = 0 occurs only for TE polarized waves, whereas a gap corresponding to \epsilon = 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.