Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals

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