Interaction between non-Bragg band gaps in 1D metamaterial photonic crystals.

We consider periodic multilayers combining ordinary positive index materials and dispersive metamaterials with negative index in some frequency range. These structures can exhibit photonic band gaps which, in contrast with the usual Bragg gaps, are not based on interference mechanisms. We focus on effects produced by the interaction between non-Bragg gaps of different nature: a) the zero averaged refractive index, b) the zero permeability and c) the zero permittivity gaps. Our analysis highlights the role played by the unavoidable dispersive character of metamaterials. We show that the degree of overlap between these bands can be varied by a proper selection of the constructive parameters, a feature that introduces novel degrees of freedom for the design of photonic band gap structures. The numerical examples illustrate the evolution of the dispersion diagrams of a periodic multilayer with the filling fraction of the ordinary material constituent and show a range of filling fractions where propagation in the multilayer is forbidden for any propagation angle and polarization.