__Role of dispersion on zero-average-index bandgaps__

We consider periodic multilayers combining ordinary positive index materials and dispersive metamaterials
with negative index in some frequency ranges. These structures can exhibit photonic bandgaps which, in contrast
with the usual Bragg gaps, are not based on interference mechanisms. Changing the dispersion models
for the constituent metamaterial, we investigate its role in the production of zero-average-index bandgaps. In
particular, we show the effect of each constitutive parameter on both bandgap edges. Finally, we give some
approximated analytical expressions in terms of average parameters for the determination of the upper and
lower limits of the zero-average refractive-index bandgap.