We examine quasiperiodic multilayers arranged according to m-bonacci sequences that combine ordinary positive index materials and dispersive metamaterials with negative index in certain frequency ranges. When the averaged refractive index, in volume, of the multilayer equals zero, the structure does not propagate light waves and exhibits a forbidden band. In this contribution we recognize some approximated analytical expressions for the determination of the upper and lower limits of the above mentioned zero-average refractive index band gap.
We explore the electromagnetic response of one-dimensional photonic crystals containing slabs of uniaxial
anisotropic indefinite metamaterials (IMMs) with hyperbolic spatial dispersion characteristics. A band structure
classification has been previously made according to the sign of the permittivity and permeability parameters
for the particular case of optical axis perpendicular to the slab interfaces. To extend this study, here we analyze
how the dispersive behavior of each constitutive parameter affects the multilayer band structure. We consider
two orientations of the optical axis, perpendicular and parallel to the slab interfaces, and TE and TM modes.
Particular attention is paid to the effects of material dispersion on the existence of non-Bragg band gaps.