Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials

We show that the frequency range of the zero averaged refractive index gap in a photonic heterostructure containing negative-index materials can be enlarged owing to the property that its lower and upper frequency edges depend on the thickness ratio of the positive- and negative-index materials. Compared to the zero averaged refractive index gap of a single photonic crystal, the frequency range of the zero averaged refractive index gaps in a photonic heterostructure can be notably enlarged. Moreover, it is shown that the band edge of the zero averaged refractive index gap is determined not only by the TM polarization but also by the TE polarization, which is obviously different from the omnidirectional band gaps in conventional photonic crystals, whose bandwidth is determined by the TM polarization.