Is the photonic crystal with a Dirac cone at its Г point a real zero-index material?

Abstract

A novel optical property of a conventional two-dimensional dielectric photonic crystal (PC) has been reported by establishing a Dirac cone at the Г point of its band structure: it manipulates waves as if it had zero refractive indices at the Dirac point frequency (Huang et al. in Nature Mater 10:582–586, 2011). However, this PC is not a real homogeneous material. What is the difference between it and a real zero-index material (ZIM) is a fundamental issue of physics itself and also crucial to their applications. In this paper, through investigating the dispersion relations and the transmission properties of this kind of PC, we found that under normal incidence, at the frequency of the Dirac point, this PC does behave like a ZIM material. However, under oblique incidence, nonzero transmittances are obtained even at large incident angles, which is quite different from the real ZIM. The physical reason of the transmission properties was also investigated. It was found that near the Г point, there is an additional flat dispersion surface which intersects with the Dirac cone at the Dirac point. It is this flat dispersion surface which supports the Dirac point energy to exist in this PC, resulting in the nonzero transmission under oblique incidence.