  Many of graphene's unique electronic properties emerge from its Dirac-like
electronic energy spectrum. Similarly, it is expected that a nanophotonic
system featuring Dirac dispersion will open a path to a number of important
research avenues. To date, however, all proposed realizations of a photonic
analog of graphene lack fully omnidirectional out-of-plane light confinement,
which has prevented creating truly realistic implementations of this class of
systems. Here we report on a novel route to achieve all-dielectric
three-dimensional photonic materials featuring Dirac-like dispersion in a
quasi-two-dimensional system. We further discuss how this finding could enable
a dramatic enhancement of the spontaneous emission coupling efficiency (the
\beta-factor) over large areas, defying the common wisdom that the \beta-factor
degrades rapidly as the size of the system increases. These results might
enable general new classes of large-area ultralow-threshold lasers,
single-photon sources, quantum information processing devices and energy
harvesting systems.
