Infinite at every frequency: the photonic density of states in (meta)materials with hyperbolic dispersion and related phenomena

We show that (meta)materials with hyperbolic dispersion exhibit a broad bandwidth singularity in the photonic density of states. As opposed to an isolated singularity found in other physical systems, with the finite density of states in its vicinity, for the systems with hyperbolic dispersion the photonic density of states diverges at every frequency over a finite bandwidth. This behavior leads to a dramatic change in a variety of phenomena, from spontaneous emission to light propagation and scattering.