  We introduce the photonic analogue of electronic Van Hove singularities (VHS)
in artificial media (metamaterials) with hyperbolic dispersion. Unlike photonic
and electronic crystals, the VHS in metamaterials is unrelated to the
underlying periodicity and occurs due to slow light modes in the structure. We
show that the VHS characteristics are manifested in the near-field local
density of optical states in spite of the losses, dispersion and finite unit
cell size of the hyperbolic metamaterial. Finally we show that this work should
lead to quantum, thermal, nano-lasing and biosensing applications of Van Hove
singularities in hyperbolic metamaterials achievable by current fabrication
technology.
