Anomalous diffraction in hyperbolic materials

We demonstrate that light is subject to anomalous (i.e., negative) diffraction when propagating in the presence of hyperbolic dispersion. We show that light propagation in hyperbolic media resembles the dynamics of a quantum particle of negative mass moving in a two-dimensional potential. The negative effective mass implies time reversal if the medium is homogeneous. Such property paves the way to diffraction compensation, spatial analogue of dispersion compensating fibers in the temporal domain. At variance with materials exhibiting standard elliptic dispersion, in inhomogeneous hyperbolic materials light waves are pulled towards regions with a lower refractive index. In the presence of a Kerr-like optical response, bright (dark) solitons are supported by a negative (positive) nonlinearity.