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

Anomalous diffraction in hyperbolic materials