  Photonic hyper-crystals combine the most interesting features of hyperbolic
metamaterials and photonic crystals. Since the dispersion law of extraordinary
photons in hyperbolic metamaterials does not exhibit the usual diffraction
limit, photonic hyper-crystals exhibit light localization on deep subwavelength
scales, leading to considerable enhancement of nonlinear photon-photon
interaction. Therefore, similar to their conventional photonic crystal
counterparts, nonlinear photonic hyper-crystals appear to be very promising in
optical limiting and optical computing applications. Nonlinear optics of
photonic hyper-crystals may be formulated in such a way that one of the spatial
coordinates would play a role of effective time in a 2+1 dimensional optical
spacetime describing light propagation in the hyper-crystal. Mapping the
conventional optical computing onto nonlinear optics of photonic hyper-crystals
results in a hyper-computing scheme, which may considerably accelerate
computation time.
