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Stable three-dimensional solitons in two-dimensional photonic lattices

A brief overview of recent theoretical results concerning the existence and stability of three-dimensional solitons in self-focusing media with imprinted two-dimensional harmonic or radially symmetric Bessel optical lattices is given. It is concluded that such photonic lattices support one-parameter families of three-dimensional solitons, which are stable within one interval of the values of their energy (for harmonic lattices) or even within two intervals of the values of their energy (for Bessel lattices), provided that the lattice strength exceeds a threshold value. The Hamiltonian versus soliton norm has two or even three cuspidal points (a "swalowtail"-like bifurcation pattern, which rarely occurs in physical models). The results suggest new approaches of making stable spatiotemporal optical solitons ("light bullets") and three-dimensional solitons in attractive Bose-Einstein condensates.