Light bullets in moiré lattices.

We predict that photonic moiré lattices produced by two mutually twisted periodic sublattices in a medium with Kerr nonlinearity can support stable three-dimensional (3D) light bullets localized in both space and time. The stability of light bullets and their properties are closely connected with the properties of linear spatial eigenmodes of moiré lattices that undergo localization-delocalization transition (LDT) upon the increase of the depth of one of the sublattices forming the moiré lattice, but only for twist angles corresponding to incommensurate, aperiodic moiré structures. Above the LDT threshold, such incommensurate moiré lattices support stable light bullets without an energy threshold. In contrast, commensurate-or periodic-moiré lattices arising at Pythagorean twist angles, whose eigenmodes are delocalized Bloch waves, can support stable light bullets only above a certain energy threshold. Moiré lattices below the LDT threshold cannot support stable light bullets for our parameters. Our results illustrate that the periodicity/aperiodicity of the underlying lattice is a crucial factor in determining the stability properties of the nonlinear 3D states.