Moire lattices consist of two identical periodic structures overlaid with a relative rotation angle. Present even in everyday life, moire lattices have been also produced, e.g., with coupled graphene-hexagonal boron nitride monolayers, graphene-graphene layers, and layers on a silicon carbide surface.A fundamental question that remains unexplored is the evolution of waves in the potentials defined by the moire lattices. Here we experimentally create two-dimensional photonic moire lattices, which, unlike their material predecessors, have readily controllable parameters and symmetry allowing to explore transitions between structures with fundamentally different geometries: periodic, general aperiodic and quasi-crystal ones. Equipped with such realization, we observe localization of light in deterministic linear lattices. Such localization is based on at band physics, in contrast to previous schemes based on light difusion in optical quasicrystals,where disorder is required for the onset of Anderson localization. Using commensurable and incommensurable moire patterns, we report the first experimental demonstration of two-dimensional localization-delocalization-transition (LDT) of light. Moire lattices may feature almost arbitrary geometry that is consistent with the crystallographic symmetry groups of the sublattices, and therefore afford a powerful tool to control the properties of light patterns, to explore the physics of transitions between periodic and aperiodic phases, and two-dimensional wavepacket phenomena relevant to several areas of science.
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