  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.
