Localization and oscillation of optical beams in Moiré lattices

We study the propagation of optical beams in two-dimensional Moiré lattices, and demonstrate position-dependent beam dynamics when a quasi-Bragg condition is satisfied. We show that when the optical beam is incident to a peak of the lattice envelop, an optical Zitterbewegung is obtained. If the optical beam is incident to a node of the envelop, a field localization effect takes place. The localized beam oscillates with a much larger spatial period than that of the optical Zitterbewegung. Variation of the oscillation period versus the split in periods is discussed. The position-dependent beam dynamics are explained by the excitation of proper bandedge eigenmodes of the Moiré lattice, and can be engineered via tuning the periods of the two superimposed Bragg lattices.