Free-space propagation of optical coherence lattices and periodicity reciprocity

We examine paraxial propagation of recently introduced optical coherence lattices in free space and demonstrate a novel phenomenon of periodicity reciprocity between their intensity and coherence properties. The periodicity reciprocity arises because an aperiodic source intensity profile of an optical coherence lattice evolves into a lattice-like far-field profile, while the periodic spectral degree of coherence at the source becomes aperiodic on free-space propagation. We discuss how the discovered periodicity reciprocity can make optical coherence lattices attractive for robust free-space optical communications.