Regular and irregular revivals of quasi-periodic random waves

Paraxial wave packets with discrete spatial, temporal, or spatiotemporal spectra are known to undergo periodic axial revivals on propagation in either free space or linear transparent, weakly dispersive media. Such spectacular revivals, ubiquitously encountered in physics, from optics and acoustics to condensed matter physics, are distinguished by their strict periodicity. We show theoretically and verify experimentally that ensembles of quasi-periodic random wave packets exhibit a unique revival network composed of regular (periodic) and irregular (aperiodic) revivals. Moreover, individual realizations of a statistical ensemble self-reconstruct, in general, at different propagation distances than do ensemble averages. Our results shed new light on the fundamental physics of self-reconstruction of random wave packets with structured correlations.