Regular and irregular revivals of quasi-periodic random waves

TL;DR

This paper reveals that quasi-periodic random wave packets can exhibit both regular and irregular revivals during propagation, with individual realizations reconstructing differently than ensemble averages, advancing understanding of wave self-reconstruction.

Contribution

It introduces the concept of a revival network in quasi-periodic random waves and demonstrates both theoretically and experimentally the coexistence of regular and irregular revivals.

Findings

Ensembles of quasi-periodic random waves show a unique revival network.

Individual realizations self-reconstruct at different distances than ensemble averages.

Experimental verification confirms theoretical predictions.

Abstract

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.