Classification of propagation-invariant space-time wave packets in free space: Theory and experiments

Abstract

Introducing correlations between the spatial and temporal degrees of freedom of a pulsed optical beam (or wave packet) can profoundly alter its propagation in free space. Indeed, appropriate spatiotemporal spectral correlations can render the wave packet propagation-invariant: the spatial and temporal profiles remain unchanged along the propagation axis. The spatiotemporal spectral locus of any such wave packet lies at the intersection of the light cone with tilted spectral hyperplanes. We investigate $(2+1)\mathrm{D}$ propagation-invariant ``space-time'' light sheets and identify ten classes categorized according to the magnitude and sign of their group velocity and the nature of their spatial spectrum---whether the low spatial frequencies are physically allowed or forbidden according to their compatibility with causal excitation and propagation. We experimentally synthesize and characterize all ten classes using an experimental strategy capable of synthesizing space-time wave packets that incorporate arbitrary spatiotemporal spectral correlations.