The space-time Talbot effect

Abstract

The Talbot effect, epitomized by periodic revivals of a freely evolving periodic field structure, has been observed with waves of diverse physical nature in space and separately in time, whereby diffraction underlies the former and dispersion the latter. To date, a combined spatio-temporal Talbot effect has not been realized in any wave field because diffraction and dispersion are independent physical phenomena, typically unfolding at incommensurable length scales. Here we report the observation of an optical 'space-time' Talbot effect, whereby a spatio-temporal optical lattice structure undergoes periodic revivals after suffering the impact of both diffraction and dispersion. The discovered space-time revivals are governed by a single self-imaging length scale, which encompasses both spatial and temporal degrees of freedom. Key to this effect is the identification of a unique pulsed optical field structure, which we refer to as a V-wave, that is endowed with intrinsically equal diffraction and dispersion lengths in free space, thereby enabling self-imaging to proceed in lockstep in space and time.

Temporal Talbot effect in free space

“…We have also reported on a ST Talbot effect based on the unique dispersive ST wave packet denoted a 'V-wave' whose diffraction and dispersion lengths are intrinsically equal [51]. Because k x and ω are linearly related in a V-wave, k x and ω can be simultaneously sampled periodically to guarantee equal spatial and temporal Talbot lengths.…”