  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.
