  "Space-time" (ST) wave packets constitute a broad class of pulsed optical
fields that are rigidly transported in linear media without diffraction or
dispersion, and are therefore propagation-invariant in absence of optical
nonlinearities or waveguiding structures. Such wave packets exhibit unique
characteristics, such as controllable group velocities in free space and exotic
refractive phenomena. At the root of these behaviors is a fundamental feature
underpinning ST wave packets: their spectra are not separable with respect to
the spatial and temporal degrees of freedom. Indeed, the spatio-temporal
structure is endowed with non-differentiable angular dispersion, in which each
spatial frequency is associated with a single prescribed wavelength.
Furthermore, deviation from this particular spatio-temporal structure yields
novel behaviors that depart from propagation invariance in a precise manner,
such as acceleration with an arbitrary axial distribution of the group
velocity, tunable dispersion profiles, and Talbot effects in space-time.
Although the basic concept of ST wave packets has been known since the 1980's,
only very recently has rapid experimental development emerged. These advances
are made possible by innovations in spatio-temporal Fourier synthesis, thereby
opening a new frontier for structured light at the intersection of beam optics
and ultrafast optics.
