Space-time wave packets

Space-time wave packets (STWPs) 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 the 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 STWPs: their spectra are not separable with respect to the spatial and temporal degrees of freedom. Indeed, the spatiotemporal structure is endowed with non-differentiable angular dispersion, in which each spatial frequency is associated with a single prescribed wavelength. Furthermore, controlled deviation from this particular spatiotemporal 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 STWPs has been known since the 1980s, only very recently has rapid experimental development emerged. These advances are made possible by innovations in spatiotemporal Fourier synthesis, thereby opening a new frontier for structured light at the intersection of beam optics and ultrafast optics. Furthermore, a plethora of novel spatiotemporally structured optical fields (such as flying-focus wave packets, toroidal pulses, and spatiotemporal optical vortices) are now providing a swath of surprising characteristics, ranging from tunable group velocities to transverse orbital angular momentum. We review the historical development of STWPs, describe the new experimental approaches for their efficient synthesis, and enumerate the various new results and potential applications for STWPs and other spatiotemporally structured fields, before casting an eye on a future roadmap for this field.