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.

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.

Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to nonlinear and quantum optics. However, synthesizing such wave packets requires introducing non-differentiable angular dispersion with high spectral precision in two transverse dimensions, a capability that has eluded optics to date. Here, we describe an experimental strategy capable of sculpting the spatio-temporal spectrum of a generic pulsed beam by introducing arbitrary radial chirp via two-dimensional conformal coordinate transformations of the spectrally resolved field. This procedure yields propagation-invariant ‘space-time’ wave packets localized in all dimensions, with tunable group velocity in the range from 0.7c to 1.8c in free space, and endowed with prescribed orbital angular momentum. By providing unprecedented flexibility in sculpting the three-dimensional structure of pulsed optical fields, our experimental strategy promises to be a versatile platform for the emerging enterprise of space-time optics.

Can an optical pulse traverse a non-dispersive material at the speed of light in vacuum? Because traditional approaches for controlling the group velocity of light manipulate either the material or structural resonances, an absence of dispersion altogether appears to exclude such a prospect. Here we demonstrate theoretically and experimentally that “space–time” wave packets—pulsed beams in which the spatial and temporal degrees of freedom are tightly intertwined—can indeed traverse a non-dispersive transparent optical material at the speed of light in vacuum. We synthesize wave packets whose spatio-temporal spectra lie along the intersection of the material’s light-cone with a spectral hyperplane tilted to coincide with the vacuum light-line. By measuring the group delay interferometrically with respect to a generic reference pulse, we confirm that the wave packet group velocity in a variety of materials (including water, glass, and sapphire) is the speed of light in vacuum.

The group velocity of ‘space-time’ wave packets – propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations – can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum – and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced ‘pilot envelope’ that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width ∼ 4 ps and a spectral uncertainty of ∼ 20 pm, we measure maximum differential group delays of approximately ±150 ps, which exceed previously reported measurements by at least three orders of magnitude.