Ultrashort pulses lay the foundation of ultra-fast optics. The ability to control all the fundamental degrees of freedom of ultrashort pulses in both space and time domains has the potential to unlock a manifold of exotic light-matter interactions, unveil new physics, and enable new applications. The unique characteristics of ultrashort pulses, including short pulse duration, wide spectral bandwidth, and high peak power, make spatio-temporal ultrashort pulse tailoring face quite challenging. As ultra-thin planar optical elements composed of an array of deep sub-wavelength nanostructures, metasurfaces enable multifunctional optical field control at the nanoscale. This controllability, combined with merits including easy fabrication, integrability, and high damage threshold, makes metasurfaces ideal candidates in sculpting ultra-fast optical fields. We review the latest developments in metasurface-enabled spatio-temporal control of ultrashort pulses, especially by leveraging the Fourier synthesis approach to achieve complete four-dimensional pulse shaping in space and time. Then, brief discussions are carried out on free-space spatio-temporal pulse shaping via metasurfaces.

Ultrashort pulse shaping is usually realized by employing the Fourier synthesis approach, where a grating and lens pair disperse and then focus different wavelength components of the pulse at the Fourier plane to spatially separate different wavelengths. A modulator, which traditionally can be a liquid-crystal-based spatial light modulator, a digital micromirror device or an acousto-optic modulator, is placed at the Fourier plane to provide the pulse-shaping masking function. Recently, finely tailored ultrashort pulse shaping operations have been realized by adopting an ingeniously designed single-layer dielectric metasurface as the modulator. Temporal phase modulation, independent temporal phase and amplitude modulation, and temporal polarization modulation of the ultrashort pulses are theoretically and experimentally demonstrated. We discuss metasurface-enabled temporal pulse shaping in Section 2, where the metasurface device is divided into hundreds of independently designed units termed as "superpixels", with each superpixel composed of a two-dimensional array of identical nanopillars. For phase-only modulation, nanopillars with square cross-sections are sufficient. Meanwhile, pulse compression and pulse distortion are demonstrated as examples of the temporal phase modulation capability. For independent phase and amplitude modulation, nanopillars with rectangular cross-sections are selected, with phase modulations along the two birefringent axes following the half-wave plate condition. As a result, the transmitted phase is controlled by the lateral size of the nanopillar, while the transmitted amplitude is engineered by the rotation angle of the nanopillar. To demonstrate the versatility of this approach, we split an input ultrashort pulse with a temporal duration of 10 fs into two replicas, separated by 30 fs. Meanwhile, the temporal polarization state of the ultrashort pulse can also be controlled with rectangular nanopillars. For a nanopillar with a rotation angle $\theta$, the phase retardation between the transmitted phase along the two birefringent axes determines the transmitted polarization change. This approach allows the conversion of any arbitrary input temporal polarization states into desired output temporal polarization states. A variety of polarization-shaped ultrashort pulses with rich instantaneous time-varying polarization states are synthesized. Additionally, by further engineering the masking function at both the superpixel and the individual nanopillar level, complete four-dimensional properties (phase, amplitude, polarization, and spatial wavefront) of an ultrashort pulse can also be manipulated via a single-layer dielectric metasurface, which is discussed in detail in Section 3. Complex spatio-temporal wave packets that previously either have only been theoretically proposed or require complicated high-harmonic nonlinear generation processes are experimentally synthesized. The packets include a light coil exhibiting a helical intensity distribution evolution and another pulse with coherently multiplexed time-varying orbital angular momentum (OAM) orders. This approach provides a universal way for controlling the complete four-dimensional properties of light, and can be easily extended to synthesize other forms of spatio-temporal wave packets by metasurface design engineering, or wavelength regimes by nonlinear response. In addition to shaping ultrashort pulses via a metasurface-enabled Fourier synthesizer, free-space spatio-temporal pulse shaping using metasurfaces is also discussed in Section 4. Compared to the Fourier approach, free-space pulse shaping greatly lowers the complexity of the shaping apparatus but puts forward more requirements for the frequency interval of the input pulse and nanopillar geometry. Thus, metasurface-enabled free-space spatio-temporal pulse shaping is still an ongoing and active research field. Till now, several spatio-temporal wave packets such as pulses carrying transverse OAMs have been yielded by free-space metasurfaces.

We have witnessed significant developments in spatio-temporal control of ultrashort pulses in the past few years, and the advancements have already shown great potential in numerous fields. With the current trajectory of ultrashort pulse shaping moving toward more extreme high brightness sources and more complex functionalities, spatio-temporal optical field control approaches with higher resolution, wider spectral coverage, higher damage threshold, more compact footprint, and higher active tunability are highly desirable. We review the outstanding performance of the metasurface-based approaches and their potential to overcome some of these challenges. It is expected that continuous studies on metasurface design, simulation, and fabrication can have more general and complete control over the spatio-temporal wave packet synthesis.