Fig. 1. Schematic illustration of recent advances in spatiotemporally structured wavepackets.

Fig. 2. Schematic of 4f ultrafast pulse shaper. (a) 1D pulse shaper for temporal modulation^[93]. (b) 2D pulse shaper for spatiotemporal phase-only modulation^[118]. (c) 2D holographic pulse shaper for spatiotemporally sculpting STWPs via a complex-amplitude modulation^[134]. (d) The intensity modulation and phase compensation analysis of a complex-amplitude modulated hologram^[135].

Fig. 3. Schematic of an afocal optical system for conformal mapping.

Fig. 4. Multi-plane light conversion (MPLC) for spatially controlling light fields. (a) Schematic for MPLC^[149]. (b) Laguerre/Hermite–Gaussian mode sorter based on MPLC^[151]. (c) A high-dimensional MPLC-based mode sorter for arbitrarily randomized spatial mode basis sorting^[152]. (d) Processing entangled photons in high dimensions with an MPLC^[153]. A pixel-entangled two-photon state undergoes a general unitary transformation implemented using an MPLC. (e) Sensing quantum-state-based rotations with an MPLC^[154].

Fig. 5. Illustration of some typical metasurfaces for the structured-light field generation. (a) Dynamic phase directly imprints a helical phase profile via phase-sensitive elements^[156]. (b) Geometric phase metasurfaces encode the helical phase profile onto the cross-polarization component from the metasurface using birefringence^[156]. (c) J-plate metasurfaces exploit the complete and independent phase and polarization control, capable of creating different OAM modes at arbitrary orthogonal polarization outputs^[156]. (d) Design and optimization of a 3D metasurface for the complete and independent manipulation of both amplitude and phase responses of transmitted light^[167]. (e) Numerical characterization of the amplitude and initial phase retardation of cross-polarization transmitted from a nanopillar with different heights (H) and lengths (L)^[167]. (f) Ultrafast optical pulse shaping using dielectric metasurfaces^[168]. In a 4f configuration, a metasurface device is used to perform the 2D complex-amplitude modulation at the frequency plane.

Fig. 6. Experimental generation and characterization of STOV wavepackets. (a) A 2D pulse shaper with a helicoidal phase is used for STOV generation, and a Mach-Zehnder-like scanning interferometer is utilized for STOV measurement^[118]. (b) Time-dependent interference fringes measured at different time delays^[118], as indicated in (c). (c) Theoretical and reconstructed 3D iso-surface and phase of an STOV^[118] based on (b). (d) Forming process of an STOV wavepacket in free space after a pulse shaper^[117].

Fig. 7. Generation of Bessel STOV (BeSTOV) wavepackets. (a) Phase-only hologram for generating BeSTOV wavepackets. Top row, from left to right: conical phase, second-order phase (GDD phase), focus/defocus phase, and helical phase. Bottom row: total phase of the above phases without topological charge (left) and with topological charge 2 (right)^[173]. (b) Experimentally reconstructed 3D iso-surface of a BeSTOV wavepacket with topological charge 1^[173]. (c) Spatiotemporal non-diffraction property of the generated BeSTOV wavepackets with topological charge 2^[173]. (d) Generation of BeSTOV wavepackets carrying extremely high topological charges^[174]. SLM phase patterns for generating BeSTOVs with topological charges of 10, 25, 50, and 100. (e) Experimental setup for generating and measuring BeSTOV wavepackets^[174]. (f) Experimentally reconstructed ultrahigh-order BeSTOVs^[174] from holograms in (d).

Fig. 8. Complicated STWP generation based on complex-amplitude modulation^[135]. (a) Realization of spatiotemporal complex amplitude modulation with redistribution of energy into other diffraction orders. (b) Demonstration of spatiotemporal complex modulation with the generation of a spatiotemporal Bessel wavepacket via complex-amplitude modulation. (c) Experimental results of spatiotemporal optical time crystals and spatiotemporal optical time quasi-crystals via complex-amplitude modulation; top row: SLM phase patterns. (d) 3D iso-surface of the generated spatiotemporal flat-top wavepacket via complex-amplitude modulation.

Fig. 9. Synthesis and characterization of STOV wavepackets with controllable radial and azimuthal quantum numbers^[134]. (a) Optical setup for synthesizing and characterizing STLG wavepackets. The apparatus comprises three sections: (i) 2D ultrafast holographic pulse shaper consisting of a diffraction grating, a cylindrical lens, and an SLM; (ii) a pulse compressor system consisting of a parallel grating pair; (iii) a time delay line system for fully reconstructing 3D profile of generated ST wavepacket. (b) Time-dependent interference fringes of STLG wavepacket of p=2,l=1 at several time delays. (c) Experimentally reconstructed 3D iso-surface, intensity, and phase of an STLG wavepacket with p=2,l=1. (d) Generation of STLG wavepackets with high-order radial and azimuthal quantum numbers of p=4,l=1; p=5,l=1; p=2,l=2; p=2,l=5; and p=2,l=10.

Fig. 10. Partially coherent STOVs and spatiotemporal coherence vortices. (a) Schematic for spatiotemporal twisted wavepacket generation^[178]. (b) Generation of STOVs with temporally partial coherence^[181]. (c) Spatiotemporal coherence vortices^[182,183].

Fig. 11. Metasurface and nanophotonic structure for STOV wavepacket generation. (a) Photonic crystal slab design for generating pulses with transverse OAM^[184]. Left: the geometry of non-symmetric nanograting, with incident pulse indicated by the red arrow. The grating cross section in the x–z plane is shown on the top left inset. Right: transmission function in the momentum space; the red line represents the transmission nodal line. (b) Spatiotemporal differentiator with spatial mirror symmetry breaking for STOV generation^[185]. (c) STOV generation in a microscale platform composed of a slanted nanograting. A tilted-view and a side-view scanning electron microscope image of this slanted nanograting^[187]. (d) The corresponding complex transmission coefficient distributions in the frequency-momentum space for slant angles of 10°, 15°, and 20°^[187]. (e) Basic principle of STOV generation utilizing topological darkness of a photonic crystal slab^[188]. A Gaussian pulse strikes a reflective photonic crystal slab with a periodic pattern on a dielectric membrane generating an STOV structure with a curved vortex line. (f) An STOV centered at a specific frequency can be generated from Gaussian pulses by a simple mirror-based resonant grating^[189]. A phase singularity in specular reflection is formed at the X point in momentum space due to resonance-induced total retroreflection. (g) Concept of 3D optical singularities in bilayer photonic crystals^[190].

Fig. 12. Diffraction and propagation properties of STOV wavepackets in free space and dispersive medium. (a) Left: experimental setup for investigating the diffraction property of STOV wavepackets by a grating. Right: diffraction pattern of STOVs with various topological charges^[191]. (b) Experimental propagation dynamics of an STOV wavepacket in free space demonstrate that the absence of dispersion leads to wavepacket splitting^[192]. (c) Calculated propagation dynamic of an STOV wavepacket in a dispersive medium with different dispersion coefficients^[193]. When dispersion and diffraction are balanced, the wavepacket remains stable; otherwise, the singularity splits. (d) Schematics of the reflection and refraction of STOV at the planar isotropic interface^[194]. STOVs carrying intrinsic transverse OAM exhibit peculiar properties of beam shifts and time delays depending on the value and orientation of the OAM.

Fig. 13. STOV wavepackets with tilted transverse OAM. (a) The intersection of spatiotemporal vortices and spatial vortices within a wavepacket leads to a tilted OAM due to the interaction of these two types of optical vortices^[202]. (b) A photonic crystal slab structure can generate STOVs with arbitrary OAM direction based on the design of transmission nodal lines^[203]. (c) Manipulating the transverse OAM direction can be achieved using a cylindrical lens system with a relative rotational angle. The additional longitudinal torque introduced by the cylindrical lenses couples with the original transverse OAM, adjusting its direction^[204]. (d) The orientation of vortices in ultrashort optical pulses can be controlled using spatial chirp^[205]. Introducing spatial chirp into a spatial vortex pulse results in an arbitrary orientation of the line phase singularity.

Fig. 14. Manipulation and interaction of multi-singularities within an STOV wavepacket. (a) Sculpturing spatiotemporal wavepackets with chirped pulses^[206]. Left: intensity distributions of STOV wavepackets with different amounts of GDD. Middle: STOV lattice with multiple STOVs multiplexed in space and time. Right: collision of two STOVs. Linear phases with opposite signs are applied on the left/right side of the input light field to advance/delay input wavepackets in the corresponding time domain. (b) Spatiotemporal intensity and phase profile of STOV wavepackets with phase singularities embedded in different space–time domains^[207]. By tuning different parameters, the magnitude and orientation of the photonic OAM in space–time can be tuned. (c) Observation of vortex reconnections within an STWP^[208]. The transverse crossing of two vortices with a topological charge of one can produce unique vortex loop reconnection patterns. Higher topological charges result in arrays of vortex loops and connection points. (d) Generation of cylindrically polarized STWP with both phase and polarization singularities by cascading a vectorial vortex plate after a pulse shaper^[209].

Fig. 15. STOV wavepackets with time-varying transverse OAM. (a) Generation of rapidly changing transverse OAM within an STOV wavepacket^[211]. Top: 3D intensity reconstruction of a wavepacket of two spatiotemporal vortices with dynamic transverse OAM and temporal separation of 0.74 ps. Bottom: corresponding phase pattern loaded onto the SLM inside a 2D pulse shaper. (b) Configuration for measuring the effect of a transient phase perturbation on the ultrafast field imposed by the ultrafast optical field ionization plasma^[212]. (c) Effect of transient wire onset time τ0 on changing the transverse OAM of STOV^[212]. (d) A phase pattern loaded on the SLM for generating STPV string with time-dependent transverse OAM^[213]. (e) Complex field of generated STOV string^[213]. (f) The temporal diffraction pattern of STOV string by a grating^[213].

Fig. 16. Synthesizing spatiotemporal vortex pulse burst with time-varying transverse OAM^[214].

Fig. 17. Harmonic generation of STOV wavepackets. (a) Second-harmonic spatiotemporal OAM pulse generation and characterization^[215]. Left: experimental setup; fundamental STOV of topological charge ℓ=1 is generated by a 2D pulse shaper. Second-harmonic STOV is generated in BBO crystals and characterized by interference with reference pulses. Right: experimentally reconstructed 3D intensity iso-surface profile of the fundamental STOV (top) and its second harmonic (bottom). (b) Complex field of fundamental STOV (left) and its second harmonic (right)^[215]. The second-harmonic fields with ℓ=2 demonstrate the conservation of OAM in an SHG process. (c) Controlling photon transverse OAM in HHG^[218]. Spatially resolved HHG spectrum driven by the fundamental STOV with hydrogen atoms.

Fig. 18. High-dimensional manipulations of STWP. (a) Simulation of the conformal mapping from a spatiotemporal vortex tube to a vortex ring through log-polar to Cartesian coordinate transformation^[129]. (b) Schematic of the experimental apparatus for STOV wavepacket generation and implementation of the conformal mapping. (c) Experimental reconstruction of the photonic toroidal vortex from different views. (d) Generation of scalar optical hopfions by further applying a spatial helical phase to the x–y domain of the generated photonic toroidal vortex^[221].

Fig. 19. Generation of high-dimensional STWP based on conformal mapper. (a) Photonic conch with symmetry breaking^[222]. (b) Generation of a light spring with time-varying OAM through the conformal mapping of a spatially azimuthal dispersive pulsed beam^[223].

Fig. 20. STOV generated in other wave phenomena. (a) Schematic of the experimental setup for acoustic STOV wavepacket generation and measurement. The acoustic STOV wavepacket is generated by an acoustic phased array and measured along a scan line. A separate pulse signal from the sound card synchronously triggers each recording. The inset shows a time sequence of acoustic signals acquired at one point^[225]. (b) A meta-grating with broken spatial mirror symmetry for the generation of acoustic STOV wavepackets. The meta-grating exhibits vortices in the transmission spectrum function in the momentum−frequency domain, which appear in pairs at the critical value of the asymmetry parameter^[226]. (c) Synthesizing 3D acoustic STOVs with OAM oriented in arbitrary directions^[227]. There are two methods for manipulating OAM orientation: the first approach involves the direct rotation of wavepackets carrying longitudinal or transverse OAM in 3D space (top left); the second approach is achieved through the intersection of vortices carrying longitudinal and transverse OAM. By modifying the topological charges of these vortices, the orientation of the tilted OAM can be adjusted (top right). (d) Plasmonic toroidal vortex generation under radially polarized beam illumination^[228]. Left: configuration of a plasmonic nanotorus under a radially polarized beam. Top: electric field evolution and surface charge distribution on a gold nanotorus at four resonance phases. Middle: simulated scattering intensity and field enhancement; comparison of light intensity with and without the nanotorus. Bottom: simulated electric and magnetic fields, and orbital momentum density of scattered light; detailed view of the electric field and orbital momentum density; broader x–z plane electric field distribution with the nanotorus marked in yellow.

Fig. 21. Diffraction-free STWPs: space–time light sheet^[126]. Top: (a)–(d) Light fields explained with the superposition of plane waves lie on the surface of a kx−ω light-cone. (a) A continuous monochromatic beam lies on the intersection of the light-cone with an iso-frequency plane, featured by a narrow temporal frequency range (Δω) and a wide spatial frequency range (Δkx). These optical fields exhibit diffractive spreading during propagation. (b) A pulsed Gaussian beam corresponding to a patch on the light-cone has a wide range in both spatial and temporal frequencies. These optical fields exhibit diffractive and dispersive spreading during propagation in a dispersive medium. (c), (d) Diffraction-free space–time light sheet lies on the intersection of the light-cone with a tilted frequency plane (parallel to kx axis), and has a tight relationship between spatial frequency and temporal frequency (each kx is associated with a unique ω). Such STWPs exhibit diffraction-free property and controllable group velocity during propagation. (e) Synthesis and analysis of diffraction-free space–time light sheets. The spatiotemporal frequency relationship is created by a phase-only mask via the 2D pulse shaper. The input pulsed beam is a pulsed plane wave. (f) Measured space–time spectral intensity |Ψ˜(kx,λ)|2 of a hollow light sheet, with the π-step implemented along kx superimposed. (g) Measured temporal integral intensity I(x,z)=∫−T+T|Ψ(x,z,t)|2dt of the space–time light sheet at various propagation distances. The insert denotes the Rayleigh length. The results verify the propagation-free property of the generated space–time light sheet wavepacket.

Fig. 22. Light spring wavepackets with time-varying properties. (a) Generation of EUV beams with self-torque. Two time-delayed, collinear IR pulses with the same wavelength (800 nm) but different OAM values are focused on an argon gas target, serving as the HHG medium^[127]. This setup produces harmonic beams with self-torque. The intensity profile varies at different radii over time during the emission process, resulting in a pulsed beam with temporally varying OAM. (b) A spatiotemporal light spring is achieved by imprinting spatially azimuthal mode indices of a Laguerre–Gauss beam onto the pulsed frequency^[232]. (c) Propagation-invariant spatiotemporal helical wavepackets carrying OAM that evolve on spiraling trajectories in both time and space in bulk media or multimode fibers^[233]. (d) Generation of spatiotemporal coupling wavepackets exhibiting both dynamic rotation and revolution is achieved by coherently adding multiple frequency comb lines^[128]. (e) Synthesizing spatiotemporal coupling wavepackets with temporally and longitudinally varying dynamics involves introducing a spectrum that includes both temporal and longitudinal wavenumbers^[234]. This spectrum is associated with specific transverse Bessel-Gaussian fields. (f) The schematic demonstrates a time-varying optical vortex generated by reflecting a laser beam off a time-modulated metasurface with an azimuthal frequency gradient^[235]. The beam exhibits a ring-shaped intensity pattern whose radius continuously and periodically oscillates due to variations in the topological charge. (g) Generating a spatiotemporal coupling wavepacket that carries time-dependent OAM and exhibits polarization-swept using a pulse shaper in conjunction with a metasurface^[236]. (h), (i) An integrated optical vortex microcomb capable of simultaneously emitting spatiotemporal light springs comprising 50 OAM modes, with each frequency of the microcomb carrying a unique OAM value^[237,238].

Fig. 23. Light coils with broadband topological-spectral correlations. (a) Characterization trace of the femtosecond pulses from the NOPA measured by polarization-gated frequency-resolved optical gating (left). The intensity spectrum covers a broad portion of the visible range (right). (b) Spectral peak distribution in the far field of the axicon characterized by a hyperspectral camera^[239]. (c) Conceptual scheme for space–time beam shaping involves an axicon grating that maps the spectral content of the input ultrashort pulse into concentric rings. A hologram displayed on an SLM in the far field of the axicon customizes a topological-spectral correlation, yielding helical wavepackets. (d) Optical profilometry image of the fabricated gray-scale axicon. Scale bar: 50 µm. (e) Diagram of the spatially resolved spectral setup designed for space-time beam characterization. This setup integrates a spatial interferometer utilizing off-axis digital holography with a temporal interferometer employing Fourier transform spectroscopy. Both are unified within a common-path birefringent interferometer. (f) Iso-intensity surfaces of synthesized helical wavepacket with specific correlations. (g) Digital Fourier space–time beam shaper for helical wavepackets with time-varying OAM at femtosecond timescale^[240]. The ultrashort pulse is incident normal an axicon grating, which is encoded as a phase hologram on the first SLM, which maps the spectral content into concentric rings in the far field. A metallic disk mask placed is used to block the zero order of the first SLM. A hologram displayed on a second SLM in the far field imparts a topological-spectral correlation. The helical wavepackets are generated at the imaging plane of the first SLM. The characterization setup combines a delay line and spatial interferometer based on off-axis digital holography. The interference images are recorded by the charge-coupled device camera located at the imaging plane of the first SLM. CM, concave mirror; BS, beam splitter; CCD; charge-coupled device. (h) Modal decomposition analysis of the synthesized helical wavepacket confirming a continuous increase in topological charges, signifying a dynamically evolving OAM and a measured self-torque of 0.36fs−1. (i) Analysis of the wavepacket’s angular position over time of a generated angular self-acceleration wavepacket, fitted with a third-degree polynomial.

Fig. 24. Synthesis of STWPs with tailored spatiotemporal properties. (a), (b) Generation of spatially and temporally correlated wavepackets using the combination of 2D pulse shaper and MPLC. The MPLC cascaded after the 2D pulse shaper enabling the precise engineering of the space–time correlation^[241]. The 2D pulse shaper is used to steer the spectrally modulated pulse to different spatial positions with distinct time delays before entering an MPLC system. The MPLC comprising an SLM and a mirror is used to modulate the spatial phase and intensity profiles of each pulse spot at different spatial positions. (c) Synthesized STWP with spectral and time-dependent OAM. (d) Synthesized STWP with an intricate spatiotemporal texture comprised of HG basis. (e) Synthesis and analysis of multidimensional ultrashort pulses^[242]. (f) Reconstructed iso-intensity profile (top) and retrieved pulse field attributes (bottom) of the optical field. (g) Transport of spatiotemporal light pulses in multimode waveguides^[243].

Fig. 25. Electric-magnetic toroidal pulses. (a), (b) Spatiotemporal and spatio-spectral structure of the toroidal pulse^[130]. (c) Schematic of the generation of an optical toroidal pulse. (d) Schematic of the generation of terahertz TM and TE toroidal pulses using plasmonic metasurfaces. (e) Side and (f) front views of the transverse electric field component of generated optical toroidal pulses. (g) Corresponding side view of the longitudinal component. (h) Propagation evolution of an elementary optical toroidal pulse^[245]. (i) Propagation evolution of nondiffracting supertoroidal pulses. (j) Topological electromagnetic and energy flow structures of nondiffracting supertoroidal pulses with parameters q2=100 and q3=1 at t=0. (k) A zoom-in of the magnetic field with the arrow plot showing the vector distribution, the black dots referring to the singularities, and surrounding red arrows marking the type of the vector singularities (vortex and saddle).

Fig. 26. Dynamic ring current radiates FD terahertz pulse^[247]. (a) Illustration of FD pulse generation: two azimuthally polarized vector pulses induce transient ring currents in GaAs. The radiation from these rapidly oscillating ring currents results in a single-cycle THz pulse with a toroidal topology and an FD pulse. (b) Spatial-vectorial distribution of ring current in GaAs. (c) Spatiotemporal structure of the radiated electric field from a dynamic ring current density source. (d) Magnetic field map of the emitted THz pulse.

Fig. 27. Experimental configuration for the generation of microwave toroidal pulses^[248]. (a), (b) Cylindrical coaxial antenna horn. (c) Driving voltage applied to the antenna feed (blue line) and transient antenna output (red line). (d) Spatiotemporal evolution of the generated toroidal pulse. (e) A schematic of the electromagnetic configuration of such toroidal pulse.

Fig. 28. (a), (b) Electromagnetic skyrmionic structure embedded as the vectorial features of toroidal and supertoroidal pulses^[250]. (c), (d) Hopfion structure established with the phase of a photonic toroidal vortex^[251].

Fig. 29. 3D laser pulse intensity diagnostic with temporally sliced off-axis interferometry^[254]. (a) Concept and schematic implementation of the diagnostic method. (b) Experimental captured “object” beam Io(x,y) (take an STOV of l=+1 as an example). (c) Experimental captured “probe” beam Ip(x,y), which has a Fourier transform limited duration of ∼122fs. (d) The interference fringe pattern of Iinter(x,y)−Ip(x,y)−Io(x,y). (e) The Fourier transformation of (d). (f), (g) Retrieved amplitude (f) and phase (g) distributions from the inverse Fourier transformation of the positive first order of (e).

Fig. 30. Automated closed-loop system for 3D characterization of STWPs (STOV as an example)^[255].

Fig. 31. SRSI for STOV characterization^[256]. (a) Experimental setup for the generation and characterization of ST-OAM light. STOV wavepackets are characterized by an SRSI, which includes collimated reference pulses and an imaging spectrometer. (b) Spectral interference fringe by SRSI. (c), (d) Reconstructed spatial-spectral amplitude and phase information by filtering fringe pattern of (b). (e), (f) Retrieved intensity and phase of an STOV by implementing 1D Fourier transformation (temporal frequency to time domain) of (c) and (d).

Fig. 32. Schematic of transient-grating single-shot supercontinuum spectral interferometry for single-frame characterization of STWP^[276]. The object pulse Es and the reference pulse εi interfered with each other at an angle θw in a fused silica witness plate, forming a transient grating. Such a grating is recorded by a probe pulse Epr.

Fig. 33. Optical trapping using transverse OAM. (a) Rotation of birefringent microparticles with transverse OAM caused by the superposition of two orthogonal circularly polarized beams (red and blue arrows)^[277]. (b) Small particles driven around a larger vaterite particle undergoing transverse spinning. (c) Generation of transverse OAM beam; when two focused, counter-propagating, linearly polarized Gaussian beams are separated along the polarization axis, an array of optical vortices carrying transverse angular momentum is generated, causing a suspended silicon nanorod to experience torque and rotate in the y–z plane^[278]. (d) Power spectral density (PSD) of the nanorod motion when driven to rotate at a frequency frot by transverse OAM (top) and without transverse OAM (bottom).

Fig. 34. (a) Experimental demonstration of transmitting STOVs through few-mode optical fiber^[281]. An STOV pulse from the 2D pulse shaper is coupled into a few-mode fiber (SMF-28) by a high-numerical-aperture aspherical lens mounted on a 3D translation stage. (b) Measured intensity and phase results for positively chirped STOV pulse transmitted by few-mode optical fiber; the topological charge is −1. (c) Scheme of data transmission based on STOV strings^[282]. The three colored wavepackets shown in the middle represent three 3-STOV strings with topological charge arrangements of 123, 231, and 312.

Fig. 35. Spatiotemporal differentiation metasurfaces. (a) The spatiotemporal amplitude and phase of the “Zhejiang University” logo pattern and the corresponding amplitude and phase after passing through a meta-grating with breaking mirror symmetry^[185]. (b) Spatiotemporal differentiator for optical nonlocal meta-grating computing^[283]. Experimental setup consists of three parts: (1) a delay line for pulse characterization; (2) dispersion-engineered metalens for tilting the pulse; and (3) a meta-grating for spatiotemporal differentiation. (c) Retrieved iso-intensity profiles of incident pulses generated by different dispersion-engineered metalenses (without spatiotemporal differentiator) with various tilted angles. (d) Retrieved iso-intensity profiles of pulses passing through the spatiotemporal differentiation meta-grating. The intensity profiles of these retrieved pulses are normalized to the peak intensity of their individual incident pulses.

Fig. 36. (a) Generation of isolated attosecond electron sheet via relativistic spatiotemporal optical manipulation. The STOV pulse is incident from the left and radiates onto the nanowire target^[284]. The electrons can be initially dragged out from the target and further phase-locked and accelerated by the longitudinal electric field (Ez) inside the STOV laser. (b)–(e) Electron density driven by an STOV pulse at (b), (c) t=16T and (d), (e) t=60T. (f), (g) Atomic photoionization by STOV pulses. (f) Calculated photoelectron momentum distributions (PMDs) for the photoionization of an H atom by an STOV pulse assisted by an XUV pulse^[286]. (g) Calculated spatially resolved photoelectron energy spectra for time delays (top) τ− and (bottom) τ+ of the XUV pulse obtained by the 3D-TDSE.

Fig. 37. (a) Experimental setup for the generation of the space–time light sheet and interferometric phase stability analysis^[290]. The generated space–time light sheet is coupled into a Michelson interferometry. (b) Measured interferometric phase recorded over 2 min for the Gaussian beam (black), GLS (red), and ST light sheet (blue). (c) Schematic diagram of 3D positioning method based on toroidal pulses^[291]. (d) Computed 3D positioning pseudo-spectrum based on toroidal pulses.

Fig. 38. (a)–(d) Concept of chirped Bragg volume gratings (r-CBGs) with various configurations^[294,295]. (a) Pulse normally incident on a CBG is temporally stretched but not spectrally resolved. (b) Pulse obliquely incident on a CBG is spectrally resolved. (c) Spectrally resolving a pulse normally incident on an r-CBG. (d) The spectrum spreading of white light by an r-CBG. (e) A passive nonlocal optical surface for the generation of 3D space–time light bullets^[296]. (f) An asymmetric grating structure for the generation of optical toroidal vortices^[297]. (g) Spatiotemporal light control with frequency-gradient metasurfaces^[298].

Fig. 39. Modal state detection and sorting in the space–time domain. (a) Scheme for recognizing radial quantum number and azimuthal quantum number of STLG wavepackets based on mode conversion^[134]. (b) Schematic of the photocurrent measurement from optical beams carrying OAM^[299].

Fig. 40. Vectorized optoelectronic control by structured light^[301,302]. (a) Schematic of left-hand circularly polarized ω optical vortex with topological charge m=+1. (b) Sketch of the 2ω radial polarized beam that can be equivalently represented as a superposition of two circularly polarized beams with opposite handedness possessing m=−1 and m=+1. (c) Illustration of coherent control in a semiconductor using two circularly polarized beams. Circular polarization enables control over the x- and y-momentum components by adjustment of Δφω,2ω. (d) Spatial arrangement of the controlled currents for different Δφω,2ω. (e) Schematic of the experimental configuration for reconfiguring electronic circuits. (f) The spatial distribution of Δφω,2ω generated by a spatial light modulator. (g) Measurement of the x (blue) and y (red) current components in one detection pixel as the global relative phase. (h) Measured vectorial current from x and y components of (g) on a phase map, demonstrating that Δφω,2ω can be used to precisely control the direction of currents.

Fig. 41. A collage of structured light. Examples of the various forms of structured light^[2] are shown as scalar beams (top) and vector beams (bottom). The first row in each is the intensity and the second row is the phase (scalar beams) and polarization (vector) structure.

Fig. 42. Sophisticated space-time topology using STWPs^[305]. (a) Illustration of a 1D space–time hopfion crystal where the 3D hopfion texture unit repeats periodically over time. (b) Depiction of a 3D space–time hopfion crystal, showcasing various views of every hopfion unit.

Fig. 43. Quantum entanglement of OAM beams. (a) Polarization entanglement is created in a parametric down-conversion process and afterward transferred to modes with high quanta of OAM^[306]. (b) Entanglement between spin and OAM on a single photon^[307]. A single photon vertically polarized is arriving from the left, as illustrated by the yellow wavepacket representing the electric field amplitude. This photon carries zero OAM, as illustrated by the yellow flat phase fronts. The single photon passes through the metasurface nanoantennas (purple) and exits as a single-particle entangled state, depicted as a superposition of the red and blue electric field amplitudes, with the corresponding vortex phase fronts opposite to one another.