Introduction

At the invitation from the founding Editor-in-Chief of Photonics Insights, Prof. Zhan Qiwen's team from the University of Shanghai for Science and Technology wrote a review article with the title of ''Spatiotemporal Optical Wavepackets: from Concepts to Applications'' published in the fourth issue of Photonics Insights in Issue 4, Volume 3, 2024 which was also featured as ''On the Cover''. (Xin Liu, Qian Cao, and Qiwen Zhan. Spatiotemporal Optical Wavepackets: from Concepts to Applications [J]. Photonics Insights, 2024, 3(4): R08)

This review provides a comprehensive overview of recent developments in spatiotemporally structured lights. It covers the fundamental concepts, shaping and manipulation techniques, and characterization methods of optical spatiotemporal wavepackets, explores their unique physical effects, discusses their applications, and concludes with a perspective on future research.

1. How to tame light in both space and time?

Time and space, enduring pillars of human understanding, have shaped the course of scientific inquiry. Light, in the form of electromagnetic waves travelling at the ultimate speed, offers a profound lens through which to explore the very fabric of spacetime. Optical Spatiotemporal wavepackets (STWPs) exhibit tightly coupled optical degrees of freedoms—including intensity, phase, polarization, frequency etc.—across both spatial and temporal dimensions, with typical durations ranging from picoseconds (10^-12 s) to femtoseconds (10^-15 s). Due to the significantly higher oscillation frequency of ultrafast lasers compared to the response speed of electro-optic modulators, direct manipulation of the optical pulse's temporal profile is impractical.

Consequently, spectral modulation in the frequency domain is commonly employed. This typically involves spatially dispersing the ultrafast pulse's spectrum using dispersive elements, followed by spatial light modulation to indirectly control the pulse's temporal waveform. The 4f pulse shaper, a common optical setup for controlling the spectral properties of ultrafast laser pulses, typically comprises a pair of diffraction gratings, a pair of cylindrical lenses, and a spatial light modulator arranged in a "4f" configuration within the optical system, as illustrated in Figure 1.

The earliest applications of 4f pulse shaping were based on spectral modulation, aimed at controlling the spectral properties of ultrashort laser pulses. In the early 1990s, Professor Andrew M. Weiner and his team introduced and popularized pulse shaping techniques based on the 4f optical architecture, as illustrated in Figure 1(a). This technique rapidly became the standard method for manipulating ultrashort laser pulses, significantly advancing the widespread adoption of ultrafast laser technologies such as femtosecond pulse shaping and optical frequency combs.

Fig. 1 Schematic of 4f ultrafast pulse shaper. (a) One-dimensional pulse shaper for temporal modulation. (b) 2D pulse shaper for spatiotemporal phase-only modulation. (c) 2D holographic pulse shaper for spatiotemporally sculpting STWPs via a complex-amplitude modulation.

Conventional ultrafast pulse shaper, employing one-dimensional amplitude or phase masks as frequency-plane filters, modulate only the one-dimensional temporal frequency components, neglecting the spatial dimension. With the successful development of two-dimensional light modulators such as liquid crystal spatial light modulators (SLMs), coordinated control of ultrafast pulses in both the temporal and spatial dimensions became feasible (as in Fig. 1(b)). Recently, the integration of 4f pulse shaping with two-dimensional spatial light modulation allows for the tight coupling of spatial and spectral phases, enabling interactions of the optical field across both spatial and temporal dimensions. As illustrated in Fig. 1(c), further integration of spatial digital holography with pulse shaping has led to the development of two-dimensional digital holographic pulse shapers. This approach not only enables two-dimensional spatiotemporal phase modulation of ultrafast pulses but also allows for amplitude modulation, achieving two-dimensional spatial-spectral complex amplitude modulation and thus enabling arbitrary and precise control and generation of STWPs. The introduction and development of these modulation techniques have significantly promoted the diversity of STWPs and laid a solid foundation for their coordinated control in multiple dimensions.

Fig. 2 Spatiotemporal manipulation cascades: (a) Metasurfaces and Micro/Nanostructures; (b) Transformation Optics; (c) Multi-Plane Light Conversion system.

A natural idea to further expand spatiotemporal modulation capabilities is to integrate the state-of-the-art pulse shaper with established spatial modulation techniques (Figure 2). On one hand, these shapers can be combined with devices offering enhanced modulation capabilities, such as metasurfaces, microstructures, and liquid crystal polymer devices, to achieve higher resolution, broader bandwidth, and greater efficiency in spatiotemporal modulation. On the other hand, cascading spatiotemporal modulation devices with spatial modulation systems, for instance, those based on conformal mapping from transformation optics system and multi-plane light conversion (MPLC), enables more sophisticated spatiotemporal structuring, unlocking virtually limitless possibilities.

2. Photon tornado carrying transverse OAM

Photons carry not only energy but also momentum. In 1992, Allen et al. discovered that spatial optical vortices can carry longitudinal orbital angular momentum (OAM), which is proportional to the topological charge and aligned with the beam's propagation direction, as shown in Fig. 3. A spatiotemporal optical vortex (STOV) is a distinct type of spatiotemporally coupled wavepacket, characterized by a helical phase structure residing within the spatiotemporal plane. Its intensity profile exhibits a null intensity core originating from a phase singularity, and it carries a transverse OAM perpendicular to the wave vector, as shown in Fig. 3(a). Through modulating specific phases or complex amplitudes within the two-dimensional spatial-spectral domain of ultrafast laser pulses, STOVs with transverse OAM can be generated. These STWPs may exhibit characteristic spatiotemporal modal structures, such as spatiotemporal Bessel vortices and spatiotemporal Laguerre-Gaussian/Hermite-Gaussian wavepackets. The generation and manipulation of these novel structured light fields not only broadens the frontiers of optical research but also promotes their applications and development in areas such as matter waves (e.g., water waves and acoustic waves) and nonlinear optics.

Fig. 3 Typical STOVs with transverse OAM: (a) Comparison between spatial optical vortices and STOVs; (b) STOVs; (c) and (d) Spatiotemporal Bessel vortices; (e) Spatiotemporal Laguerre/Hermite-Gaussian STWPs; (f) Second harmonic generation of STOVs.

Complementarily, the use of integrated micro/nano-devices, engineered by breaking the structural symmetry of optical materials, offers an avenue for efficient generation of STOVs carrying specific OAM at miniature scales (Figure 4). This strategy leads to simplified system architectures, decreased complexity, and improved generation efficiency, thereby paving the way for novel STOV applications in areas such as optical information processing, laser micro/nano-fabrication, and nonlinear optics.

Fig. 4 Metasurfaces and nanostructures as STOV generators.

Spatiotemporal torus and topology

The generation of STWPs possessing three-dimensional spatiotemporal structures has become feasible through the cascading of novel spatial light modulation techniques, including transformation optics and polarization control via micro/nano-devices (Figure 5). These 3D STWPs are characterized by complex spatiotemporal coupling, giving rise to unique physical properties and intricate spatiotemporal topological structures. These novel wave packets may find significant applications in fundamental physics investigations and nonlinear light field manipulation, potentially driving the advancement of optical research toward higher-dimensional and more complex regimes.

Fig. 5 3D spatiotemporal toroidal vortices and their topologies.

3. Non-diffraction space-time light sheet

Space-time light sheets are a unique type of STWPs exhibiting remarkable non-diffracting propagation in free space. Precise spatial-spectral modulation allows for the creation of such STWPs with tightly correlated frequencies of space and time (Figure 6). This inherent spatiotemporal coupling maintains a consistent intensity profile during propagation, revealing rich new physics. Such STWPs offer exciting prospects for applications in areas such as plasma physics and ultrafast optics, providing new avenues for investigating light-matter interactions.

Fig. 6 Non-diffracted space-time light sheet wavepacket.

4. Helical wavepackets with time-varying properties

Unlike conventional STWPs with their typically static optical characteristics, helical wavepackets carrying time-varying photon properties (such as OAM, as in Figure 7), showcase rich temporal dynamics. This dynamic spatiotemporal structure offers immense possibilities for applications in light-matter interactions and nonlinear optics. Thorough research into spatiotemporal wave packets enables precise manipulation of light's temporal and spatial characteristics, charting new territories in optical science.

Fig. 7 Typical helical STWPs with time-dependent optical properties.

5. Characterization of STWPs

The simultaneous structuring in time and space of STWPs, combined with their ultrashort pulse durations and complex spatiotemporal profiles, presents a significant measurement challenge. Conventional methods are inherently limited in their ability to retrieve complete information across both domains concurrently. To address this challenge and fully characterize these wavepackets, researchers have developed various measurement techniques, notably time-delay off-axis interferometry and spatial-spectral interferometry, as well as single-shot measurements via the introduction of nonlinear effects (Figure 8). The principles, merits, and limitations of these measurement approaches are thoroughly examined in this review.

Fig. 8 Typical linear and nonlinear methods for characterizing STWPs.

6. Summary and Outlook

Spatiotemporal structured light is an emerging field poised to revolutionize optical technology and open up new frontiers in optics. It will not only deepen our understanding of fundamental photonics but also usher in a new era of advanced optical technologies and applications. This review aims to provide a comprehensive and systematic overview of recent progress in the field of spatiotemporal optical wavepackets, spanning fundamental theory to state-of-the-art techniques. In addition to highlight key achievements in the field, it also critically examines current challenges and future opportunities as crucial guidance for researchers. Recognizing the rapid growth of this nascent field, the authors concluded with a detailed discussion of the transformative potential of STWPs in areas such as light-matter interactions, optical computing, information encoding and multiplexing, and quantum information, presenting a systematic and forward-looking perspective on future research directions.

Looking ahead, spatiotemporal optical wavepackets has the potential to underpin next-generation optical technologies to revolutionize information transmission, quantum information, and optical imaging. Maturing of the associated technologies may enable the realization of increasingly sophisticated control of light to unlock unprecedented optical functionalities with broad societal benefits. Moreover, research on spatiotemporally structured light will inevitably promote further interdisciplinary convergence between optics and other scientific disciplines, leading to new breakthroughs in both fundamental science and technological innovation.