Spatiotemporal Vortex Pulses: Angular Momenta and Spin-Orbit Interaction

Spatiotemporal vortex strings

Light carrying orbital angular momentum (OAM) holds unique properties and boosts myriad applications in diverse fields. However, the generation of an ultrafast wave packet carrying numerous vortices with various transverse OAM modes, i.e., vortex string, remains challenging, and the corresponding detection method is lacking. Here, we demonstrate that a vortex string with 28 spatiotemporal optical vortices (STOVs) with customizable topological charge (TC) arrangements can be generated in one wave packet. The diffraction rules of STOV strings are revealed theoretically and experimentally. Following these rules, the TC values and positions of all STOVs in a vortex string can be simultaneously recognized from the diffraction pattern. Such STOV strings facilitate STOV-based optical communication. As a proof-of-principle demonstration, the transmission of an image is realized with 16-STOV strings. This work provides guidance for revealing the underlying properties of the transverse OAM light and opens up opportunities for applications of the structured light in optical communication, quantum information processing, etc.

Observation of Chiral Symmetry Breaking in Toroidal Vortices of Light

In this Letter, we explore the intersection of chirality and recently discovered toroidal spatiotemporal optical vortices (STOVs). We introduce "photonic conchs" theoretically as a new type of toroidal-like state exhibiting geometrical chirality, and experimentally observe these wave packets with controllable topological charges. Unlike toroidal STOVs, photonic conchs exhibit unique chirality-related dynamical evolution in free space and possess an orbital angular momentum correlated with all the dimensions of space-time. This research deepens our understanding of toroidal light states and potentially advances various fields by unveiling similar wave phenomena in a broader scope of physics systems, including acoustics and electronics.

Water-Wave Vortices and Skyrmions

Topological wave structures-phase vortices, skyrmions, merons, etc.-are attracting enormous attention in a variety of quantum and classical wave fields. Surprisingly, these structures have never been properly explored in the most obvious example of classical waves: water-surface (gravity-capillary) waves. Here, we fill this gap and describe (i) water-wave vortices of different orders carrying quantized angular momentum with orbital and spin contributions, (ii) skyrmion lattices formed by the instantaneous displacements of the water-surface particles in wave interference, and (iii) meron (half-skyrmion) lattices formed by the spin-density vectors, as well as (iv) spatiotemporal water-wave vortices and skyrmions. We show that all these topological entities can be readily generated in linear water-wave interference experiments. Our findings can find applications in microfluidics and show that water waves can be employed as an attainable playground for emulating universal topological wave phenomena.

Generation of Spatiotemporal Vortex Pulses by Resonant Diffractive Grating

Spatiotemporal vortex pulses are wave packets that carry transverse orbital angular momentum, exhibiting exotic structured wave fronts that can twist through space and time. Existing methods to generate these pulses require complex setups like spatial light modulators or computer-optimized structures. Here, we demonstrate a new approach to generate spatiotemporal vortex pulses using just a simple diffractive grating. The key is constructing a phase vortex in frequency-momentum space by leveraging symmetry, resonance, and diffraction. Our approach is applicable to any wave system. We use a liquid surface wave (gravity wave) platform to directly demonstrate and observe the real-time generation and evolution of spatiotemporal vortex pulses. This straightforward technique provides opportunities to explore pulse dynamics and potential applications across different disciplines.

Exploiting Topological Darkness in Photonic Crystal Slabs for Spatiotemporal Vortex Generation

Spatiotemporal optical vortices (STOVs) with swirling phase singularities in space and time hold great promise for a wide range of applications across diverse fields. However, current approaches to generate STOVs lack integrability and rely on bulky free-space optical components. Here, we demonstrate routine STOV generation by harnessing the topological darkness phenomenon of a photonic crystal slab. Complete polarization conversion enforced by symmetry enables topological darkness to arise from photonic bands of guided resonances, imprinting vortex singularities onto an ultrashort reflected pulse. Utilizing time-resolved spatial mapping, we provide the first observation of STOV generation using a photonic crystal slab, revealing the imprinted STOV structure manifested as a curved vortex line in the pulse profile in space and time. Our work establishes photonic crystal slabs as a versatile and accessible platform for engineering STOVs and harnessing the topological darkness in nanophotonics.

Spatiotemporal diffractive deep neural networks

A spatiotemporal diffractive deep neural network (STD2NN) is proposed for spatiotemporal signal processing. The STD2NN is formed by gratings, which convert the signal from the frequency domain to the spatial domain, and multiple layers consisting of spatial lenses and space light modulators (SLMs), which conduct spatiotemporal phase modulation. An all-optical backpropagation (BP) algorithm for SLM phase tuning is proposed, with the gradient of the loss function computed by the inner product of the forward propagating optical field and the backward propagating conjugated error field. As a proof of concept, a spatiotemporal word "OPTICA" is generated by the STD2NN. Afterwards, a spatiotemporal optical vortex (STOV) beam multiplexer based on the STD2NN is demonstrated, which converts the spatially separated Gaussian beams into the STOV wave-packets with different topological charges. Both cases illustrate the capability of the proposed STD2NN to generate and process the spatiotemporal signals.

Method for generating spatiotemporal coherency vortices and spatiotemporal dislocation curves

A simple method for designing spatiotemporal coherency vortices (STCVs) and spatiotemporal dislocation curves (STDCs) is introduced by means of coherent-mode representation and Fourier transforms. A partially coherent pulsed beam is represented by an incoherent superposition of a Gaussian and a Hermite-Gaussian pulsed beam with different waist positions. It well demonstrates that there exist STCVs and STDCs in the space-time plane. The detailed numerical calculations are performed to address the dependence of waist distance of two modes, reference position, beam order, distribution of original spectrum, topological charge and mode weights ratio on the STCVs and STDCs. The physical interpretation behind numerical results is shown. A possible scheme for experimental synthesis of the STCVs is proposed. The obtained results may have potential applications in the fields of light-matter interaction, spatiotemporal spin-orbit angular momentum coupling and STCV-based optical trapping and optical manipulation.

Spherical Gauss-Laguerre beam propagation in 4D space-time

In this paper, what we believe to be a novel class of beams, which are referred to as the spherical Gauss-Laguerre beams, are proposed. The beams propagate stably in the anomalous dispersive media, within which the second order derivative with respect to t could be combined with the two-dimensional (2D) Laplacian operator in the transverse direction and forms a three-dimensional (3D) Laplacian operator, which describes the beam propagation in the z direction within the four-dimensional (4D) x-y-z-t space-time. The wave equation is solved by the variable separation method and the analytical expression for the spherical Gauss-Laguerre beams is derived. The beams have a 3D Gaussian field distribution with a variable beam waist with respect to the propagation distance. Unlike any 2D spatial vortex beams, the 3D beams could possess either the spatial vortex or the spatiotemporal optical vortex (STOV) by choosing the vortex plane in the 3D x-y-t space-time. The derived spherical Gauss-Laguerre beam expression in the 4D space-time is verified by the numerical simulations with excellent agreement.

Generation and periodic evolution of third harmonics carrying transverse orbital angular momentum in air-plasma filaments

Spatiotemporal optical vortex (STOV) pulses, possessing inherent transverse orbital angular momentum (OAM) and exhibiting phase singularity and intensity null in the spatiotemporal (ST) domain, have received increasing attention in recent years. Here, we investigate theoretically the third harmonic generation and evolution properties of STOV pulses via the interaction of 800-nm-STOV pulses with air-plasma filaments. We show that beautiful third harmonic STOV pulses are generated at a propagation distance of several millimeters. During further propagation, the ST intensity profiles of the third harmonics undergo variations in a periodic way, leading to the distortion and subsequent restoration to the initial ring pattern. The periodic evolution is a result of the interference effects between the third harmonics generated with different phases. Consequently, the evolution period is roughly twice the dephasing length of the third harmonics. Meanwhile, additional singularities emerge in the intensity patterns due to destructive interference occurring at specific dephasing lengths for the specific frequency components. The high-frequency components experience destructive interference earlier than the low-frequency components during each evolution period because the dephasing length decreases with frequency. This results in the sequentially appearance of the additional singularities from top to bottom in the ST intensity patterns. The proposed scheme demonstrates a way for higher-order STOV generation and manipulation in air-plasma filaments, which can be of interest for experiments related to vortex light science.

Topologically crafted spatiotemporal vortices in acoustics

Vortices in fluids and gases have piqued the human interest for centuries. Development of classical-wave physics and quantum mechanics highlighted wave vortices characterized by phase singularities and topological charges. In particular, vortex beams have found numerous applications in modern optics and other areas. Recently, optical spatiotemporal vortex states exhibiting the phase singularity both in space and time have been described. Here, we report the topologically robust generation of acoustic spatiotemporal vortex pulses. We utilize an acoustic meta-grating with broken mirror symmetry which exhibits a topological phase transition with a pair of phase singularities with opposite topological charges emerging in the momentum-frequency domain. We show that these vortices are topologically robust against structural perturbations of the meta-grating and can be employed for the generation of spatiotemporal vortex pulses. Our work paves the way for studies and applications of spatiotemporal structured waves in acoustics and other wave systems.

Transversal optical singularity induced precision measurement of step-nanostructures

Optical singularities indicate zero-intensity points in space where parameters, such as phase, polarization, are undetermined. Vortex beams such as the Laguerre-Gaussian modes are characterized by a phase factor eilθ, and contain a phase singularity in the middle of its beam. In the case of a transversal optical singularity (TOS), it occurs perpendicular to the propagation, and its phase integral is 2π in nature. Since it emerges within a nano-size range, one expects that TOSs could be sensitive in the light-matter interaction process and could provide a great possibility for accurate determination of certain parameters of nanostructure. Here, we propose to use TOSs generated by a three-wave interference to illuminate a step nanostructure. After interaction with the nanostructure, the TOS is scattered into the far field. The scattering direction can have a relation with the physical parameters of the nanostructure. We show that by monitoring the spatial coordinates of the scattered TOS, its propagation direction can be determined, and as consequence, certain physical parameters of the step nanostructure can be retrieved with high precision.

Quantum vortices of strongly interacting photons

Vortices are topologically nontrivial defects that generally originate from nonlinear field dynamics. All-optical generation of photonic vortices-phase singularities of the electromagnetic field-requires sufficiently strong nonlinearity that is typically achieved in the classical optics regime. We report on the realization of quantum vortices of photons that result from a strong photon-photon interaction in a quantum nonlinear optical medium. The interaction causes faster phase accumulation for copropagating photons, producing a quantum vortex-antivortex pair within the two-photon wave function. For three photons, the formation of vortex lines and a central vortex ring confirms the existence of a genuine three-photon interaction. The wave function topology, governed by two- and three-photon bound states, imposes a conditional phase shift of π per photon, a potential resource for deterministic quantum logic operations.

Spatiotemporal Acoustic Vortex Beams with Transverse Orbital Angular Momentum

Recently, the discovery of optical spatiotemporal (ST) vortex beams with transverse orbital angular momentum (OAM) has attracted increasing attention and is expected to extend the research scope and open new opportunities for practical applications of OAM states. The ST vortex beams are also applicable to other physical fields that involve wave phenomena, and here we develop the ST vortex concept in the field of acoustics and report the generation of Bessel-type ST acoustic vortex beams. The ST vortex beams are fully characterized using the scalar approach for the pressure field and the vector approach for the velocity field. We further investigate the transverse spreading effect and construct ST vortex beams with an ellipse-shaped spectrum to reduce the spreading effect. We also experimentally demonstrated the orthogonality relations between ST vortex beams with different charges. Our study successfully demonstrates the versatility of the acoustic system for exploring and discovering spatiotemporally structured waves, inspiring further investigation of exotic wave physics.

Generation of terahertz spatiotemporal optical vortices with frequency-dependent orbital angular momentum

Optical vortices with longitudinal orbital angular momentum (OAM) as a powerful tool for particle control, imaging and communication have been greatly developed. We introduce a novel property of broadband terahertz (THz) pulse, represented by frequency-dependent OAM orientation in spatiotemporal domain with transverse and longitudinal OAM projection. We illustrate a frequency-dependent broadband THz spatiotemporal optical vortex (STOV) in plasma-based THz emission driven by cylindrical symmetry broken two-color vortex field. We detect the evolution of OAM by time-delayed 2D electro-optic sampling combined with Fourier transform. This THz optical vortices tunability in spatiotemporal domain expands a new way for studying STOV and plasma-based THz radiation.

Nonlocality-mediated spatiotemporal optical vortex generation in nanorod-based epsilon-near-zero metamaterials

Optical vortices have myriad applications in photonics. Very recently, promising concepts of spatiotemporal optical vortex (STOV) pulses based on the phase helicity in the space-time coordinates have attracted much attention owing to their donut shape. We elaborate on the molding of STOV under the transmission of femtosecond pulses through a thin epsilon-near-zero (ENZ) metamaterial slab based on a silver nanorod array in a dielectric host. At the heart of the proposed approach is the interference of the so-called main and additional optical waves enabled by strong optical nonlocality of these ENZ metamaterials, which leads to the appearance of phase singularities in transmission spectra. The cascaded metamaterial structure is proposed for high-order STOV generation.

Deflection of a reflected intense spatiotemporal optical vortex beam

In this Letter, we reveal a new deflection effect in the reflection of an intense spatiotemporal optical vortex (STOV) beam. When a STOV beam with relativistic intensities (>10¹⁸ W cm^-2) impacts on an overdense plasma target, the reflected beam deviates from the specular reflection direction in the incident plane. Using two-dimensional (2D) particle-in-cell simulations, we demonstrated that the typical deflection angle is of a few milliradians and can be enhanced by using a stronger STOV beam with tightly focused size and higher topological charge. Though similar to the angular Goos-Hänchen effect, however, it is worth emphasizing that the deviation induced by a STOV beam exists, even in normal incidence, revealing an essentially nonlinear effect. This novel effect is explained from the viewpoint of angular momentum conservation, as well as the Maxwell stress tensor. It is shown that an asymmetrical light pressure of the STOV beam breaks the rotational symmetry of the target surface and leads to nonspecular reflection. Unlike the shear press of an Laguerre-Gaussian beam, which only acts in oblique incidence, the deflection caused by the STOV beam exists more widely, including in normal incidence.

Propagation of higher-order spatiotemporal vortices

Closed-form, analytical expressions for higher-order, multi-charged spatiotemporal optical vortices (STOVs) propagating in free space or non-dispersive media are provided. We consider two relevant and complementary situations where the multi-charged STOV spreads freely, and where it is focused. Previously reported multi-charged STOV breakup upon spreading is merely an effect of diffraction, not an instability effect. The focused STOV reverses the sign of its topological charge upon passage through the focus. While the spreading STOV carries transverse orbital angular momentum, the ideally focused STOV from the far field does not.

Towards optical toroidal wavepackets through tight focusing of the cylindrical vector two dimensional spatiotemporal optical vortex

Spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentum (OAM) are of rapidly growing interest for the field of optics due to the new degree of freedom that can be exploited. In this paper, we propose cylindrical vector two dimensional STOVs (2D-STOVs) containing two orthogonal transverse OAMs in both x-t and y-t planes for the first time, and investigate the tightly focusing of such fields using the Richards-Wolf vectorial diffraction theory. Highly confined spatiotemporal wavepackets with polarization structure akin to toroidal topology is generated, whose spatiotemporal intensity distributions resemble the shape of Yo-Yo balls. Tightly focused radially polarized 2D-STOVs will produce wavepackets towards transverse magnetic toroidal topology, while the focused azimuthally polarized 2D-STOVs will give rise to wavepackets towards transverse electric toroidal topology. The presented method may pave a way to experimentally generate the optical toroidal wavepackets in a controllable way, with potential applications in electron acceleration, nanophotonics, energy, transient light-matter interaction, spectroscopy, quantum information processing, etc.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LG_ℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

Universal orbital angular momentum detection scheme for any vortex beam

Existing methods for probing the orbital angular momentum carried by vortex beams have many limitations and are generally only applicable to specific types of vortex beam. In this work, we present a concise and efficient universal method for probing the orbital angular momentum that is applicable for any type of vortex beam. The vortex beam could range from being fully to partially coherent, with different spatial modes including Gaussian vortex beam, Bessel-Gaussian beam, Laguerre-Gaussian beam, etc., of any wavelength including x rays, matter waves such as electron vortices, and with high topological charge. This protocol only requires a (commercial) angular gradient filter, making it very easy to implement. The feasibility of the proposed scheme is demonstrated both theoretically and experimentally.

Arbitrary-Order and Multichannel Optical Vortices with Simultaneous Amplitude and Phase Modulation on Plasmonic Metasurfaces

The highly localized and uneven spatial distribution of the subwavelength light field in metal metasurfaces provides a promising means for the generation of optical vortices (OVs) with arbitrary topological charges. In this paper, a simple and reliable way for generating multichannel OVs on gold nanoporous metasurfaces is reported. The instantaneous field of arbitrary-order OVs can be regulated and concentrated on the same focal surface by adapting photonic spin-orbit interaction (SOI) and geometric phase. The focal ring energy distribution of OVs along the conical propagation path is accurately calculated, and the double phase of units induced by spin rotation is confirmed. Based on the parameter optimization of the nanohole arrangement, the simultaneous amplitude and phase modulation of multichannel OVs has been realized. Furthermore, the average multichannel signal-to-noise ratio exceeds 15 dB, which meets the requirements of high resolution and low crosstalk. Our study obtains broadband and efficient OVs, which can contribute to improving the capacity storage and security of optical information and possess great application prospects in beam shaping, optical tweezers, and communication coding.

Single-Frame Characterization of Ultrafast Pulses with Spatiotemporal Orbital Angular Momentum

Light that carries spatiotemporal orbital angular momentum (ST-OAM) makes possible new types of optical vortices arising from transverse OAM. ST-OAM pulses exhibit novel properties during propagation, transmission, refraction, diffraction, and nonlinear conversion, attracting growing experimental and theoretical interest and studies. However, one major challenge is the lack of a simple and straightforward method for characterizing ultrafast ST-OAM pulses. Using spatially resolved spectral interferometry, we demonstrate a simple, stationary, single-frame method to quantitatively characterize ultrashort light pulses carrying ST-OAM. Using our method, the presence of an ST-OAM pulse, including its main characteristics such as topological charge numbers and OAM helicity, can be identified easily from the unique and unambiguous features directly seen on the raw data-without any need for a full analysis of the data. After processing and reconstructions, other exquisite features, including pulse dispersion and beam divergence, can also be fully characterized. Our fast characterization method allows high-throughput and quick feedback during the generation and optical alignment processes of ST-OAM pulses. It is straightforward to extend our method to single-shot measurement by using a high-speed camera that matches the pulse repetition rate. This new method can help advance the field of spatially and temporally structured light and its applications in advanced metrologies.

Time diffraction-free transverse orbital angular momentum beams

The discovery of optical transverse orbital angular momentum (OAM) has broadened our understanding of light and is expected to promote optics and other physics. However, some fundamental questions concerning the nature of such OAM remain, particularly whether they can survive from observed mode degradation and hold OAM values higher than 1. Here, we show that the strong degradation actually origins from inappropriate time-delayed kx-ω modulation, instead, for transverse OAM having inherent space-time coupling, immediate modulation is necessary. Thus, using immediate x-ω modulation, we demonstrate theoretically and experimentally degradation-free spatiotemporal Bessel (STB) vortices with transverse OAM even beyond 102. Remarkably, we observe a time-symmetrical evolution, verifying pure time diffraction on transverse OAM beams. More importantly, we quantify such nontrivial evolution as an intrinsic dispersion factor, opening the door towards time diffraction-free STB vortices via dispersion engineering. Our results may find analogues in other physical systems, such as surface plasmon-polaritons, superfluids, and Bose-Einstein condensates.

Towards higher-dimensional structured light

Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.

Photonic orbital angular momentum with controllable orientation

Vortices are whirling disturbances, commonly found in nature, ranging from tremendously small scales in Bose-Einstein condensations to cosmologically colossal scales in spiral galaxies. An optical vortex, generally associated with a spiral phase, can carry orbital angular momentum (OAM). The optical OAM can either be in the longitudinal direction if the spiral phase twists in the spatial domain or in the transverse direction if the phase rotates in the spatiotemporal domain. In this article, we demonstrate the intersection of spatiotemporal vortices and spatial vortices in a wave packet. As a result of this intersection, the wave packet hosts a tilted OAM that provides an additional degree of freedom to the applications that harness the OAM of photons.

Source coherence-induced control of spatiotemporal coherency vortices

A novel method to achieve the coherence control of spatiotemporal coherency vortices of spatially and temporally partially coherent pulsed vortex (STPCPV) beams is proposed. The influence of spatial and temporal coherence of the source on the phase distributions and the positions of spatiotemporal coherency vortices of the STPCPV beams propagating through fused silica is investigated in detail, for the first time to our knowledge. It is found that the coherence width and the coherence time of the incident beam can be regarded as a perfect tool for controlling the phase distribution and position of a spatiotemporal coherency vortex. The results obtained in this paper will benefit a number of applications relating to light-matter interaction, quantum entanglement, quantum imaging, optical trapping and spatiotemporal spin-orbit angular momentum coupling.

Transversely oriented cylindrically polarized optical fields

Cylindrical vector (CV) beams have nonuniform polarization vector distribution with a singularity line directed along the optical axis. In this paper, we propose a method to synthesize transversely oriented cylindrically polarized optical fields in the focal region with a singularity line perpendicular to the optical axis. The scheme is based on the time-reversal method, the vectorial diffraction theory, and the 4Pi optical configuration. Both transversely oriented radially polarized and azimuthally polarized optical fields are demonstrated. The superposition of transverse cylindrically polarized optical fields leads to a peculiar distribution carrying controllable transverse spin angular momentum (SAM) and transverse orbital angular momentum (OAM) that may find applications in optical tweezing, light-matter interaction, and unidirectional beam propagation excitation.

Time-varying orbital angular momentum in tight focusing of ultrafast pulses

The orbital angular momentum (OAM) of light has important applications in a variety of fields, including optical communication, quantum information, super-resolution microscopic imaging, particle trapping, and others. However, the temporal properties of OAM in ultrafast pulses and in the evolution process of spin-orbit coupling has yet to be revealed. In this work, we theoretically studied the spatiotemporal property of time-varying OAM in the tightly focused field of ultrafast light pulses. The focusing of an incident light pulse composed of two time-delayed femtosecond sub-pulses with the same OAM but orthogonal spin states is investigated, and the ultrafast dynamicsa time delay of OAM variation during the focusing process driven by the spin-orbit coupling is visualized. Temporal properties of three typical examples, including formation, increase, and transformation of topological charge are investigated to reveal the non-uniform evolutions of phase singularities, local topological charges, self-torques, and time-varying OAM per photon. This work could deepen the understanding of spin-orbit coupling in time domain and promote many promising applications such as ultrafast OAM modulation, laser micromachining, high harmonic generation, and manipulation of molecules and nanostructures.

Controlling Photon Transverse Orbital Angular Momentum in High Harmonic Generation

High harmonic generation (HHG) with longitudinal optical orbital angular momentum has attracted much attention over the past decade. Here, we present the first study on the HHG with transverse orbital angular momentum driven by the spatiotemporal optical vortex (STOV) pulses. We show that the produced spatial-resolved harmonic spectra reveal unique structures, such as the spatially spectral tilt and the fine interference patterns. We show these spatiospectral structures originate from both the macroscopic and microscopic effect of spatiotemporal optical singularity in HHG. Employing two-color counterspin and countervorticity STOV pulses, we further discuss a robust method to control the spatiotemporal topological charge and spectral structure of high-order harmonics. The conservation rule of photon transverse orbital angular momentum in HHG process is also discussed when mixing with photon spin angular momenta.

Mode Structure and Orbital Angular Momentum of Spatiotemporal Optical Vortex Pulses

We identify a class of modal solutions for spatiotemporal optical vortex (STOV) electromagnetic pulses propagating in dispersive media with orbital angular momentum (OAM) orthogonal to propagation. We find that symmetric STOVs in vacuum can carry half-integer intrinsic OAM; for general asymmetric STOVs in a dispersive medium, the OAM is quantized in integer multiples of a parameter that depends on the STOV symmetry and the group velocity dispersion. Our results suggest that STOVs propagating in dispersive media are accompanied by a polaritonlike quasiparticle. The modal theory is in excellent agreement with measurements of free space propagation of STOVs.