Transverse Angular Momentum Research Articles

Wigner function and intensity moments of spatio-temporal light fields

Abstract The Wigner distribution function and its spatial-angular moments (intensity-moments) are known as efficient instruments for characterization of complex quasimonochromatic light beams and their transformations. In this paper, the generalization of the WF-based approach to spatio-temporal (ST) light fields (wave packets, short pulses) is considered. It is shown that the ST intensity moments are related with the important characteristics of the wave-packet structure, especially, with the transverse orbital angular momentum (OAM) being a specific feature of the ST optical vortices (STOV). The ST moments’ transformations in a paraxial optical system obey simple and unified rules involving the ray-transfer ABCD-matrix of the system. On this base, and with simple examples of the OAM-carrying optical pulses, the schemes and mechanisms of the STOV generation and transformation are presented. Examples of non-vortex ST wave packets with the transverse OAM, their possible realizations are discussed as well as the relations between the OAM and the visible pulse rotations. The regular and unified formalism, developed in this paper, can be generalized and applied to more complex situations where the ST field propagates through inhomogeneous and random (scattering) media.

Scheme for generation of spatiotemporal optical vortex attosecond pulse trains

The realization of spatiotemporal vortex structure of various physical fields with transverse orbital angular momentum (OAM) has attracted much attention and is expected to expand the research scope and open new opportunities in their respective fields. Here we present theoretically the first, to the best of our knowledge, study on the generation of attosecond pulse trains featuring a spatiotemporal optical vortex (STOV) structure by a two-color femtosecond light field, with each color carrying transverse OAM. Through careful optimization of relative phase and intensity ratio, we validate the efficient upconversion of the infrared pulse into its tens of order harmonics, showing that each harmonic preserves a corresponding intact topological charge. This unique characteristic enables the synthesis of an extreme ultraviolet attosecond pulse train with transverse OAM. In addition, we reveal that ionization depletion plays an outsize role therein. Our studies pave the way for the generation and utilization of light fields with STOV in the attosecond regime.

Formation and Controlling of Optical Hopfions in High Harmonic Generation.

Toroidal vortex is a kind of novel and exotic structured light with potential applications in photonic topology and quantum information. Here, we present the study on high harmonic generation from the interaction of the intense toroidal vortices with atoms. We show that the spatial distribution of harmonic spectra reveal unique structures, which are kinds of high-order topological toroidal vortex because of the rotating of the driving fields with transverse orbital angular momentum. Then we show that, by synthesizing the toroidal vortices and optical vortices with longitudinal orbital angular momentum, it is able to generate the optical hopfions in the extreme ultraviolet range, which exhibit a completely different topological property compared with both the driving fields. Harnessing the spin angular momentum selection rules, we further show that one can control the topological texture and channel each harmonic into a single mode of controllable Hopf invariant.

Generation of high-order harmonics with hybrid spin and transverse orbital angular momentum from a crystalline solid

Generation of high-order harmonics with hybrid spin and transverse orbital angular momentum from a crystalline solid

Controllable orbital-to-spin angular momentum conversion in tight focusing of spatiotemporal vortex wavepacket

In this paper, we investigate the tight focusing of the radially polarized spatiotemporal vortex (STV) wavepackets. We find that, by changing the initial phase of the incident polarization state, the intensity envelope of the tightly focused first-order radially polarized STV wavepacket can be well controlled, yet the intensity envelope just rotates in whole for the tightly focused high-order radially polarized STV wavepacket. Furthermore, we show that, when the initial phase of incident polarization state takes π/2, the transverse double vortex structure arises in the focal region. More interestingly, when the initial phase takes π/2, the pure longitudinal spin angular momentum and transverse orbital angular momentum can be obtained in the tight focusing of the first-order radially polarized STV wavepacket. These effects are the manifestation of the spin-orbit interaction determined by the transverse orbital angular momentum and the incident polarization state. Our works present a technique to modulate the optical angular momentum in the tight focusing of the radially polarized STOV wavepacket, have potential application in the fields of optical switches, optical capture, quantum communication and nano-manipulation.

Quantum theory of orbital angular momentum in spatiotemporal optical vortices

Spatiotemporal Optical Vortices (STOVs) are structured electromagnetic fields propagating in free space with phase singularities in the space-time domain. Depending on the tilt of the helical phase front, STOVs can carry both longitudinal and transverse orbital angular momentum (OAM). Although STOVs have gained significant interest in the recent years, the current understanding is limited to the semi-classical picture. Here, we develop a quantum theory for STOVs with an arbitrary tilt, extending beyond the paraxial limit. We demonstrate that quantum STOV states, such as Fock and coherent twisted photon pulses, display non-vanishing longitudinal OAM fluctuations that are absent in conventional monochromatic twisted pulses. We show that these quantum fluctuations exhibit a unique texture, i.e. a spatial distribution which can be used to experimentally isolate these quantum effects. Our findings represent a step towards the exploitation of quantum effects of structured light for various applications such as OAM-based encoding protocols and platforms to explore novel light–matter interaction in 2D material systems.

Clarification of the transverse orbital angular momentum of spatiotemporal optical vortices

Advances in the generation and the application of spatiotemporal optical vortices (STOV) are proceeding fast, but fundamental aspects of their nature remain obscure. Bliokh (2023 Phys. Rev. A 107 L031501) (PRA) and Porras (2023 Prog. Electromagn. Res. 177 95) (PIER) provide contradictory results on the transverse orbital angular momentum (OAM) carried by STOVs. We show that the results by Porras in PIER and by Bliokh in PRA refer to different STOVs and are all correct. In PIER, STOVs are elliptical at given cross section and time, or in space-time, but not in three-dimensional space. In PRA, STOVs are elliptical in space but not in space-time. This is evidenced from two dual, equivalent theories on the transverse OAM where a wave packet is seen in space-time evolving with propagation distance or in space evolving in time, that account for all values of the total, intrinsic and extrinsic OAM in PIERS and PRA. However, the intrinsic OAM with respect to the photon wave function center in PRA is not generally conserved, which advocates for the energy center in PIER as the STOV center. We argue that STOVs are generated in experiments to purportedly have elliptical symmetry in space-time. The values provided in PIER should then be taken as the reference for elliptical STOVs, and the theory therein to evaluate the transverse OAM of other wave packets. Hancock et al (2021 Phys. Rev. Lett. 127 193901; 2024 Phys. Rev. X 14 011031) erroneously attribute the transverse OAM of elliptical STOVs in space to the elliptical STOVs in space-time that they consider theoretically and can generate in their experiments.

Generation of gamma photons and pairs with transverse orbital angular momentum via spatiotemporal optical vortex pulse

We present the generation of well-collimated gamma photons and pairs with extrinsic transverse orbital angular momentum (TOAM) through the head-on collision of an intense spatiotemporal optical vortex (STOV) pulse carrying intrinsic TOAM and a high-energy electron beam. It is found that the TOAM of STOV pulse remains almost unchanged, and the TOAM is conserved in the center-of-mass frame. Moreover, there exhibits a duality for particles TOAM in the CMF and laboratory frame when the initial location of high-energy electron beam is different. Furthermore, the TOAM of gamma photons in the CMF increases while that of positrons decreases as the topological charge of STOV pulse increases, whereas in the LF, the TOAM of both gamma photons and positrons decreases. The result under the same pulse intensity is better than that under the same pulse energy. The increase in the initial energy of high-energy electrons leads to an enhancement of the TOAM of both gamma photons and positrons in both frames. Gamma photons and electrons/positrons with TOAM as a new degree of freedom may have extensive applications in optical communication, astrophysics, nanomaterials, and other fields.

Spatiotemporal optical vortices with controllable radial and azimuthal quantum numbers

Optical spatiotemporal vortices with transverse photon orbital angular momentum (OAM) have recently become a focal point of research. In this work we theoretically and experimentally investigate optical spatiotemporal vortices with radial and azimuthal quantum numbers, known as spatiotemporal Laguerre-Gaussian (STLG) wavepackets. These 3D wavepackets exhibit phase singularities and cylinder-shaped edge dislocations, resulting in a multi-ring topology in its spatiotemporal profile. Unlike conventional ST optical vortices, STLG wavepackets with non-zero p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{\\boldsymbol{p}}}}}}$$\\end{document} and l\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{\\boldsymbol{l}}}}}}$$\\end{document} values carry a composite transverse OAM consisting of two directionally opposite components. We further demonstrate mode conversion between an STLG wavepacket and an ST Hermite-Gaussian (STHG) wavepacket through the application of strong spatiotemporal astigmatism. The converted STHG wavepacket is de-coupled in intensity in space-time domain that can be utilized to implement the efficient and accurate recognition of ultrafast STLG wavepackets carried various p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{\\boldsymbol{p}}}}}}$$\\end{document} and l.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{\\boldsymbol{l}}}}}}.$$\\end{document} This study may offer new insights into high-dimensional quantum information, photonic topology, and nonlinear optics, while promising potential applications in other wave phenomena such as acoustics and electron waves.

Effects of primary aberration on the spatiotemporal optical vortex focus

A spatiotemporal optical vortex (STOV) with transverse orbital angular momentum has several potential applications. However, refractive index mismatch, beam tilt and optical path misalignment are often inevitable during the application of an optical system. To investigate the focusing field of light pulse, the effects of primary aberrations such as the spherical aberration, coma, and astigmatism were analyzed. The simulation results indicate that three-dimension spatiotemporal distributions of the focusing light pulse are affected by primary aberration. On the principal coordinate planes, coma can distort the intensity structure and shift the STOV focus perpendicular to the propagation direction, while spherical aberration and astigmatism induce the actual STOV focus to shift along the propagation direction. Astigmatism do not affect the intensity structure of spatiotemporal plane without spiral phase, but stretch the 3D STOV focus along one spatial axis. Coma and astigmatism are necessary to be avoided to obtain a perfect STOV focus. It is helpful to improve the applications of STOV focus, such as optical tweezers, microscopy, and communications.

Twisted spatiotemporal optical vortex beams in dispersive media

We derive a closed-form expression for the mutual coherence function (MCF) of a twisted spatiotemporal optical vortex (STOV) beam after propagating a distance z in a linear dispersive medium. A twisted STOV beam is a partially coherent optical field that possesses a coherent STOV and a stochastic twist coupling its space and time dimensions. These beams belong to a special class of space–time-coupled light fields that carry transverse (to the direction of propagation) orbital angular momentum, making them potentially useful in numerous applications including quantum optics, optical manipulation, and optical communications. After presenting the derivation, we validate our new general MCF by showing that it simplifies to the MCFs for two example beams from the literature. Lastly, we present and analyze space–time beam profiles and complex arguments (phases) of the MCF at multiple z and differing amounts of material dispersion, field correlation or coherence, and beam twist to gain insight into how twisted STOV beams evolve in dispersive media. We conclude with a brief summary.

Isolated attosecond electron and hard x-ray pulse generation by ultra-intense spatiotemporal vortex laser

The spatiotemporal optical vortex (STOV) laser pulse, characterized by containing a space-time dependent spiral phase structure and intrinsic transverse orbital angular momentum (OAM), has been of much recent research interest for basic physics as well as potential applications in optical communication and manipulation, as well as the attosecond sciences. Here we consider electron acceleration and generation of attosecond hard x-rays by irradiating a thin foil with intense STOV laser pulse. It is found that the affected foil electrons can be trapped and acquire transverse OAM, or synchrotron-like motion, from the STOV, as well as accelerated forward by the transverse and enhanced axial laser electric fields to form a tiny energetic bunch at the front of the laser pulse and emit short ( ∼400 attosecond) high-flux ( >109 photons per pulse) hard (100–1000 keV) x rays.

Spatial-temporal optical vortex pendulum on a curved surface.

Spatial-temporal optical vortices (STOVs) have recently become the focus of newly structured optical fields. In this paper, their propagation on a 2D curved surface named the constant Gaussian curvature surface (CGCS) is studied. Using the matrix optics approach, we provide the analytical solution of the STOV propagation under the paraxial approximation on the CGCS with positive curvature. One method of creating timers is made possible by the spatiotemporal distribution direction of STOV light intensity, which swings like a pendulum throughout the evolution, in contrast to propagation on a flat surface. This swing, however, stops when the curved surface's curvature radius matches the light's Rayleigh distance. Besides, the transverse orbital angular momentum of STOV is deduced, and we find that the intrinsic and extrinsic OAM periodically exchange, but the total transverse OAM is always zero during the propagation on CGCS. It aids in controlling the transverse extrinsic orbital angular momentum of STOV in nontrivial space.

Observation of spatiotemporal optical vortices enabled by symmetry-breaking slanted nanograting

Providing additional degrees of freedom to manipulate light, spatiotemporal optical vortex (STOV) beams carrying transverse orbital angular momentum are of fundamental importance for spatiotemporal control of light-matter interactions. Unfortunately, existing methods to generate STOV are plagued by various limitations such as inefficiency, bulkiness, and complexity. Here, we theoretically propose and experimentally demonstrate a microscale singlet platform composed of a slanted nanograting to generate STOV. Leveraging the intrinsic topological singularity induced by C2 symmetry and z-mirror symmetry breaking of the slanted nanograting, STOV is generated through the Fourier transform of the spiral phase in the momentum-frequency space to the spatiotemporal domain. In experiments, we observe the space-time evolution of STOV carried by femtosecond pulses using a time-resolved interferometry technique and achieve a generation efficiency exceeding 40%. Our work sheds light on a compact and versatile platform for light pulse shaping, and paves the way towards a fully integrated system for spatiotemporal light manipulation.

Procedure for imparting transverse orbital angular momentum by focusing spatiotemporally coupled ultrashort pulses

Procedure for imparting transverse orbital angular momentum by focusing spatiotemporally coupled ultrashort pulses

Spatiotemporal Torquing of Light

We demonstrate the controlled spatiotemporal transfer of transverse orbital angular momentum (OAM) to electromagnetic waves: the spatiotemporal torquing of light. This is a radically different situation from OAM transfer to longitudinal, spatially defined OAM light by stationary or slowly varying refractive-index structures such as phase plates or air turbulence. We show that net transverse OAM per photon can be spatiotemporally imparted to a light pulse only if (1) a transient phase perturbation is well overlapped with the pulse in spacetime, or (2) the pulse initially has nonzero transverse OAM density, and the perturbation removes energy from it. Physical insight is provided by the mechanical analogy of torquing a wheel or removing mass as it spins. Our OAM theory for spatiotemporal optical vortex (STOV) pulses [S. W. Hancock ,] correctly quantifies the light-matter interaction of our experiments and provides a spatiotemporal-torque-based explanation for the first measurement of STOVs [N. Jhajj , ]. Published by the American Physical Society 2024

Three-Dimensional Reconfigurable Optical Singularities in Bilayer Photonic Crystals.

Metasurfaces and photonic crystals have revolutionized classical and quantum manipulation of light and opened the door to studying various optical singularities related to phases and polarization states. However, traditional nanophotonic devices lack reconfigurability, hindering the dynamic switching and optimization of optical singularities. This paper delves into the underexplored concept of tunable bilayer photonic crystals (BPhCs), which offer rich interlayer coupling effects. Utilizing silicon nitride-based BPhCs, we demonstrate tunable bidirectional and unidirectional polarization singularities, along with spatiotemporal phase singularities. Leveraging these tunable singularities, we achieve dynamic modulation of bound-state-in-continuum states, unidirectional guided resonances, and both longitudinal and transverse orbital angular momentum. Our work paves the way for multidimensional control over polarization and phase, inspiring new directions in ultrafast optics, optoelectronics, and quantum optics.

Spatiotemporal coupling induced controllable orientation of photonic orbital angular momentum at subwavelength scale.

Recently, the emergence of transverse orbital angular momentum (OAM) as a novel characteristic of light has captured substantial attention, and the significance of adjustable OAM orientation has been underscored due to its pivotal role in the interaction between light and matter. In this work, we introduce a novel approach to manipulate the orientation of photonic OAM at subwavelength scales, leveraging spatiotemporal coupling. By tightly focusing a wavepacket containing dual spatiotemporal vortices and a spatial vortex through a high numerical aperture lens, the emergence of intricate coupling phenomena leads to entangled and intricately twisted vortex tunnels. As a consequence, the orientation of spatial OAM deviates from the conventional light axis. Through theoretical scrutiny, we unveil that the orientation of photonic OAM within the focal field is contingent upon the signs of the topological charges in both spatiotemporal and spatial domains. Additionally, the absolute values of these charges govern the precise orientation of OAM within their respective quadrants. Moreover, augmenting the pulse width of the incident light engenders a more pronounced deflection angle of photonic OAM. By astutely manipulating these physical parameters, unparalleled control over the spatial orientation of OAM becomes achievable. The augmented optical degrees of freedom introduced by this study hold considerable potential across diverse domains, including optical tweezers, spin-orbit angular momentum coupling, and quantum communication.

Optical skipping rope induced transverse OAM for particle orbital motion parallel to the optical axis

Abstract In structured light tweezers, it is a challenging technical issue to realize the complete circular motion of the trapped particles parallel to the optical axis. Herein, we propose and generate a novel optical skipping rope via combining beam shaping technology, Fourier shift theorem, and beam grafting technology. This optical skipping rope can induce the transverse orbital angular momentum (OAM) (i.e., nominal OAM, whose direction is perpendicular to the optical axis) and transfer it to the particles, so that the particles have a transverse torque, thereby causing the particles to rotate parallel to the optical axis. Experimentally, our optical tweezers validate that the designed optical skipping rope realizes the orbital motion of polystyrene particles parallel to the optical axis. Additionally, the experiments also demonstrate that the optical skipping ropes manipulate particles to move along the oblique coil trajectory and three-dimensional (3D) cycloidal trajectory. Using the laser beam induced OAM, this innovative technology increases the degree of freedom for manipulating particles, which is of great significance for the application of optical tweezers in optical manipulation, micromechanics, and mimicry of celestial orbits.

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.