Spatiotemporal Vortex Research Articles

Atomic photoionization by spatiotemporal optical vortex pulses

Electromagnetic waves with a helical-like wavefront are known as optical vortices. One of their main characteristics is a phase structure that has a circulation around a singularity and that they carry orbital angular momentum (OAM). OAM is a fundamental property that governs the interaction of these sources with matter. In the present paper, we study the electron dynamics driven by a so-called spatiotemporal optical vortex (STOV). Contrary to the conventional optical vortices, a STOV carries transverse OAM. By designing a streakinglike technique, we aim to fully characterize the OAM of the STOV. Using both quantum mechanical and semiclassical models, we are able to dissect the spatially resolved photoelectron energy spectra and accurately retrieve the OAM. Our approach paves the way toward a complete understanding of the interaction of complex spatiotemporal light fields with atomic targets.

Orbital angular momentum of optical, acoustic, and quantum-mechanical spatiotemporal vortex pulses

The author addresses a recent controversy about the orbital angular momentum of spatiotemporal vortex pulses by calculating the probability centroids of the pulses and corresponding extrinsic and intrinsic parts of the angular momentum. Electromagnetic, acoustic, and quantum-relativistic spatiotemporal pulses are analyzed.

Partially coherent sources whose coherent modes are spatiotemporal optical vortex beams

We analyze three non-stationary partially coherent sources whose coherent modes are spatiotemporal optical vortex (STOV) beams. Using spatiotemporal (ST) Bessel–Gauss and Laguerre–Gauss beams (STOV-carrying solutions to the space-time paraxial wave equation) as eigenfunctions in the coherent-modes representation of the mutual coherence function, we derive the ST versions of J 0-Bessel-correlated, I n -Bessel-correlated, and twisted Gaussian Schell-model beams. We model, in simulation, these ST random beams via their coherent-modes expansions, compare and contrast the simulated results to theory, and analyze/discuss their free-space propagation characteristics. The work presented in this paper will be useful for simulating or physically generating these ST beams for use in applications or future studies.

Dynamical Modulation of Transverse Orbital Angular Momentum in Highly Confined Spatiotemporal Optical Vortex

Spatiotemporal optical vortices (STOVs) have attracted numerous attention from researchers in recent years due to their intriguing characteristics with transverse orbital angular momentum (OAM) in the spatiotemporal domain. In this work, we numerically analyze the tightly focusing characteristics of higher-order STOVs and present a method to dynamically modulate the transverse OAM in highly confined STOVs. Richards–Wolf vectorial diffraction theory was employed to simulate the three-dimensional spatiotemporal distribution of the focused STOV corresponding to the incident wave packet of topological charge of −2. The simulation results show that the higher-order spatiotemporal vortices in the transversely polarized components of the focused wave packets split into two first-order vortices with topological charge of −1 when the waist radius of the incident wave packet was larger than 40% of the pupil radius of the focusing lens, and the spacing of the two split vortices could be tailored by adjusting the waist radius of the incident wave packet. Meanwhile, the incident spatial waist radius also affected the tilt angle of the phase singularity trace in the z-polarized component of the focused field. The presented method provides a flexible way to dynamically engineer the spatiotemporal vortices in the tightly focused wave packet and may find potential applications in nanophotonics, light–matter interaction, quantum information processing, etc.

Spatiotemporal Optical Vortices: Toward Tailoring Orbital Angular Momentum of Light in Full Space-Time

Longitudinal orbital angular momentum (OAM) is a fundamental property of light that has been the subject of extensive research and applied to diverse important applications, such as optical tweezers, super-resolution imaging, and optical information processing. Recently, photons have been observed to possess transverse OAM, where the OAM vector is orthogonal to the direction of light propagation. As the carrier for this unique OAM, the spatiotemporal (ST) optical vortex has attracted considerable interest. Here, we provide a general overview of recent experimental and theoretical advances on such vortices, presenting their synthesis and measurement strategies, highlighting their nontrivial properties in linear propagation and interaction with nonlinear matter, and discussing the possible future trends and challenges.

Plasmonic Generation of Spatiotemporal Optical Vortices

We investigate the transformation of spatiotemporal optical signals using the Kretschmann configuration with an additional dielectric layer, which can be referred to as the “generalized Kretschmann setup”. We demonstrate that in the considered structure, it is possible to achieve the condition of generating a reflected optical pulse containing a spatiotemporal optical vortex, which appears to be impossible in the conventional Kretschmann configuration. High-quality generation of spatiotemporal optical vortices using the investigated structure was confirmed by the results of rigorous numerical simulations. The obtained results are promising for applications in analog optical computing and optical information processing systems.

Manipulation of Scattering Spectra with Topology of Light and Matter

AbstractStructured lights, including beams carrying spin and orbital angular momenta, radially and azimuthally polarized vector beams, as well as spatiotemporal optical vortices, have attracted significant interest due to their unique amplitude, phase front, polarization, and temporal structures, enabling a variety of applications in optical and quantum communications, micromanipulation, and super‐resolution imaging. In parallel, structured optical materials, metamaterials, and metasurfaces consisting of engineered unit cells—meta‐atoms, opened new avenues for manipulating the flow of light and optical sensing. While several studies explored structured light effects on the individual meta‐atoms, their shapes are largely limited to simple spherical geometries. However, the synergy of the structured light and complex‐shaped meta‐atoms has not been fully explored. In this paper, the role of the helical wavefront of Laguerre–Gaussian beams in the excitation and suppression of higher‐order resonant modes inside all‐dielectric meta‐atoms of various shapes, aspect ratios, and orientations, is demonstrated and the excitation of various multipolar moments that are not accessible via unstructured light illumination is predicted. The presented study elucidates the role of the complex phase distribution of the incident light in shape‐dependent resonant scattering, which is of utmost importance in a wide spectrum of applications ranging from remote sensing to spectroscopy.

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.

Spatiotemporal optical vortices: Advances and mysteries - INVITED

The amount of transverse orbital angular momentum (OAM) carried by the spatiotemporal optical vortices (STOVs) is being hotly debated. In this contribution I unveil the mystery of the amount of total, intrinsic and extrinsic transverse OAM carried by STOVs. They do not carry any total transverse OAM about a static transverse axis crossing the STOV center. Yet, STOVs carry a transverse OAM about a moving transverse axis crossing the STOV center permanently, which is identified with the intrinsic OAM, and an opposite extrinsic transverse OAM about the fixed axis. These results raise questions about the interpretation of second-harmonic and high-harmonic experiments or simulations with STOVs, and the capability of STOVs to transmit OAM to particles. Other advances such as observation of vortex splitting and topological charge flipping of high-order STOVs in free space and in dispersive media, and the transverse torque exerted by optical elements will be discussed.

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.

The generation and manipulation of spatiotemporal vortex in nonlocal self-temporal photorefractive media

The generation and manipulation of spatiotemporal vortex in nonlocal self-temporal photorefractive media

Scalar optical hopfions

Hopfions are three-dimensional (3D) topological states discovered in field theory, magnetics, and hydrodynamics that resemble particle-like objects in physical space. Hopfions inherit the topological features of the Hopf fibration, a homotopic mapping from unit sphere in 4D space to unit sphere in 3D space. Here we design and demonstrate dynamic scalar optical hopfions in the shape of a toroidal vortex and expressed as an approximate solution to Maxwell’s equations. Equiphase lines correspond to disjoint and interlinked loops forming complete ring tori in 3D space. The Hopf invariant, product of two winding numbers, is determined by the topological charge of the poloidal spatiotemporal vortices and toroidal spatial vortices in toroidal coordinates. Optical hopfions provide a photonic testbed for studying topological states and may be utilized as high-dimensional information carriers.

Spatiotemporal multi-vortex and multi-pole mode soliton solutions in PT symmetric media with variable coefficients

The mathematical model of the PT media with variable coefficients is introduced, and the spatiotemporal vortex and multi-pole mode solutions are derived by the bilinear transformation method. Then, the modulation propagation of the solutions is also studied. In addition, a novel control approach for constructing the distribution and the quantity of multi-vortex solitons by using different nonlinear hyperbolic tangent function are proposed. Finally, the effectiveness of the method is validated.

Wigner time delays and Goos–Hänchen shifts of 2D quantum vortices scattered by potential barriers

We consider reflection and transmission of 2D quantum wavepackets with phase vortices (also known in optics as spatiotemporal vortex pulses) at potential step-like, delta-function, and rectangular barriers. The presence of a vortex significantly modifies the Wigner time delays and Goos–Hänchen shifts, previously studied for Gaussian-like wavepackets. In particular, the scattered wavepackets undergo non-zero time delays and lateral shifts even for purely real scattering coefficients, when the standard Wigner and Artmann formulae vanish. We derive analytical expressions for the vortex-induced times delays and spatial shifts and verify these with numerical calculations of the Schrödinger equation. The time delays and shifts are resonantly enhanced in the vicinity of the critical-angle incidence for a step-like potential and near transmission resonances for a rectangular barrier.

Numerical modeling for the characteristics study of a focusing ultrashort spatiotemporal optical vortex.

Spatiotemporal (ST) wave packet carrying pure transverse orbital angular moment (OAM) with subwavelength spatial size has attracted increasing attentions in recent years, which can be obtained by tightly focusing a linear superposition of ST vortices with different topological charges. In this work, numerical models are proposed to explore the impact of the pulse width of the ST vortex on the characteristics of its focal field. We demonstrate that the rigorous model for calculating the focused ST wave packet is essential for ultrashort optical pulse, while the simplified model has the advantage of high efficiency but can only provide credible results when the pulse width of the illumination is long enough. Specifically, when the pulse width decreases from 100 fs to 5 fs, the accuracy of the simplified model would decrease significantly from 99% to 65.5%. In addition, it is found that the pulse duration would still lead to the collapse of transverse OAM structure near the focus of a high numerical aperture lens, even though the ST astigmatism has already been corrected. To analyze the physical mechanism behind this distortion, Levenberg-Marquardt algorithm is adopted to retrieve the OAM distribution of the focal field. It is shown that the contributions from undesired OAM modes would become nontrivial for short pulse width, leading to the formation of the focal field with hybrid OAM structures. These findings provide insight for the focusing and propagation studies of ultrashort ST wave packets, which could have wide potential applications in microscopy, optical trapping, laser machining, nonlinear light-matter interactions, etc.

Space-time wave packets

Space-time wave packets (STWPs) constitute a broad class of pulsed optical fields that are rigidly transported in linear media without diffraction or dispersion, and are therefore propagation-invariant in the absence of optical nonlinearities or waveguiding structures. Such wave packets exhibit unique characteristics, such as controllable group velocities in free space and exotic refractive phenomena. At the root of these behaviors is a fundamental feature underpinning STWPs: their spectra are not separable with respect to the spatial and temporal degrees of freedom. Indeed, the spatiotemporal structure is endowed with non-differentiable angular dispersion, in which each spatial frequency is associated with a single prescribed wavelength. Furthermore, controlled deviation from this particular spatiotemporal structure yields novel behaviors that depart from propagation-invariance in a precise manner, such as acceleration with an arbitrary axial distribution of the group velocity, tunable dispersion profiles, and Talbot effects in space–time. Although the basic concept of STWPs has been known since the 1980s, only very recently has rapid experimental development emerged. These advances are made possible by innovations in spatiotemporal Fourier synthesis, thereby opening a new frontier for structured light at the intersection of beam optics and ultrafast optics. Furthermore, a plethora of novel spatiotemporally structured optical fields (such as flying-focus wave packets, toroidal pulses, and spatiotemporal optical vortices) are now providing a swath of surprising characteristics, ranging from tunable group velocities to transverse orbital angular momentum. We review the historical development of STWPs, describe the new experimental approaches for their efficient synthesis, and enumerate the various new results and potential applications for STWPs and other spatiotemporally structured fields, before casting an eye on a future roadmap for this field.

Relativistic high-order harmonic generation of spatiotemporal optical vortices

It is well known that light can possess spin angular momentum (SAM) and orbital angular momentum (OAM) in the longitudinal direction. Interesting novel light with transverse SAM or OAM has also been discovered recently, with the latter being called spatiotemporal optical vortices. Here we present a route to generate spatiotemporal optical vortices by means of high harmonic generation from relativistic laser plasma interactions. Three-dimensional particle-in-cell simulations show the evidence of edge dislocations in wave front structures and circulating energy flow in space-time. Further calculations of the SAM, OAM and total angular momentum confirm the harmonics carrying pure transverse OAM with noninteger values. The results open up a possibility to generate intense spatiotemporal optical vortices in the extreme ultraviolet region with attosecond duration.

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.

Diffraction properties of light with transverse orbital angular momentum

The spatiotemporal optical vortex (STOV) is unique, owing to its phase singularity in the space–time domain, and it can carry transverse orbital angular momentum (OAM). Diffraction is a fundamental wave phenomenon that is well known for conventional light; however, studies on the diffraction of light with transverse OAM are limited. Furthermore, methods that enable the fast detection of STOVs are lacking. Here, we theoretically and experimentally study the diffraction behaviors of STOVs, which are different from those of conventional light. The diffraction patterns of STOV pulses that are diffracted by a grating exhibit multilobe structures with a gap number that corresponds to the topological charge. The diffraction rules of STOVs are also revealed. An approach for the fast detection of STOVs is provided using their special diffraction properties. This method has potential applications in fields that require fast STOV recognition, such as STOV-based optical communications.

Spatiotemporal optical vortices with arbitrary orbital angular momentum orientation by astigmatic mode converters

Abstract We generate a spatiotemporal optical vortex (STOV) with tunable orbital angular momentum (OAM) orientation by a simple lens system. We utilize a cylindrical lens system, which is an astigmatic mode converter, to add longitudinal angular momentum to tilt the purely transverse OAM in an arbitrary direction. The amount of tilt is tunable by adjusting the lens system, and thus the OAM direction is continuously adjustable. STOVs with adjustable OAM directions have been verified theoretically and experimentally. We believe such direction controllable OAMs will enrich future applications.