Benchmarking Functionals for Strong-Field Light-Matter Interactions in Adiabatic Time-Dependent Density Functional Theory

In recent years, time-dependent density functional theory (TDDFT) has been extensively employed for highly nonlinear optics in molecules and solids, including high harmonic generation (HHG), photoemission, and more. TDDFT exhibits a relatively low numerical cost while still describing both light-matter and electron-electron interactions ab initio, making it highly appealing. However, the majority of implementations of the theory utilize the simplest possible approximations for the exchange-correlation (XC) functional-either the local density or generalized gradient approximations, which are traditionally considered to have rather poor chemical accuracy. We present the first systematic study of the XC functional effect on molecular HHG, testing various levels of theory. Our numerical results suggest justification for using simpler approximations for the XC functional, showing that hybrid and meta functionals (as well as Hartree-Fock) can, at times, lead to poor and unphysical results. The specific source of the failure in more elaborate functionals should be topic of future work, but we hypothesize that its origin might be connected to the adiabatic approximation of TDDFT.

Single-shot probing of sub-picosecond solid-to-overdense-plasma dynamics

A single-shot near-infrared probing method has been developed to characterize the formation and evolution of the pre-plasma dynamics over sub-picosecond timescales, which is essential for the societal applications of laser-accelerated ion technologies.

Orbital Hall diffraction and its application for vortex measurement

We observe significant orbital angular momentum (OAM)-helicity-dependent centroid shifts in the Fraunhofer patterns for the far-field diffraction of optical vortex beams passing through a thin single wire, thus suggesting the orbital Hall effect (OHE) of light in diffraction. Based on the OHE with a thin cross wire, we further experimentally develop a compact and robust alignment-free method to measure the OAM states of light. These findings indicate that not only does the OHE of light offer insights into vortex diffraction with broken rotational symmetry, it may also provide a reliable and efficient way to simplify the vortex measurement for waves of different natures.

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 and l 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 and l . 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.

Nondiffracting supertoroidal pulses and optical "Kármán vortex streets"

Supertoroidal light pulses, as space-time nonseparable electromagnetic waves, exhibit unique topological properties including skyrmionic configurations, fractal-like singularities, and energy backflow in free space, which however do not survive upon propagation. Here, we introduce the non-diffracting supertoroidal pulses (NDSTPs) with propagation-robust skyrmionic and vortex field configurations that persists over arbitrary propagation distances. Intriguingly, the field structure of NDSTPs has a similarity with the von Kármán vortex street, a pattern of swirling vortices in fluid and gas dynamics with staggered singularities that can stably propagate forward. NDSTPs will be of interest as directed channels for information and energy transfer applications.

High-harmonic spin-shearing interferometry for spatially resolved EUV magneto-optical spectroscopy

We present a method for achieving hyperspectral magnetic imaging in the extreme ultraviolet (EUV) region based on high-harmonic generation (HHG). By interfering two mutually coherent orthogonally-polarized and laterally-sheared HHG sources, we create an EUV illumination beam with spatially-dependent ellipticity. By placing a magnetic sample in the beamline and sweeping the relative time delay between the two sources, we record a spatially resolved interferogram that is sensitive to the EUV magnetic circular dichroism of the sample. This image contains the spatially-resolved magneto-optical response of the sample at each harmonic order, and can be used to measure the magnetic properties of spatially inhomogeneous magnetic samples.

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 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.

Orbital angular momentum-mediated machine learning for high-accuracy mode-feature encoding

Machine learning with optical neural networks has featured unique advantages of the information processing including high speed, ultrawide bandwidths and low energy consumption because the optical dimensions (time, space, wavelength, and polarization) could be utilized to increase the degree of freedom. However, due to the lack of the capability to extract the information features in the orbital angular momentum (OAM) domain, the theoretically unlimited OAM states have never been exploited to represent the signal of the input/output nodes in the neural network model. Here, we demonstrate OAM-mediated machine learning with an all-optical convolutional neural network (CNN) based on Laguerre-Gaussian (LG) beam modes with diverse diffraction losses. The proposed CNN architecture is composed of a trainable OAM mode-dispersion impulse as a convolutional kernel for feature extraction, and deep-learning diffractive layers as a classifier. The resultant OAM mode-dispersion selectivity can be applied in information mode-feature encoding, leading to an accuracy as high as 97.2% for MNIST database through detecting the energy weighting coefficients of the encoded OAM modes, as well as a resistance to eavesdropping in point-to-point free-space transmission. Moreover, through extending the target encoded modes into multiplexed OAM states, we realize all-optical dimension reduction for anomaly detection with an accuracy of 85%. Our work provides a deep insight to the mechanism of machine learning with spatial modes basis, which can be further utilized to improve the performances of various machine-vision tasks by constructing the unsupervised learning-based auto-encoder.

Few-cycle optical vortices for strong-field physics

We report on the generation of optical vortices with few-cycle pulse durations, 500μJ per pulse, at a repetition rate of 1 kHz. To do so, a 25 fs laser beam at 800 nm is shaped with a helical phase and coupled into a hollow-core fiber filled with argon gas, in which it undergoes self-phase modulation. Then, 5.5 fs long pulses are measured at the output of the fiber using a dispersion-scan setup. To retrieve the spectrally resolved spatial profile and orbital angular momentum (OAM) content of the pulse, we introduce a method based on spatially resolved Fourier-transform spectroscopy. We find that the input OAM is transferred to all frequency components of the post-compressed pulse. The combination of these two information shows that we obtain few-cycle, high-intensity vortex beams with a well-defined OAM, and sufficient energy to drive strong-field processes.

Phase-matching of high-order harmonic generation in the extreme ultraviolet region with orbital angular momentum

High-order harmonics can generate vortex beams with orbital angular momentum (OAM) in the extreme ultraviolet region. However, experimental research on their phase-matching (PM) characteristics is limited. In this study, vortex high-order harmonic generation (HHG) in the extreme ultraviolet region was generated with Ar gas. Phase-matched HHG with OAM was obtained by optimizing the focus position, laser energy, and gas pressure. The dependence of the PM characteristics on these parameters was analyzed. In addition, we conducted an experimental analysis of the dimensional properties of vortex harmonics under PM conditions. This study is a contribution towards the intense vortex high-order harmonic light sources and their applications.

Control of the annular spatial profile of high harmonics using a Bessel-Gaussian beam carrying the nonzero orbital angular momentum

We propose to generate vortex high harmonics in the extreme ultraviolet (XUV) with a controllable spatial profile by using a Bessel-Gaussian (BG) beam carrying a nonzero orbital angular momentum (OAM). Such BG beam has quite a different intensity profile at the focus compared to the generally used BG beam without carrying the OAM. We show that the BG beam is capable of generating single-ring structured high harmonics, which is quite different from an Laguerre-Gaussian (LG) beam with a similar intensity distribution at the laser focus. We reveal that favorable phase-matching conditions can be achieved off-axis and away from the laser focus because a single-atom intrinsic phase due to the short electron trajectory can be well compensated by a geometric phase of the BG beam. We thus give a general rule that vortex high harmonics with a single annular profile can be efficiently generated when a gas medium is located at 1.5zred to 2.0zred before or after the laser focus of the BG beam, here zred is a reduced length. We also show the validity of this rule when the BG beam carries a higher OAM. This work is expected to be useful for synthesizing attosecond vortex pulses.

Revealing the Interplay between Strong Field Selection Rules and Crystal Symmetries

Symmetries are ubiquitous in condensed matter physics, playing an important role in the appearance of different phases of matter. Nonlinear light matter interactions serve as a coherent probe for resolving symmetries and symmetry breaking via their link to selection rules of the interaction. In the extreme nonlinear regime, high harmonic generation (HHG) spectroscopy offers a unique spectroscopic approach to study this link, probing the crystal spatial properties with high sensitivity while opening new paths for selection rules in the XUV regime. In this Letter we establish an advanced HHG polarimetry scheme, driven by a multicolor strong laser field, to observe the structural symmetries of solids and their interplay with the HHG selection rules. By controlling the crystal symmetries, we resolve nontrivial polarization states associated with new spectral features in the HHG spectrum. Our scheme opens new opportunities in resolving the symmetries of quantum materials, as well as ultrafast light driven symmetries in condensed matter systems.

Wavefront control of subcycle vortex pulses via carrier-envelope-phase tailoring

The carrier-envelope phase (CEP) of an ultrashort laser pulse is becoming more crucial to specify the temporal characteristic of the pulse's electric field when the pulse duration becomes shorter and attains the subcycle regime; here, the pulse duration of the intensity envelope is shorter than one cycle period of the carrier field oscillation. When this subcycle pulse involves a structured wavefront as is contained in an optical vortex (OV) pulse, the CEP has an impact on not only the temporal but also the spatial characteristics owing to the spatiotemporal coupling in the structured optical pulse. However, the direct observation of the spatial effect of the CEP control has not yet been demonstrated. In this study, we report on the measurement and control of the spatial wavefront of a subcycle OV pulse by adjusting the CEP. To generate subcycle OV pulses, an optical parametric amplifier delivering subcycle Gaussian pulses and a Sagnac interferometer as a mode converter were integrated and provided an adequate spectral adaptability. The pulse duration of the generated OV pulse was 4.7 fs at a carrier wavelength of 1.54 µm. To confirm the wavefront control with the alteration of the CEP, we developed a novel [Formula: see text]-2[Formula: see text] interferometer that exhibited spiral fringes originating from the spatial interference between the subcycle OV pulse and the second harmonic of the subcycle Gaussian pulse producing a parabolic wavefront as a reference; this resulted in the successful observation of the rotation of spiral interference fringes during CEP manipulation.

Nanophotonic Materials for Twisted-Light Manipulation

Twisted light, an unbounded set of helical spatial modes carrying orbital angular momentum (OAM), offers not only fundamental new insights into structured light-matter interactions, but also a new degree of freedom to boost optical and quantum information capacity. However, current OAM experiments still rely on bulky, expensive, and slow-response diffractive or refractive optical elements, hindering today's OAM systems to be largely deployed. In the last decade, nanophotonics has transformed the photonic design and unveiled a diverse range of compact and multifunctional nanophotonic devices harnessing the generation and detection of OAM modes. Recent metasurface devices developed for OAM generation in both real and momentum space, presenting design principle and exemplary devices, are summarized. Moreover, recent development of whispering-gallery-mode-based passive and tunable microcavities, capable of extracting degenerate OAM modes for on-chip vortex emission and lasing, is summarized. In addition, the design principle of different plasmonic devices and photodetectors recently developed for on-chip OAM detection is discussed. Current challenges faced by the nanophotonic field for twisted-light manipulation and future advances to meet these challenges are further discussed. It is believed that twisted-light manipulation in nanophotonics will continue to make significant impact on future development of ultracompact, ultrahigh-capacity, and ultrahigh-speed OAM systems-on-a-chip.

Short-wavelength radiation pulses with time-varying orbital angular momentum from tailored relativistic electron beams

In this Letter, we propose a novel, to the best of our knowledge, technique to generate short-wavelength radiation carrying time-varying orbital angular momentum (OAM) by tailoring relativistic beams in free-electron lasers. To manipulate the temporal properties of OAM beams, two time-delayed seed lasers with different OAM values are used to interact with the electron beam in the undulator. With this method, high-harmonic electron beam microbunching with a time-varying helical distribution can be tailored to match the time-varying instantaneous helical phase structure of the x ray beams. Theoretical and simulation results demonstrate that high-power x ray beams with time-varying OAM can be produced by the proposed technique, which opens new routes to scientific research in x ray science.

High-power femtosecond vortices generated from a Kerr-lens mode-locked solid-state Hermite-Gaussian oscillator

We report the generation of high-order transverse modes from a Kerr-lens mode-locked femtosecond laser. Two different orders of Hermite-Gaussian modes were realized by non-collinear pumping, which were converted into the corresponding Laguerre-Gaussian vortex modes using a cylindrical lens mode converter. The mode-locked vortex beams, with an average power of 1.4 W and 0.8 W, contained pulses as short as 126 fs and 170 fs at the first and second Hermite-Gaussian mode orders, respectively. This work demonstrates the possibility of developing Kerr-lens mode-locked bulk lasers with various pure high-order modes and paves the way for generating ultrashort vortex beams.

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.

Observation of Anomalous Orbital Angular Momentum Transfer in Parametric Nonlinearity

Orbital angular momentum (OAM) conservation plays an important role in shaping and controlling structured light with nonlinear optics. The OAM of a beam originating from three-wave mixing should be the sum or difference of the other two inputs because no light-matter OAM exchange occurs in parametric nonlinear interactions. Here, we report anomalous OAM transfer in parametric upconversion, in which a Hermite-Gauss mode signal interacts with a specially engineered pump capable of astigmatic transformation, resulting in Laguerre-Gaussian mode sum-frequency generation (SFG). The anomaly here refers to the fact that the pump and signal both carry no net OAM, while their SFG does. We reveal experimentally that there is also an OAM inflow to the residual pump, having the same amount of that to the SFG but with the opposite sign, and thus holds system OAM conservation. This unexpected OAM selection rule improves our understanding of OAM transfer among interacting waves and may inspire new ideas for controlling OAM states via nonlinear optics.

Nonlinear up-conversion of a polarization Möbius strip with half-integer optical angular momentum

Symmetries and conservation laws of energy, linear momentum, and angular momentum play a central role in nonlinear optics. Recently, paraxial light fields with nontrivial topology have been attracting a keen interest. Despite not being eigenstates of the orbital and spin angular momenta (OAM and SAM), they are eigenstates of the generalized angular momentum (GAM) operator-a mixture of the OAM and SAM operators with fractional eigenvalues. By driving high harmonic generation with a polarization Möbius strip carrying a half-integer GAM charge and implementing angular momentum characterization methods in the extreme ultraviolet range, we demonstrate the linear scaling of the GAM with the harmonic order, each harmonic carrying a precise half-integer GAM charge. Our work shows that beyond SAM and OAM, the GAM is, in some situations, an appropriate quantum number. It paves the way for finer manipulations and applications of light beams containing fractional-order polarization singularities.

A Third Angular Momentum of Photons

Photons that acquire orbital angular momentum move in a helical path and are observed as a light ring. During helical motion, if a force is applied perpendicular to the direction of motion, an additional radial angular momentum is introduced, and alternate dark spots appear on the light ring. Here, a third, centrifugal angular momentum has been added by twisting the helical path further according to the three-step hierarchical assembly of helical organic nanowires. Attaining a third angular momentum is the theoretical limit for a photon. The additional angular momentum converts the dimensionless photon to a hollow spherical photon condensate with interactive dark regions. A stream of these photon condensates can interfere like a wave or disintegrate like matter, similar to the behavior of electrons.

Generation of spatiotemporal optical vortices in ultrashort laser pulses using rotationally interleaved multispirals

Ultrashort optical vortex pulses carrying spatiotemporal orbital angular momentum (OAM) have inspired versatile applications such as the micromachining of integrated quantum chips and discoveries such as optical toroidal structures and OAM-carrying X-waves. Generating high-quality ultrashort vortices with controllable topological charges remains a crucial issue. Thus, we propose a rotationally interleaved multispiral to generate such vortices. A multispiral comprises multiple identical spirals rotated around the center in the equal-azimuthal interval and interleaved in equal-radius increments; this structure overcomes the previous structural asymmetry of the single spiral and improves the vortex quality. Accordingly, we conducted theoretical analyses, numerical simulations, and experimental investigations that demonstrated the feasibility of multispirals in generating the ultrashort vortices with symmetric distributions and flexibly controlling the topological charges. The proposed study is significant for broader applications involving ultrashort vortices and extensive investigations in related areas such as research on electron vortices, plasmonic vortices, and other matter vortices.

Role of fractional high harmonics with non-integer OAM on the generation of a helical attosecond pulse train

Extreme-ultraviolet pulses of attosecond duration carrying orbital angular momentum (OAM) can be produced by spectrally filtering vortex high harmonics generated in a gas medium. Here we reveal that fractional high harmonics (FHHs) with non-integer OAM generated by a short duration Laguerre-Gaussian laser beam are origins for the change of helical attosecond pulse train (APT) with azimuthal angle. We show that these harmonics have gap and minimum structures in the annular intensity profile and discontinue phase distribution along azimuthal angle. And each FHH can be expressed as a superposition of OAM modes with integer topological charges. Features of FHH can be identified by coherently combining selected OAM modes. We also uncover that these features are formed after FHH is propagated in gas medium and in vacuum. We finally demonstrate that the generation of FHHs and the dependence of helical APTs on azimuthal angle are changed by varying the macroscopic condition.

Tunability of space-time wave packet carrying tunable and dynamically changing OAM value

Space-time (ST) wave packets have gained much interest due to their dynamic optical properties. Such wave packets can be generated by synthesizing frequency comb lines, each having multiple complex-weighted spatial modes, to carry dynamically changing orbital angular momentum (OAM) values. Here, we investigate the tunability of such ST wave packets by varying the number of frequency comb lines and the combinations of spatial modes on each frequency. We experimentally generate and measure the wave packets with tunable OAM values from +1 to +6 or from +1 to +4 during a ∼5.2-ps period. We also investigate, in simulation, the temporal pulse width of the ST wave packet and the nonlinear variation of the OAM values. The simulation results show that: (i) a pulse width can be narrower for the ST wave packet carrying dynamically changing OAM values using more frequency lines; and (ii) the nonlinearly varying OAM value can result in different frequency chirps along the azimuthal direction at different time instants.

Synthesizing ultrafast optical pulses with arbitrary spatiotemporal control

The ability to control the instantaneous state of light, from high-energy pulses down to the single-photon level, is an indispensable requirement in photonics. This has, for example, facilitated spatiotemporal probing and coherent control of ultrafast light-matter interactions, and enabled capabilities such as generation of exotic states of light with complexity, or at wavelengths, that are not easily accessible. Here, by leveraging the multifunctional control of light at the nanoscale offered by metasurfaces embedded in a Fourier transform setup, we present a versatile approach to synthesize ultrafast optical transients with arbitrary control over its complete spatiotemporal evolution. Our approach, supporting an ultrawide bandwidth with simultaneously high spectral and spatial resolution, enables ready synthesis of complex states of structured space-time wave packets. We expect our results to offer unique capabilities in coherent ultrafast light-matter interactions and facilitate applications in microscopy, communications, and nonlinear optics.

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.

X-ray pulse generation with ultra-fast flipping of its orbital angular momentum

A method to temporally tailor the properties of X-ray radiation carrying Orbital Angular Momentum (OAM) is presented. In simulations, an electron beam is prepared with a temporally modulated micro-bunching structure which, when radiating at the second harmonic in a helical undulator, generates OAM light with a corresponding temporally modulated intensity. This method is shown to generate attosecond pulse trains of OAM light without the need for any additional external optics, making the wavelength range tunable. In addition to the OAM pulse train, the method can be adapted to generate radiation where the handedness of the OAM mode may also be temporally modulated (flipped).

High-resolution, wavefront-sensing, full-field polarimetry of arbitrary beams using phase retrieval

Recent advances in structured illumination are enabling a wide range of applications from imaging to metrology, which can benefit from advanced beam characterization techniques. Solving uniquely for the spatial distribution of polarization in a beam typically involves the use of two or more polarization optics, such as a polarizer and a waveplate, which is prohibitive for some wavelengths outside of the visible spectrum. We demonstrate a technique that circumvents the use of a waveplate by exploiting extended Gerchberg-Saxton phase retrieval to extract the phase. The technique enables high-resolution, wavefront-sensing, full-field polarimetry capable of solving for both simple and exotic polarization states, and moreover, is extensible to shorter wavelength light.

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 k_x–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.

It remains unclear whether transverse orbital angular momentum beams can maintain OAM values above 1. Here the authors demonstrate the generation of beams with transverse OAM up to 100 by the inverse design of phase and find an intrinsic dispersion factor to describe the nontrivial evolution of such beams.

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.

Orbital angular momentum of paraxial propagation-invariant laser beams

For propagation-invariant laser beams represented as a finite superposition of the Hermite-Gaussian beams with the same Gouy phase and with arbitrary weight coefficients, we obtain an analytical expression for the normalized orbital angular momentum (OAM). This expression is represented also as a finite sum of weight coefficients. We show that a certain choice of the weight coefficients allows obtaining the maximal OAM, which is equal to the maximal power of the Hermite polynomial in the sum. In this case, the superposition describes a single-ringed Laguerre-Gaussian beam with a topological charge equal to the maximal OAM and to the maximal power of the Hermite polynomial.

Broadband and high-efficiency photonic spin-Hall effect with all-metallic metasurfaces

In this paper, all-metallic reflective metasurfaces comprising S-shape streamline structures are proposed to achieve the photonic spin-Hall effect with average cross-polarization conversion efficiency exceeding ∼84% in the range of 8-14 µm. By comparing with all-metallic nanobricks, it is demonstrated that the electric field coupling could be enhanced by constructing a similar split ring resonator between adjacent unit elements to further improve its efficiency and bandwidth. As a proof of concept, the photonic spin Hall effect and spin-to-orbit angular momentum conversion could be observed by two metadevices with the maximum diffraction efficiency of ∼95.7%. Such an all-metallic configuration may provide a platform for various high-efficiency electromagnetic components, catenary optics, and practical applications.

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.

Observation of Magnetic Helicoidal Dichroism with Extreme Ultraviolet Light Vortices

We report on the experimental evidence of magnetic helicoidal dichroism, observed in the interaction of an extreme ultraviolet vortex beam carrying orbital angular momentum with a magnetic vortex. Numerical simulations based on classical electromagnetic theory show that this dichroism is based on the interference of light modes with different orbital angular momenta, which are populated after the interaction between light and the magnetic topology. This observation gives insight into the interplay between orbital angular momentum and magnetism and sets the framework for the development of new analytical tools to investigate ultrafast magnetization dynamics.

Probing the orbital angular momentum of intense vortex pulses with strong-field ionization

With the rapid development of femtosecond lasers, the generation and application of optical vortices have been extended to the regime of intense-light-matter interaction. The characterization of the orbital angular momentum (OAM) of intense vortex pulses is very critical. Here, we propose and demonstrate a novel photoelectron-based scheme that can in situ distinguish the OAM of the focused intense femtosecond optical vortices without the modification of light helical phase. We employ two-color co-rotating intense circular fields in the strong-field photoionization experiment, in which one color light field is a plane wave serving as the probing pulses and the other one is the vortex pulses whose OAM needs to be characterized. We show that by controlling the spatial profile of the probing pulses, the OAM of the vortex pulses can be clearly identified by measuring the corresponding photoelectron momentum distributions or angle-resolved yields. This work provides a novel in situ detection scenario for the light pulse vorticity and has implications for the studies of ultrafast and intense complex light fields with optical OAM.

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs-particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.

Polarized phonons carry angular momentum in ultrafast demagnetization

Magnetic phenomena are ubiquitous in nature and indispensable for modern science and technology, but it is notoriously difficult to change the magnetic order of a material in a rapid way. However, if a thin nickel film is subjected to ultrashort laser pulses, it loses its magnetic order almost completely within femtosecond timescales¹. This phenomenon is widespread^2-7 and offers opportunities for rapid information processing^8-11 or ultrafast spintronics at frequencies approaching those of light^8,9,12. Consequently, the physics of ultrafast demagnetization is central to modern materials research^1-7,13-28, but a crucial question has remained elusive: if a material loses its magnetization within mere femtoseconds, where is the missing angular momentum in such a short time? Here we use ultrafast electron diffraction to reveal in nickel an almost instantaneous, long-lasting, non-equilibrium population of anisotropic high-frequency phonons that appear within 150-750 fs. The anisotropy plane is perpendicular to the direction of the initial magnetization and the atomic oscillation amplitude is 2 pm. We explain these observations by means of circularly polarized phonons that quickly absorb the angular momentum of the spin system before macroscopic sample rotation. The time that is needed for demagnetization is related to the time it takes to accelerate the atoms. These results provide an atomistic picture of the Einstein-de Haas effect and signify the general importance of polarized phonons for non-equilibrium dynamics and phase transitions.

Novel ultrafast structured EUV/x-ray sources from nonlinear optics

Coherent extreme-ultraviolet (EUV)/x-ray laser sources, structured in their temporal/spectral, spatial and angular momentum properties are emerging as unique tools to probe the nanoworld. One of the key ingredients for the emergence of such sources is the extraordinary coherence in the up-conversion of infrared laser sources through the highly nonlinear process of high-order harmonic generation. In this contribution we will review the advances during the last decade that led to the generation of structured EUV/xray sources, such as circularly polarized attosecond pulses, harmonic vortices with time-varying orbital angular momentum, ultrafast vector and vector/vortex beams, tunable high-order harmonic combs or attosecond pulse trains with time-dependent polarization states. The use of such sources is being already applied to the investigation of chiral matter or magnetic materials. In the latter case, structured ultrafast sources are very promising to achieve a complete understanding of the electronic and spin interactions that govern sub-femtosecond magnetization dynamics.

Towards complete band structure of microscopic MoS2 flakes

The occupied and unoccupied electronic states of MoS2 monolayer isolated flake were studied using laboratory based photoemission electron microscope (PEEM) nanoESCA equipped with He-I photon source. PEEM real-space imaging allowed selecting the high quality flake. Altogether, the data will allow accurately recovering the band structures of MoS2. The band structures will be used in future pump-probe experiments to explore the dynamics of electrons in the conduction band and photo-induced multitopological states using trefoil polarization.

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.

Coherence in macroscopic high harmonic generation for spatial focal phase distributions of monochromatic and broadband Gaussian laser pulses

Efficient application of ultrafast laser sources from high harmonic generation requires an understanding of how the spectrum can be controlled - the extent of the highest harmonics and the strength and cleanness of the harmonic lines. We study one important aspect in the coherent build-up of macroscopic high-order harmonic generation, namely the impact of different phase distributions in the focal area on the features of the generated radiation. Specifically, we compare the high harmonic signals for the commonly-used Gouy distribution of a monochromatic beam with those for the phase distribution of a short broadband Gaussian pulse. To this end, we apply a theoretical model in which the microscopic yields are obtained via interpolation of results of the time-dependent Schrödinger equation, which are then used in an individual-emitter approach to determine the macroscopic signals. Regions of poor and good coherent build-up as a function of the position of the gas jet are identified using measures for the strength of the harmonic lines and for the impact of off-harmonic radiation. While the largest extent of the spectra as well as the strongest contribution of off-harmonic radiation is found for positioning the gas jet after the focus for both distributions, the relative strength of the harmonics is overall weaker for the short Gaussian pulse distribution and the spectra differ for a gas jet positioned at the focus. These differences are mainly caused by the additional dependence of the focal phase in the transverse direction for the short Gaussian pulse distribution.

Bright, single helicity, high harmonics driven by mid-infrared bicircular laser fields

High-harmonic generation (HHG) is a unique tabletop light source with femtosecond-to-attosecond pulse duration and tailorable polarization and beam shape. Here, we use counter-rotating femtosecond laser pulses of 0.8 µm and 2.0 μm to extend the photon energy range of circularly polarized high-harmonics and also generate single-helicity HHG spectra. By driving HHG in helium, we produce circularly polarized soft x-ray harmonics beyond 170 eV-the highest photon energy of circularly polarized HHG achieved to date. In an Ar medium, dense spectra at photon energies well beyond the Cooper minimum are generated, with regions composed of a single helicity-consistent with the generation of a train of circularly polarized attosecond pulses. Finally, we show theoretically that circularly polarized HHG photon energies can extend beyond the carbon K edge, extending the range of molecular and materials systems that can be accessed using dynamic HHG chiral spectro-microscopies.

Shaping the topology of light with a moving Rabi-oscillating vortex

Quantum vortices are the analogue of classical vortices in optics, Bose-Einstein condensates, superfluids and superconductors, where they provide the elementary mode of rotation and orbital angular momentum. While they mediate important pair interactions and phase transitions in nonlinear fluids, their linear dynamics is useful for the shaping of complex light, as well as for topological entities in multi-component systems, such as full Bloch beams. Here, setting a quantum vortex into directional motion in an open-dissipative fluid of microcavity polaritons, we observe the self-splitting of the packet, leading to the trembling movement of its center of mass, whereas the vortex core undergoes ultrafast spiraling along diverging and converging circles, in a sub-picosecond precessing fashion. This singular dynamics is accompanied by vortex-antivortex pair creation and annihilation and a periodically changing topological charge. The spiraling and branching mechanics represent a direct manifestation of the underlying Bloch pseudospin space, whose mapping is shown to be rotating and splitting itself. Its reshaping is due to three simultaneous drives along the distinct directions of momentum and complex frequency, by means of the differential group velocities, Rabi frequency and dissipation rates, which are natural assets in coupled fields such as polaritons. This state, displaying linear momentum dressed with oscillating angular momentum, confirms the richness of multi-component and open quantum fluids and their innate potentiality to implement sophisticated and dynamical topological textures of light.

Multidimensional phase singularities in nanophotonics

[Figure: see text].

Conservation laws for electron vortices in strong-field ionisation

ABSTRACT

We investigate twisted electrons with a well-defined orbital angular momentum, which have been ionised via a strong laser field. By formulating a new variant of the well-known strong field approximation, we are able to derive conservation laws for the angular momenta of twisted electrons in the cases of linear and circularly polarised fields. In the case of linear fields, we demonstrate that the orbital angular momentum of the twisted electron is determined by the magnetic quantum number of the initial bound state. The condition for the circular field can be related to the famous ATI peaks, and provides a new interpretation for this fundamental feature of photoelectron spectra. We find the length of the circular pulse to be a vital factor in this selection rule and, employing an effective frequency, we show that the photoelectron OAM emission spectra are sensitive to the parity of the number of laser cycles. This work provides the basic theoretical framework with which to understand the OAM of a photoelectron undergoing strong field ionisation.

The 2021 ultrafast spectroscopic probes of condensed matter roadmap

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light-matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

Generation of necklace-shaped high harmonics in a two-color vortex field

We numerically studied gas high-harmonic generation in a two-color vortex laser field using the non-adiabatic Lewenstein model. Macroscopic responses were calculated by numerically solving the three-dimensional propagation equation in cylindrical coordinates. It was confirmed that unique high-harmonic signals with necklace-like shapes exhibit orbital angular momentum (OAM). The azimuthally distributed necklace harmonics exhibit periodic modulation as a function of laser frequency and topological charges of the driving field. Phase investigation showed that the OAM of the necklace harmonics is attributable to the tuning of the relative intensity of the two driving pulses. These findings provide a new dimension for high-harmonic manipulation in the vortex field. The two-color vortex field is the first scheme proposed for manipulating the intensity profile of high harmonics.

Manipulating twisted electrons in strong-field ionization

We investigate the discrete orbital angular momentum (OAM) of photoelectrons freed in strong-field ionization. We use these 'twisted' electrons to provide an alternative interpretation on existing experimental work of vortex interferences caused by strong field ionization mediated by two counter-rotating circularly polarized pulses separated by a delay. Using the strong field approximation, we derive an interference condition for the vortices. In computations for a neon target we find very good agreement of the vortex condition with photoelectron momentum distributions computed with the strong field approximation, as well as with the time-dependent methods Qprop and R-Matrix. For each of these approaches we examine the OAM of the photoelectrons, finding a small number of vortex states localized in separate energy regions. We demonstrate that the vortices arise from the interference of pairs of twisted electron states. The OAM of each twisted electron state can be directly related to the number of arms of the spiral in that region. We gain further understanding by recreating the vortices with pairs of twisted electrons and use this to determine a semiclassical relation for the OAM. A discussion is included on measuring the OAM in strong field ionization directly or by employing specific laser pulse schemes as well as utilizing the OAM in time-resolved imaging of photo-induced dynamics.

Switchable X-Ray Orbital Angular Momentum from an Artificial Spin Ice

Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in x-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a patterned topological defect, a double edge dislocation, imparts OAM to scattered x rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AFM) ground state. The topological charge of the defect differs with respect to the structural and magnetic order; thus, x-ray diffraction from the ASI produces photons with even and odd OAM quantum numbers at the structural and AFM Bragg conditions, respectively. The magnetic transitions of the ASI allow the AFM OAM beams to be switched on and off by modest variations of temperature and applied magnetic field. These results demonstrate ASIs can serve as metasurfaces for reconfigurable x-ray optics that could enable selective probes of electronic and magnetic properties.

Coherent Fourier scatterometry using orbital angular momentum beams for defect detection

Defect inspection on lithographic substrates, masks, reticles, and wafers is an important quality assurance process in semiconductor manufacturing. Coherent Fourier scatterometry (CFS) using laser beams with a Gaussian spatial profile is the standard workhorse routinely used as an in-line inspection tool to achieve high throughput. As the semiconductor industry advances toward shrinking critical dimensions in high volume manufacturing using extreme ultraviolet lithography, new techniques that enable high-sensitivity, high-throughput, and in-line inspection are critically needed. Here we introduce a set of novel defect inspection techniques based on bright-field CFS using coherent beams that carry orbital angular momentum (OAM). One of these techniques, the differential OAM CFS, is particularly unique because it does not rely on referencing to a pre-established database in the case of regularly patterned structures with reflection symmetry. The differential OAM CFS exploits OAM beams with opposite wavefront or phase helicity to provide contrast in the presence of detects. We numerically investigated the performance of these techniques on both amplitude and phase defects and demonstrated their superior advantages-up to an order of magnitude higher in signal-to-noise ratio-over the conventional Gaussian beam CFS. These new techniques will enable increased sensitivity and robustness for in-line nanoscale defect inspection and the concept could also benefit x-ray scattering and scatterometry in general.