Synthesis and characterization of attosecond light vortices in the extreme ultraviolet

Generation and applications of x-ray and extreme ultraviolet beams carrying orbital angular momentum

In addition to spin angular momentum, light can carry orbital angular momentum. The orbital angular momentum degree of freedom in the extreme ultraviolet and x-ray regimes enables fundamental studies of light-matter interactions and new methods to study materials. Advances in x-ray optics, as well as undulator radiation and high harmonic generation techniques, lead to the creation of beams with non-trivial phase structure, such as a helical phase structure, creating new possibilities for the use of extreme ultraviolet and x-ray photons with orbital angular momentum in probing complex electronic structures in matter. In this article, we review the generation and applications of orbital angular momentum beams in the x-ray and extreme ultraviolet regime. We discuss several recent works that exploit the orbital angular momentum degree of freedom and showcase the potential advantages of using these beams.

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.

Nonlinear post-compression of a hybrid vortex mode in a gas-filled capillary

We demonstrate nonlinear temporal compression of a vortex beam by propagation in a gas-filled capillary. Starting from an ytterbium-based laser delivering 700 μJ 640 fs pulses at a 100 kHz repetition rate, the vortex beam is generated using a spiral phase plate and coupled to a capillary where it excites a set of four modes that have an overlap integral of 97% with a Laguerre-Gauss LG10 mode. Nonlinear propagation of this hybrid, orbital angular momentum (OAM)-carrying mode results in temporal compression down to 74 fs at the output. Beam and pulse characterizations are carried out to determine the spatial profile and temporal duration of compressed pulses. This result in multimode nonlinear optics paves the way towards the generation of OAM-carrying few-cycle pulses, isolated attosecond XUV pulses, and tunable UV pulses through resonant dispersive wave emission.

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.

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.

High-order femtosecond vortices up to the 30th order generated from a powerful mode-locked Hermite-Gaussian laser

Femtosecond vortex beams are of great scientific and practical interest because of their unique phase properties in both the longitudinal and transverse modes, enabling multi-dimensional quantum control of light fields. Until now, generating femtosecond vortex beams for applications that simultaneously require ultrashort pulse duration, high power, high vortex order, and a low cost and compact laser source has been very challenging due to the limitations of available generation methods. Here, we present a compact apparatus that generates powerful high-order femtosecond vortex pulses via astigmatic mode conversion from a mode-locked Hermite-Gaussian Yb:KGW laser oscillator in a hybrid scheme using both the translation-based off-axis pumping and the angle-based non-collinear pumping techniques. This hybrid scheme enables the generation of femtosecond vortices with a continuously tunable vortex order from the 1st up to the 30th order, which is the highest order obtained from any femtosecond vortex laser source based on a mode-locked oscillator. The average powers and pulse durations of all resulting vortex pulses are several hundred milliwatts and <650 fs, respectively. In particular, 424-fs 11th-order vortex pulses have been achieved with an average power of 1.6 W, several times more powerful than state-of-the-art oscillator-based femtosecond vortex sources.

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.

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.

Entanglement of orbital angular momentum in non-sequential double ionization

Entanglement has a capacity to enhance imaging procedures, but this remains unexplored for attosecond imaging. Here, we elucidate that possibility, addressing orbital angular momentum (OAM) entanglement in ultrafast processes. In the correlated process non-sequential double ionization (NSDI) we demonstrate robust photoelectron entanglement. In contrast to commonly considered continuous variables, the discrete OAM allows for a simpler interpretation, computation, and measurement of entanglement. The logarithmic negativity reveals that the entanglement is robust to incoherence and an entanglement witness minimizes the number of measurements to detect the entanglement, both quantities are related to OAM coherence terms. We quantify the entanglement for a range of targets and field parameters to find the most entangled photoelectron pairs. This methodology provides a general way to use OAM to quantify and measure entanglement, well-suited to attosecond processes, and can be exploited to enhance imaging capabilities through correlated measurements, or for generation of OAM-entangled electrons.

In strong field ionization, entanglement between an electron and an ion has been discussed previously. Here the authors explore orbital angular momentum entanglement between the electrons released in non-sequential double ionization.

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.

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.

Enhancing circularly polarized XUV vortices from bicircular Laguerre-Gaussian fields

In this work, we theoretically study the generation of circularly polarized XUV vortices from high harmonic generation driven by bicircular Laguerre-Gaussian (LG) fields with different frequency ratios, by using the strong-field approximation theory. Our simulation shows that the amplitude of the generated vortices from the ω-3ω bicircular LG field is about one order of magnitude larger than that from the ω-2ω field, irrespective of the harmonic order and the orbital angular momentum of the bicircular driving fields. Our analysis shows that the great increase of the vortex amplitude for the ω-3ω field originates from the harmonic enhancement of a single atom. Furthermore, in terms of quantum-orbit theory, the underlying physics of the harmonic enhancement of the single atom for the ω-3ω field is revealed. Our work provides a simple and robust method to increase the amplitude of the circularly polarized XUV vortices.

Direct generation of ultrafast vortex beam from a Tm:CaYAlO4 oscillator featuring pattern matching of a folded-cavity resonator

Optical vortices, beams with spiral wavefronts and screw phase dislocations have been explored in applications in optical manipulation, quantum optics, and the next generation of optical communications. In traditional methods, optical vortices are generated using space light modulators or spiral phase plates, which would sharply decrease the integration of optical systems. Different from previous transverse mode conversion outside the cavity, here we experimentally demonstrate a direct generation of ultrafast vortex beam from a Tm:CaYAlO₄ oscillator by pattern matching of a six-mirror-folded-cavity resonator. By accurately adjusted the angle of the end mirror and the distance L between the M4 and the SESAMs to control the beam diameter of laser incidence on the gain medium in the sagittal and tangential planes, a stable 2 µm ultrafast vortex laser emission of annular Laguerre-Gaussian (LG) mode was obtained with a maximum output power of 327 mW and pulse duration of 2.1 ps. A simple YAG crystal plate was used as handedness selector and a homemade Mach-Zehnder (MZ) interferometer has verified the vortical property of the LG₀₁ mode. By furtherly controlling the cavity mode pattern matching, other stable transverse-mode operations for TEM₀₀, high-order Hermite-Gaussian (HG) transverse mode and doughnut-shaped beams were successfully realized. This work provides a flexible and reliable way to generate mid-infrared ultrafast vortex beams and is of special significance for applications in the areas of molecular spectroscopy and organic material processing amongst others.

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.

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.

Dense-code free space transmission by local demultiplexing optical states of a composed vortex

We describe an innovative data transmission scheme exploiting optical vortices to multiplex and demultiplex independent data channels in a standard asynchronous laser link. We report extensive results of the proof of concept of the method, successfully used to transmit two parallel ASCII strings, demultiplexed and decoded in the far field of the radiation beam. A phase locked two arms interferometer is proved to be effective even accessing a small portion of the beam only. Results prove the robustness and reliability of the method to perform dense-code free space transmissions over long distances even in presence of wavefront distortions. Applications and the extension to a larger number of parallel channels are discussed.

EUV and Hard X-ray Hartmann Wavefront Sensing for Optical Metrology, Alignment and Phase Imaging

For more than 15 years, Imagine Optic have developed Extreme Ultra Violet (EUV) and X-ray Hartmann wavefront sensors for metrology and imaging applications. These sensors are compatible with a wide range of X-ray sources: from synchrotrons, Free Electron Lasers, laser-driven betatron and plasma-based EUV lasers to High Harmonic Generation. In this paper, we first describe the principle of a Hartmann sensor and give some key parameters to design a high-performance sensor. We also present different applications from metrology (for manual or automatic alignment of optics), to soft X-ray source optimization and X-ray imaging.

Highly multimodal structure of high topological charge extreme ultraviolet vortex beams

Optical beams carrying orbital angular momentum are a very active field of research for their prospective applications, especially at short wavelengths. We consider here such beams produced through high-harmonic generation (HHG) in a rare gas and analyze the characterization of their high-charge vortex structure by an extreme ultraviolet Hartmann wavefront sensor. We show that such HHG beams are generally composed of a set of numerous vortex modes. The sensitivity of the intensity and phase of the HHG beam to the infrared laser aberrations is investigated using a deformable mirror.

Topological light fields for highly non-linear charge quantum dynamics and high harmonic generation

We study theoretically the electron quantum dynamics in atoms driven by intense IR laser pulses that are phase and/or polarization structured. The extremely non-linear electron dynamics causes high harmonic emission, which we calculate, analyze, and characterize. Results are presented for three different types of structured lasers: radially polarized and azimuthally polarized beams and optical skyrmions. We identify a topological index that is inherent to the driving pulse topology and is taken over by the high harmonics. All harmonics are found to have the same topological index. For vector IR pulses as driving fields, the far-field emitted beam tightens with a higher topological order and remains unchanged when the atom is driven by an optical skyrmion.

Generation of a mid-infrared femtosecond vortex beam from an optical parametric oscillator

Mid-infrared femtosecond vortex beams generated by optical parametric oscillators (OPO) are reported for the first time, to the best of our knowledge. Order-tunable femtosecond Hermite-Gauss beams from the first to sixth order are produced from a synchronously pumped OPO and then converted into the corresponding first through sixth-order femtosecond vortex beams by a cylindrical lens mode converter. By slightly tuning the cavity length, the wavelength of the vortex beam can be continuously tunable in the range from 2323 to 2382 nm, and the pulse duration can be changeable from ${\sim}{400}\;{\rm fs}$∼400fs to ${\sim}{1.1}\;{\rm ps}$∼1.1ps. The work provides a flexible and reliable way to generate mid-infrared femtosecond vortex beams, and is of special significance for expanding the wavelength range of femtosecond vortex beams and their application fields.

Intense attosecond pulses carrying orbital angular momentum using laser plasma interactions

Light beams with helical phase-fronts are known to carry orbital angular momentum (OAM) and provide an additional degree of freedom to beams of coherent light. While OAM beams can be readily derived from Gaussian laser beams with phase plates or gratings, this is far more challenging in the extreme ultra-violet (XUV), especially for the case of high XUV intensity. Here, we theoretically and numerically demonstrate that intense surface harmonics carrying OAM are naturally produced by the intrinsic dynamics of a relativistically intense circularly-polarized Gaussian beam (i.e. non-vortex) interacting with a target at normal incidence. Relativistic surface oscillations convert the laser pulses to intense XUV harmonic radiation via the well-known relativistic oscillating mirror mechanism. We show that the azimuthal and radial dependence of the harmonic generation process converts the spin angular momentum of the laser beam to orbital angular momentum resulting in an intense attosecond pulse (or pulse train) with OAM.

Vortices in light fields are of growing importance in the XUV and X-ray ranges. Here the authors show by simulations that high harmonics and attosecond pulses, generated while irradiating a deformed thin foil with circularly-polarized Gaussian laser pulses, carry a well-defined orbital angular momentum.

High-harmonic spectroscopy of transient two-center interference calculated with time-dependent density-functional theory

We demonstrate high-harmonic spectroscopy in many-electron molecules using time-dependent density-functional theory. We show that a weak attosecond-pulse-train ionization seed that is properly synchronized with the strong driving mid-infrared laser field can produce experimentally relevant high-harmonic generation (HHG) signals, from which we extract both the spectral amplitude and the target-specific phase (group delay). We also show that further processing of the HHG signal can be used to achieve molecular-frame resolution, i.e., to resolve the contributions from rescattering on different sides of an oriented molecule. In this framework, we investigate transient two-center interference in CO2 and OCS, and how subcycle polarization effects shape the oriented/aligned angle-resolved spectra.

Generation of extreme-ultraviolet beams with time-varying orbital angular momentum

Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. This class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.

Probing Molecular Chirality by Orbital-Angular-Momentum-Carrying X-ray Pulses

A twisted X-ray beam with orbital angular momentum is employed in a theoretical study to probe molecular chirality. A nonlocal response description of the matter-field coupling is adopted to account for the field short wavelength and the structured spatial profile. We use the minimal-coupling Hamiltonian, which implicitly takes into account the multipole contributions to all orders. The combined interactions of the spin and orbital angular momentum of the X-ray beam give rise to circular-helical dichroism signals, which are stronger than ordinary circular dichroism signals, and may serve as a useful tool for the study of molecular chirality in the X-ray regime.

Conservation of Torus-knot Angular Momentum in High-order Harmonic Generation

High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum J_{γ}, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations. We demonstrate that the charge J_{γ} of the emitted harmonics scales linearly with the harmonic order, and that this conservation law is imprinted onto the polarization distribution of the emitted spiral of attosecond pulses. We also demonstrate how the nonperturbative physics of high-order harmonic generation affect the torus-knot angular momentum of the harmonics, and we show that this configuration harnesses the spin selection rules to channel the full yield of each harmonic into a single mode of controllable orbital angular momentum.

Generation of terahertz vortex pulses without any need of manipulation in the terahertz region

Converting a Gaussian mode to a vortex beam is much more inconvenient in the terahertz (THz) region than in the near-infrared (NIR) region due to underdevelopment of THz components and strong THz diffraction. This Letter reports the direct generation of THz vortex pulses by optical difference-frequency between two NIR chirped pulses with different topological charges (TCs). By designing a passive and transmissive device for a collinear NIR pulse pair with conjugated TCs, we have experimentally obtained stable THz vortex pulses with a TC value of 2 or -2. The process needs no THz components and so is flexible to be realized and has promising applications in the THz field.

Spatio-temporal and spatiospectral metrology of terahertz broadband uniformly topologically charged vortex beams

A comprehensive characterization of the diffraction properties of terahertz (THz) pulsed broadband vortex beams consisting of several electromagnetic field oscillations requires state-of-the-art techniques for studying the evolution of a wavefront as it propagates. For this purpose, we have applied the capabilities offered by THz pulse time domain holography. Accurate metrological study of pulsed single-period THz field propagation allowed us to reveal the spatio-temporal and spatiospectral couplings in broadband uniformly topologically charged vortex beams. Here, we reveal dynamics of such beam propagation in a free space as well as in the experiment with edge diffraction with 50% blocking of the beam focal waist. In this study, we compare the dynamics of freely propagating and edge-diffracted THz vortex. Despite the fact that in the amplitude representation one can observe the emergence of strong asymmetry, analysis of the spectral trajectory of the singular point at some distance from the obstacle and the visualization of phase distribution for individual spectral components testify to the conservation of transverse energy circulation. Similar to the edge diffraction of monochromatic optical vortices, it can be interpreted as self-reconstruction of vortex properties. The given term has not previously been used for the case of pulsed broadband THz beams, to the best of our knowledge.

Orbital angular momentum from semiconductor high-order harmonics

Light beams carrying orbital angular momentum (OAM) have led to stunning applications in various fields from quantum information to microscopy. We examine OAM from the recently observed high-harmonic generation (HHG) in semiconductor crystals. HHG from solids could be a valuable approach for integrated high-flux short-wavelength coherent light sources. First, we verify the transfer and conservation of the OAM in the strong-field regime of interaction from the generation laser to the harmonics. Secondly, we create OAM beams by etching a spiral zone structure directly at the surface of a zinc oxide crystal. Such diffractive optics act on the generated harmonics and produces focused optical vortices with sub-micrometric size.

Conservation of orbital angular momentum for high harmonic generation of fractional vortex beams

This work demonstrates conservation of average orbital angular momentum for high harmonic generation of fractional vortex beams. High harmonics are generated in reflected light beams in a three-dimensional particle-in-cell simulation. The average orbital angular momentum of the beam is calculated when a relativistic linearly polarized fractional vortex beam impinges on a solid foil. The harmonic generation progress can be well explained by using the vortex oscillating mirror model. Both simulation and theoretical analysis show that the average orbital momentum of the nth harmonic is n times that of the fundamental frequency beam. This provides evidence that the average orbital angular momentum obeys momentum conservation during the harmonic generation of fractional vortex beams.

Hartmann wavefront sensor characterization of a high charge vortex beam in the extreme ultraviolet spectral range

We demonstrate for the first time, to the best of our knowledge, the ability of extreme ultraviolet (XUV) Hartmann wavefront sensors to characterize high charge vortex beams produced by high-order harmonic generation up to the order of 25. We also show that phase matched absorption limited high harmonic generation is able to maintain the high charge vortex structure of the XUV beam even in a rather long (1 cm) generation medium.

Orbital angular momentum symmetry in a driven optical parametric oscillator

We investigate the dynamics of a driven optical parametric oscillator under the injection of orbital angular momentum. The injected mode is adiabatically driven through arbitrary transformations on the Poincaré sphere of first-order paraxial beams. As a result, the down-converted beam conjugated to the seed is shown to follow a path imposed by a nontrivial symmetry on the Poincaré sphere. This symmetry allows controllable distinguishability between the spatial modes of the down-converted beams. In this Letter, we provide convincing experimental evidence of this effect.

Polarization-controlled orbital angular momentum switching in nonlinear wave mixing

We demonstrate polarization-controlled switching of the orbital angular momentum (OAM) transfer in nonlinear wave mixing. By adjusting the input beam geometry, we are able to produce a three-channel orbital OAM, with arbitrary topological charges simultaneously generated and spatially resolved in the second-harmonic wavelength. The use of path and polarization degrees of freedom allows nearly perfect optical switching between different OAM operations. These results are supported by a theoretical model showing very good agreement with the experiments.

Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin-orbit momentum conservation

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light-matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses-from linear to circular-and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin-orbit momentum conservation

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light-matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses-from linear to circular-and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

Tunable mid-infrared source of light carrying orbital angular momentum in the femtosecond regime

We report on a tunable intense femtosecond mid-infrared (mid-IR) light source carrying orbital angular momentum (OAM). Our setup is based on an optical parametric amplification system with an 800 nm pump shaped with a spiral phase plate. We confirm the anisotropic OAM transfer from the pump to the idler through stimulated difference frequency generation by measuring the diffraction patterns of a triangular aperture illuminated by the signal, pump, and idler beams. The tunability of the setup is demonstrated by performing measurements at 3.0 and 3.6 μm idler wavelengths. This result provides a robust method of controlling OAM in strong field physics and designing secondary sources carrying OAM in the extreme ultraviolet spectral range through high-order harmonics generation.

Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ω_λ with correlated linear phase (ϕ₀ ≥ 0.025 λ) and lateral shear (y₀ ≥ 0.05 ω_λ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

Controlling the orbital angular momentum of high harmonic vortices

Optical vortices, which carry orbital angular momentum (OAM), can be flexibly produced and measured with infrared and visible light. Their application is an important research topic for super-resolution imaging, optical communications and quantum optics. However, only a few methods can produce OAM beams in the extreme ultraviolet (XUV) or X-ray, and controlling the OAM on these beams remains challenging. Here we apply wave mixing to a tabletop high-harmonic source, as proposed in our previous work, and control the topological charge (OAM value) of XUV beams. Our technique enables us to produce first-order OAM beams with the smallest possible central intensity null at XUV wavelengths. This work opens a route for carrier-injected laser machining and lithography, which may reach nanometre or even angstrom resolution. Such a light source is also ideal for space communications, both in the classical and quantum regimes.

Few methods can produce orbital angular momentum beams in the extreme ultraviolet or X-ray, and controlling orbital angular momentum on these beams remains challenging. Here the authors apply wave mixing to a tabletop high-harmonic source and control the topological charge of extreme ultraviolet beams.

Tunable orbital angular momentum in high-harmonic generation

Optical vortices are currently one of the most intensively studied topics in optics. These light beams, which carry orbital angular momentum (OAM), have been successfully utilized in the visible and infrared in a wide variety of applications. Moving to shorter wavelengths may open up completely new research directions in the areas of optical physics and material characterization. Here, we report on the generation of extreme-ultraviolet optical vortices with femtosecond duration carrying a controllable amount of OAM. From a basic physics viewpoint, our results help to resolve key questions such as the conservation of angular momentum in highly nonlinear light-matter interactions, and the disentanglement and independent control of the intrinsic and extrinsic components of the photon's angular momentum at short-wavelengths. The methods developed here will allow testing some of the recently proposed concepts such as OAM-induced dichroism, magnetic switching in organic molecules and violation of dipolar selection rules in atoms.

Extreme Ultraviolet Fractional Orbital Angular Momentum Beams from High Harmonic Generation

We investigate theoretically the generation of extreme-ultraviolet (EUV) beams carrying fractional orbital angular momentum. To this end, we drive high-order harmonic generation with infrared conical refraction (CR) beams. We show that the high-order harmonic beams emitted in the EUV/soft x-ray regime preserve the characteristic signatures of the driving beam, namely ringlike transverse intensity profile and CR-like polarization distribution. As a result, through orbital and spin angular momentum conservation, harmonic beams are emitted with fractional orbital angular momentum, and they can be synthesized into structured attosecond helical beams –or “structured attosecond light springs”– with rotating linear polarization along the azimuth. Our proposal overcomes the state of the art limitations for the generation of light beams far from the visible domain carrying non-integer orbital angular momentum and could be applied in fields such as diffraction imaging, EUV lithography, particle trapping, and super-resolution imaging.

Interaction of Ultraintense Laser Vortices with Plasma Mirrors

Laser beams carrying orbital angular momentum (OAM) have found major applications in a variety of scientific fields, and their potential for ultrahigh-intensity laser-matter interactions has since recently been considered theoretically. We present an experiment where such beams interact with plasma mirrors up to laser intensities such that the motion of electrons in the laser field is relativistic. By measuring the spatial intensity and phase profiles of the high-order harmonics generated in the reflected beam, we obtain evidence for the helical wavefronts of the high-intensity laser at focus, and study the conservation of OAM in highly nonlinear optical processes at extreme laser intensities. The physical effects determining the field mode content of the twisted harmonic beams are elucidated.

Nonperturbative Twist in the Generation of Extreme-Ultraviolet Vortex Beams

High-order harmonic generation (HHG) has been recently proven to produce extreme-ultraviolet (XUV) vortices from the nonlinear conversion of infrared twisted beams. Previous works have demonstrated a linear scaling law of the vortex charge with the harmonic order. We demonstrate that this simple law hides an unexpectedly rich scenario for the buildup of orbital angular momentum (OAM) due to the nonperturbative behavior of HHG. The complexity of these twisted XUV beams appears only when HHG is driven by nonpure vortex modes, where the XUV OAM content is dramatically increased. We explore the underlying mechanisms for this diversity and derive a general conservation rule for the nonperturbative OAM buildup. The simple scaling found in previous works corresponds to the collapse of this scenario for the particular case of pure (single-mode) OAM driving fields.