Prediction of strong dichroism induced by x rays carrying orbital momentum

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.

Toward high-energy few-cycle optical vortices with minimized topological charge dispersion

A simple approach to generate high-energy few-cycle optical vortices with minimized topological charge dispersion is introduced. By means of numerical simulations, it is shown that, by leveraging the intrinsic properties of optical parametric chirped pulse amplification (OPCPA), clean transfer of topological charge from a high-energy narrowband pump pulse to a broadband idler is feasible under certain particular conditions, enabling the generation of high-energy few-cycle vortex pulses with extremely low topological charge dispersion.

Generation of superposed orbital angular momentum beams using a free-electron laser oscillator

With wavelength tunability, free-electron lasers (FELs) are well-suited for generating orbital angular momentum (OAM) beams in a wide photon energy range. We report here the first experimental demonstration of OAM beam generation using an oscillator FEL with the tens of picosecond pulse duration. Lasing around 458 nm, we have produced the four lowest orders of superposed Laguerre-Gaussian beams using a very long FEL resonator of 53.73 m. The produced beams have good beam quality, excellent stability, and substantial average power. We have also developed a pulsed operation mode for these beams with a highly reproducible temporal structure for a range of repetition rate of 1-30 Hz. This development can be extended to short wavelengths, for example to x-rays using a future x-ray FEL oscillator. The OAM operation of such a storage-ring FEL also paves the way for the generation of OAM gamma-ray beams via inverse Compton scattering.

Fundamental symmetry origins in the chiral interactions of optical vortices

Recently, a variety of mechanisms have been discovered that extend the range of optical techniques for identifying and characterizing molecular chirality, beyond those associated with optical polarization. It is now evident that beams of light with a twisted wavefront, known as optical vortices, can also interact with chiral matter with a specificity determined by relative handedness. Exploring this chiral sensitivity of vortex light in its interactions with matter requires careful consideration of the symmetry properties that engage in such processes. Most of the familiar measures of chirality are directly applicable to either matter, or to light itself-but only to one or the other. To elicit the principles that determine the viability of distinctly optical vortex-based forms of chiral discrimination invites a more universal approach to symmetry analysis, as is afforded by the common, fundamental physics of CPT symmetry. Taking this approach supports a comprehensive and straightforward analysis to identify the mechanistic origins of vortex chiroptical interactions. Careful inspection of selection rules for absorption also elicits the principles governing any identifiable engagement with vortex structures, providing a reliable basis to ascertain the viability of other forms of enantioselective vortex interaction.

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.

Highly efficient harmonic vortex generation from a laser irradiated hollow-cone target

It has been recently reported that ultraviolet harmonic vortices can be produced when a high-power circular-polarized laser pulse travels through a micro-scale waveguide. However, the harmonic generation quenches typically after a few tens of microns of propagation, due to the buildup of electrostatic potential that suppresses the amplitude of the surface wave. Here we propose to use a hollow-cone channel to overcome this obstacle. When traveling in a cone target, the laser intensity at the entrance is relatively low to avoid extracting too many electrons, while the slow focusing by the cone channel subsequently counters the established electrostatic potential, allowing the surface wave to maintain a high amplitude for a much longer distance. According to three-dimensional particle-in-cell simulations, the harmonic vortices can be produced with very high efficiency >20%. The proposed scheme paves the way for the development of powerful optical vortices sources in the extreme ultraviolet regime-an area of significant fundamental and applied physics potential.

Conservation of orbital angular momentum throughout amplification of high order harmonics in Ni-like krypton and silver plasmas

In this article we present modelling results of the amplification of High Order Harmonics (HOH) carrying orbital angular momentum (OAM) in plasma amplifiers created from krypton gas and silver solid targets. The resulting amplified beam is characterized in terms of intensity, phase and decomposition in helical and Laguerre-Gauss modes. Results show that the amplification process conserves OAM, although some degradation is apparent. Several structures appear in the intensity and phase profiles. These structures have been characterized with our model and related to refraction and interference with the plasma self-emission. Thus, these results not only demonstrate the capability of plasma amplifiers to deliver HOH amplified beams carrying OAM but also pave the way towards using HOH carrying OAM as a probe beam to diagnose the dynamics of hot, dense plasmas.

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).

Material-specific high-resolution table-top extreme ultraviolet microscopy

Microscopy with extreme ultraviolet (EUV) radiation holds promise for high-resolution imaging with excellent material contrast, due to the short wavelength and numerous element-specific absorption edges available in this spectral range. At the same time, EUV radiation has significantly larger penetration depths than electrons. It thus enables a nano-scale view into complex three-dimensional structures that are important for material science, semiconductor metrology, and next-generation nano-devices. Here, we present high-resolution and material-specific microscopy at 13.5 nm wavelength. We combine a highly stable, high photon-flux, table-top EUV source with an interferometrically stabilized ptychography setup. By utilizing structured EUV illumination, we overcome the limitations of conventional EUV focusing optics and demonstrate high-resolution microscopy at a half-pitch lateral resolution of 16 nm. Moreover, we propose mixed-state orthogonal probe relaxation ptychography, enabling robust phase-contrast imaging over wide fields of view and long acquisition times. In this way, the complex transmission of an integrated circuit is precisely reconstructed, allowing for the classification of the material composition of mesoscopic semiconductor systems.

Symmetry and Quantum Features in Optical Vortices

Optical vortices are beams of laser light with screw symmetry in their wavefront. With a corresponding azimuthal dependence in optical phase, they convey orbital angular momentum, and their methods of production and applications have become one of the most rapidly accelerating areas in optical physics and technology. It has been established that the quantum nature of electromagnetic radiation extends to properties conveyed by each individual photon in such beams. It is therefore of interest to identify and characterize the symmetry aspects of the quantized fields of vortex radiation that relate to the beam and become manifest in its interactions with matter. Chirality is a prominent example of one such aspect; many other facets also invite attention. Fundamental CPT symmetry is satisfied throughout the field of optics, and it plays significantly into manifestations of chirality where spatial parity is broken; duality symmetry between electric and magnetic fields is also involved in the detailed representation. From more specific considerations of spatial inversion, amongst which it emerges that the topological charge has the character of a pseudoscalar, other elements of spatial symmetry, beyond simple parity inversion, prove to repay additional scrutiny. A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables. The analysis supports a persistence in features of significance for the material interactions of vortex beams, which may indicate further scope for suitably tailored experimental design.

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.

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.

Electromagnetic chirality: from fundamentals to nontraditional chiroptical phenomena

Chirality arises universally across many different fields. Recent advancements in artificial nanomaterials have demonstrated chiroptical responses that far exceed those found in natural materials. Chiroptical phenomena are complicated processes that involve transitions between states with opposite parities, and solid interpretations of these observations are yet to be clearly provided. In this review, we present a comprehensive overview of the theoretical aspects of chirality in light, nanostructures, and nanosystems and their chiroptical interactions. Descriptions of observed chiroptical phenomena based on these fundamentals are intensively discussed. We start with the strong intrinsic and extrinsic chirality in plasmonic nanoparticle systems, followed by enantioselective sensing and optical manipulation, and then conclude with orbital angular momentum-dependent responses. This review will be helpful for understanding the mechanisms behind chiroptical phenomena based on underlying chiral properties and useful for interpreting chiroptical systems for further studies.

Generation and characterization of focused helical x-ray beams

The phenomenon of orbital angular momentum (OAM) affects a variety of important applications in visible optics, including optical tweezers, free-space communication, and 3D localization for fluorescence imaging. The lack of suitable wavefront shaping optics such as spatial light modulators has inhibited the ability to impart OAM on x-ray and electron radiation in a controlled way. Here, we report the experimental observation of helical soft x-ray beams generated by holographically designed diffractive optical elements. We demonstrate that these beams rotate as a function of propagation distance and measure their vorticity and coherent mode structure using ptychography. Our results establish an approach for controlling and shaping of complex focused beams for short wavelength scanning microscopy and OAM-driven applications.

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.

Refractive hard x-ray vortex phase plates

In this Letter, we report on the creation of hard x-ray beams carrying orbital angular momentum of topological charge -ℏ and -3ℏ at a photon energy of 8.2 keV via spiral phase plates made out of fused silica by ultrashort-pulsed laser ablation. The phase plates feature a smooth phase ramp with a 0.5 μm nominal step height and a surface roughness of 0.5 μm. The measured vortex beams show submicrometer-sized donut rings and agree well with numerical modeling. Fused silica phase plates are potentially suited to manipulate the electromagnetic field in highly intense x-ray beams at x-ray free-electron laser sources.

Torque of guided light on an atom near an optical nanofiber

We calculate analytically and numerically the axial orbital and spin torques of guided light on a two-level atom near an optical nanofiber. We show that the generation of these torques is governed by the angular momentum conservation law in the Minkowski formulation. The orbital torque on the atom near the fiber has a contribution from the average recoil of spontaneously emitted photons. Photon angular momentum and atomic spin angular momentum can be converted into atomic orbital angular momentum. The orbital and spin angular momenta of the guided field are not transferred separately to the orbital and spin angular momenta of the atom.

A unified formulation of dichroic signals using the Borrmann effect and twisted photon beams

Dichroic X-ray signals derived from the Borrmann effect and a twisted photon beam with topological charge l = 1 are formulated with an effective wavevector. The unification applies for non-magnetic and magnetic materials. Electronic degrees of freedom associated with an ion are encapsulated in multipoles previously used to interpret conventional dichroism and Bragg diffraction enhanced by an atomic resonance. A dichroic signal exploiting the Borrmann effect with a linearly polarized beam presents charge-like multipoles that include a hexadecapole. A difference between dichroic signals obtained with a twisted beam carrying spin polarization (circular polarization) and opposite winding numbers presents charge-like atomic multipoles, whereas a twisted beam carrying linear polarization alone presents magnetic (time-odd) multipoles. Charge-like multipoles include a quadrupole, and magnetic multipoles include a dipole and an octupole. We discuss the practicalities and relative merits of spectroscopy exploiting the two remarkably closely-related processes. Signals using beams with topological charges l ≥ 2 present additional atomic multipoles.

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.

Helical Phase Structure of Radiation from an Electron in Circular Motion

We theoretically show that a single free electron in circular motion radiates an electromagnetic wave possessing helical phase structure, which is closely related to orbital angular momentum carried by it. We experimentally demonstrate it by interference and double-slit diffraction experiments on radiation from relativistic electrons in spiral motion. Our results indicate that photons carrying orbital angular momentum should be created naturally by cyclotron/synchrotron radiations or Compton scatterings in various situations in cosmic space. We propose promising laboratory vortex photon sources in various wavelengths ranging from radio wave to gamma-rays.

Gamma-ray vortices from nonlinear inverse Thomson scattering of circularly polarized light

Inverse Thomson scattering is a well-known radiation process that produces high-energy photons both in nature and in the laboratory. Nonlinear inverse Thomson scattering occurring inside an intense light field is a process which generates higher harmonic photons. In this paper, we theoretically show that the higher harmonic gamma-ray produced by nonlinear inverse Thomson scattering of circularly polarized light is a gamma-ray vortex, which means that it possesses a helical wave front and carries orbital angular momentum. Our work explains a recent experimental result regarding nonlinear inverse Thomson scattering that clearly shows an annular intensity distribution as a remarkable feature of a vortex beam. Our work implies that gamma-ray vortices should be produced in various situations in astrophysics in which high-energy electrons and intense circularly polarized light fields coexist. Nonlinear inverse Thomson scattering is a promising radiation process for realizing a gamma-ray vortex source based on currently available laser and accelerator technologies, which would be an indispensable tool for exploring gamma-ray vortex science.

Angular Momentum of Twisted Radiation from an Electron in Spiral Motion

We theoretically demonstrate for the first time that a single free electron in circular or spiral motion emits twisted photons carrying well-defined orbital angular momentum along the axis of the electron circulation, in adding to spin angular momentum. We show that, when the electron velocity is relativistic, the radiation field contains harmonic components and the photons of lth harmonic carry lℏ total angular momentum for each. This work indicates that twisted photons are naturally emitted by free electrons and are more ubiquitous in laboratories and in nature than ever thought.

Influence of the photon orbital angular momentum on electric dipole transitions: negative experimental evidence

We describe an experiment of atomic spectroscopy devoted to ascertaining whether the orbital angular momentum (OAM) of photons has the same property of interacting with atoms or molecules as occurs for the spin angular momentum (SAM). In our experiment, rubidium vapors are excited by means of laser radiation with different combinations of OAM and SAM, particularly selected to inhibit or enhance the fluorescence according to the selection rules for the electric dipole transitions between the fundamental state and the first excited doublet. Our results clearly show that an electric-dipole-type transition is insensitive to the OAM value, and provide an original validation of a problem long debated in theoretical works.

Compton Scattered X-Gamma Rays with Orbital Momentum

We study the possibility of producing x-gamma rays with orbital angular momentum by means of the inverse Compton backscattering between a high brightness electron beam and a twisted laser pulse. We use the classical electrodynamics retarded fields for evaluating the orbital angular momentum of the radiation and connecting it to that of the primary laser pulse. We then propose the dimensioning of a linearly polarized x-ray source with orbital angular momentum, starting from the parameters of operating Thomson setups.

Synthesis and characterization of attosecond light vortices in the extreme ultraviolet

Infrared and visible light beams carrying orbital angular momentum (OAM) are currently thoroughly studied for their extremely broad applicative prospects, among which are quantum information, micromachining and diagnostic tools. Here we extend these prospects, presenting a comprehensive study for the synthesis and full characterization of optical vortices carrying OAM in the extreme ultraviolet (XUV) domain. We confirm the upconversion rules of a femtosecond infrared helically phased beam into its high-order harmonics, showing that each harmonic order carries the total number of OAM units absorbed in the process up to very high orders (57). This allows us to synthesize and characterize helically shaped XUV trains of attosecond pulses. To demonstrate a typical use of these new XUV light beams, we show our ability to generate and control, through photoionization, attosecond electron beams carrying OAM. These breakthroughs pave the route for the study of a series of fundamental phenomena and the development of new ultrafast diagnosis tools using either photonic or electronic vortices.

Twisted light beams have found several applications in the infrared and visible regime, but reaching the extreme ultraviolet has been difficult due to lack of sources. Here the authors report generation of helically shaped extreme ultraviolet trains of attosecond pulses via high harmonic generation.

Ultrafast optical vortex beam generation in the ultraviolet

We report on the generation of ultrafast vortex beams in the deep ultraviolet (DUV) wavelength range at 266 nm, for the first time to our knowledge. Using a Yb-fiber-based green source in combination with two spiral phase plates of orders 1 and 2, we were able to generate picosecond Laguerre-Gaussian (LG) beams at 532 nm. Subsequently, these LG beams were frequency doubled by single-pass, second-harmonic generation in a 10 mm-long β-BaB₂O₄ crystal to generate ultrafast vortex beams at 266 nm with a vortex order as high as 12, providing up to 383 mW of DUV power at a single-pass, green-to-DUV conversion efficiency of 5.2%. The generated picosecond UV vortex beam has a spectral width of 1.02 nm with a passive power stability better than 1.2% rms over >1.5  h.

Bragg–von Laue diffraction generalized to twisted X-rays

A pervasive limitation of nearly all practical X-ray methods for the determination of the atomic scale structure of matter is the need to crystallize the molecule, compound or alloy in a sufficiently large (∼10 × 10 × 10 µm) periodic array. In this paper an X-ray method applicable to structure determination of some important noncrystalline structures is proposed. It is designed according to a strict mathematical analog of von Laue's method, but replacing the translation group by another symmetry group, and simultaneously replacing plane waves by different exact closed-form solutions of Maxwell's equations. Details are presented for helical structures like carbon nanotubes or filamentous viruses. In computer simulations the accuracy of the determination of structure is shown to be comparable to the periodic case.

Creating high-harmonic beams with controlled orbital angular momentum

A beam with an angular-dependant phase Φ = ℓϕ about the beam axis carries an orbital angular momentum of ℓℏ per photon. Such beams are exploited to provide superresolution in microscopy. Creating extreme ultraviolet or soft-x-ray beams with controllable orbital angular momentum is a critical step towards extending superresolution to much higher spatial resolution. We show that orbital angular momentum is conserved during high-harmonic generation. Experimentally, we use a fundamental beam with |ℓ| = 1 and interferometrically determine that the harmonics each have orbital angular momentum equal to their harmonic number. Theoretically, we show how any small value of orbital angular momentum can be coupled to any harmonic in a controlled manner. Our results open a route to microscopy on the molecular, or even submolecular, scale.

Attosecond extreme ultraviolet vortices from high-order harmonic generation

We present a theoretical study of high-order harmonic generation (HHG) and propagation driven by an infrared field carrying orbital angular momentum (OAM). Our calculations unveil the following relevant phenomena: extreme-ultraviolet harmonic vortices are generated and survive to the propagation effects, vortices transport high-OAM multiples of the corresponding OAM of the driving field and, finally, the different harmonic vortices are emitted with similar divergence. We also show the possibility of combining OAM and HHG phase locking to produce attosecond pulses with helical pulse structure.

First observation of photons carrying orbital angular momentum in undulator radiation

Photon beams of 99 eV energy carrying orbital angular momentum (OAM) have been observed in the 2nd harmonic off-axis radiation of a helical undulator at the 3rd generation synchrotron radiation light source BESSY II. For detection, the OAM carrying photon beam was superimposed with a reference beam without OAM. The interference pattern, a spiral intensity distribution, was recorded in a plane perpendicular to the propagation direction. The orientation of the observed spiral structure is related to the helicity of the undulator radiation. Excellent agreement between measurements and simulations has been found.

Echo-enabled x-ray vortex generation

A technique to generate high-brightness electromagnetic vortices with tunable topological charge at extreme ultraviolet and x-ray wavelengths is described. Based on a modified version of echo-enabled harmonic generation for free-electron lasers, the technique uses two lasers and two chicanes to produce high-harmonic microbunching of a relativistic electron beam with a corkscrew distribution that matches the instantaneous helical phase structure of the x-ray vortex. The strongly correlated electron distribution emerges from an efficient three-dimensional recoherence effect in the echo-enabled harmonic generation transport line and can emit fully coherent vortices in a downstream radiator for access to new research in x-ray science.

Generation of extreme ultraviolet vortex beams using computer generated holograms

We fabricate computer generated holograms for the generation of phase singularities at extreme ultraviolet (EUV) wavelengths using electron beam lithography and demonstrate their ability to generate optical vortices in the nonzero diffraction orders. To this end, we observe the characteristic intensity distribution of the vortex beam and verify the helical phase structure interferometrically. The presented method forms the basis for further studies on singular light fields in the EUV frequency range, i.e., in EUV interference lithography. Since the method is purely achromatic, it may also find applications in various fields of x ray optics.

Generating optical orbital angular momentum in a high-gain free-electron laser at the first harmonic

A scheme to generate intense coherent light that carries orbital angular momentum (OAM) at the fundamental wavelength of an x-ray free-electron laser (FEL) is described. The OAM light is emitted as the dominant mode of the system until saturation provided that the helical microbunching imposed on the electron beam is larger than the shot-noise bunching that leads to self-amplified emission. Operating at the fundamental, this scheme is more efficient than alternate schemes that rely on harmonic emission, and can be applied to x-ray FELs without using external optical mode conversion elements.

Photoionization with orbital angular momentum beams

Intense laser ionization expands Einstein's photoelectric effect rules giving a wealth of phenomena widely studied over the last decades. In all cases, so far, photons were assumed to carry one unit of angular momentum. However it is now clear that photons can possess extra angular momentum, the orbital angular momentum (OAM), related to their spatial profile. We show a complete description of photoionization by OAM photons, including new selection rules involving more than one unit of angular momentum. We explore theoretically the interaction of a single electron atom located at the center of an intense ultraviolet beam bearing OAM, envisaging new scenarios for quantum optics.

Proposal for generating brilliant x-ray beams carrying orbital angular momentum

We consider use of a variable polarizing undulator for generating brilliant x-ray beams carrying orbital angular momentum. We find that higher harmonics of the radiation correspond to Laguerre-Gaussian modes with azimuthal mode indices l equal to one less than the harmonic number when the undulator is operated to produce circularly polarized light. Beams with nonzero l carry orbital angular momentum quantized in units of lvariant Planck's over 2pi per photon. When operated to produce linear polarization, the harmonics correspond to Hermite-Gaussian modes. Selection of these modes with conventional monochromator optics opens the door for new research with x-ray synchrotron and free-electron laser sources.