Production and application of electron vortex beams

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.

Optical vortex-antivortex crystallization in free space

Stable vortex lattices are basic dynamical patterns which have been demonstrated in physical systems including superconductor physics, Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV) ensembles can be produced, self-organizing into the respective polar lattices. However, these structures are in general highly unstable due to the strong VAV attraction. Here, we demonstrate that multiple optical VAV clusters nested in the propagating coherent field can crystallize into patterns which preserve their lattice structures over distance up to several Rayleigh lengths. To explain this phenomenon, we present a model for effective interactions between the vortices and antivortices at different lattice sites. The observed VAV crystallization is a consequence of the globally balanced VAV couplings. As the crystallization does not require the presence of nonlinearities and appears in free space, it may find applications to high-capacity optical communications and multiparticle manipulations. Our findings suggest possibilities for constructing VAV complexes through the orbit-orbit couplings, which differs from the extensively studied spin-orbit couplings.

Structured electrons with chiral mass and charge

Chirality is a phenomenon with widespread relevance in fundamental physics, material science, chemistry, optics, and spectroscopy. In this work, we show that a free electron can be converted by the field cycles of laser light into a right-handed or left-handed coil of mass and charge. In contrast to phase-vortex beams, our electrons maintained a flat de Broglie wave but obtained their chirality from the shape of their expectation value in space and time. Measurements of wave function densities by attosecond gating revealed the three-dimensional shape of coils and double coils with left-handed or right-handed pitch. Engineered elementary particles with such or related chiral geometries should be useful for applications in chiral sensing, free-electron quantum optics, particle physics or electron microscopy.

Strongly correlated multielectron bunches from interaction with quantum light

Strongly correlated electron systems are a cornerstone of modern physics, being responsible for groundbreaking phenomena from superconducting magnets to quantum computing. In most cases, correlations in electrons arise exclusively because of Coulomb interactions. In this work, we reveal that free electrons interacting simultaneously with a light field can become highly correlated via mechanisms beyond Coulomb interactions. In the case of two electrons, the resulting Pearson correlation coefficient for the joint probability distribution of the output electron energies is enhanced by more than 13 orders of magnitude compared to that of electrons interacting with the light field in succession (one after another). These highly correlated electrons are the result of momentum and energy exchange between the participating electrons via the external quantum light field. Our findings pave the way to the creation and control of highly correlated free electrons for applications including quantum information and ultrafast imaging.

Visualizing a single wavefront dislocation induced by orbital angular momentum in graphene

Phase singularities are phase-indeterminate points where wave amplitudes are zero, which manifest as phase vertices or wavefront dislocations. In the realm of optical and electron beams, the phase singularity has been extensively explored, demonstrating a profound connection to orbital angular momentum. Direct local imaging of the impact of orbital angular momentum on phase singularities at the nanoscale, however, remains challenging. Here, we study the role of orbital angular momentum in phase singularities in graphene, particularly at the atomic level, through scanning tunneling microscopy and spectroscopy. Our experiments demonstrate that the scatterings between different orbital angular momentum states, which are induced by local rotational symmetry-breaking potentials, can generate additional phase singularities, and result in robust single-wavefront dislocations in real space. Our results pave the way for exploring the effects of orbital degree of freedom on quantum phases in quasiparticle interference processes.

Manipulation of optical orbit-induced localized spin angular momentum using the periodic edge dislocation

Orbit-induced localized spin angular momentum (OILS) has recently garnered significant attention. This paper introduces periodic edge dislocation (PED) into the tight focusing system. The study delves into the tight focusing characteristics of the radially polarized vortex plane beam with PED, demonstrating that PED serves as a straightforward and effective means of manipulating OILS, especially when both the orbital angular momentum and the polarization of the incident beam are fixed. Our findings indicate that the longitudinal OILS reaches its maximum when the difference between the period of PED and the vortex topological charge is equal to 1. Conversely, when the difference is 0, the transverse OILS reaches its maximum, while the longitudinal OILS reaches its minimum. Similar patterns are also observed in linearly polarized vortex beams. This research proposes a simple and practical way to control OILS, contributing to our understanding of optical orbit-spin coupling.

Free-electron crystals for enhanced X-ray radiation

Bremsstrahlung-the spontaneous emission of broadband radiation from free electrons that are deflected by atomic nuclei-contributes to the majority of X-rays emitted from X-ray tubes and used in applications ranging from medical imaging to semiconductor chip inspection. Here, we show that the bremsstrahlung intensity can be enhanced significantly-by more than three orders of magnitude-through shaping the electron wavefunction to periodically overlap with atoms in crystalline materials. Furthermore, we show how to shape the bremsstrahlung X-ray emission pattern into arbitrary angular emission profiles for purposes such as unidirectionality and multi-directionality. Importantly, we find that these enhancements and shaped emission profiles cannot be attributed solely to the spatial overlap between the electron probability distribution and the atomic centers, as predicted by the paraxial and non-recoil theory for free electron light emission. Our work highlights an unprecedented regime of free electron light emission where electron waveshaping provides multi-dimensional control over practical radiation processes like bremsstrahlung. Our results pave the way towards greater versatility in table-top X-ray sources and improved fundamental understanding of quantum electron-light interactions.

Generation of a terahertz quasi-Pearcey beam and its investigation in ptychography

The terahertz structured beams played a significant role in imaging. We utilized the transmitter with 0.1 THz to generate the quasi-Pearcey beam. The beam is produced by combining the self-designed parabola-slit modulated plate and Fourier lens, showing stripe-shaped pattern and self-focusing property. Based on that, introducing it into the testing of ptychography, we discovered there are decent effects in field reconstruction of the probe and sample with this beam by comparisons both in the simulations and the experiments. The beam has good spatial coherence through the analysis of the spatial frequency spectrums. It suggests that the beam with such features can take advantage of rapid reconstruction in full-field imaging.

Cathodoluminescence Nanoscopy: State of the Art and Beyond

Cathodoluminescence (CL) nanoscopy is proven to be a powerful tool to explore nanoscale optical properties, whereby free electron beams achieve a spatial resolution far beyond the diffraction limit of light. With developed methods for the control of electron beams and the collection of light, the dimension of information that CL can access has been expanded to include polarization, momentum, and time, holding promise to provide invaluable insights into the study of materials and optical near-field dynamics. With a focus on the burgeoning field of CL nanoscopy, this perspective outlines the recent advancements and applications of this technique, as illustrated by the salient experimental works. In addition, as an outlook for future research, several appealing directions that may bring about developments and discoveries are highlighted.

Optical polarization analogs in inelastic free-electron scattering

Advances in the ability to manipulate free-electron phase profiles within the electron microscope have spurred development of quantum-mechanical descriptions of electron energy loss (EEL) processes involving transitions between phase-shaped transverse states. Here, we elucidate an underlying connection between two ostensibly distinct optical polarization analogs identified in EEL experiments as manifestations of the same conserved scattering flux. Our work introduces a procedure for probing general tensorial target characteristics including global mode symmetries and local polarization.

Design of Electrostatic Aberration Correctors for Scanning Transmission Electron Microscopy

In a scanning transmission electron microscope (STEM), producing a high-resolution image generally requires an electron beam focused to the smallest point possible. However, the magnetic lenses used to focus the beam are unavoidably imperfect, introducing aberrations that limit resolution. Modern STEMs overcome this by using hardware aberration correctors comprised of many multipole elements, but these devices are complex, expensive, and can be difficult to tune. We demonstrate a design for an electrostatic phase plate that can act as an aberration corrector. The corrector is comprised of annular segments, each of which is an independent two-terminal device that can apply a constant or ramped phase shift to a portion of the electron beam. We show the improvement in image resolution using an electrostatic corrector. Engineering criteria impose that much of the beam within the probe-forming aperture be blocked by support bars, leading to large probe tails for the corrected probe that sample the specimen beyond the central lobe. We also show how this device can be used to create other STEM beam profiles such as vortex beams and probes with a high degree of phase diversity, which improve information transfer in ptychographic reconstructions.

Generation of femtosecond optical vortices with multiple separate phase singularities from a Kerr-lens mode-locked Yb:KGW oscillator

Femtosecond optical vortices with a phase singular point have diverse applications such as microscopic particles manipulation, special-structure micro-processing and quantum information. Raising the number of singularity points can provide additional dimensions of control. Here we report for what we believe is the first time the generation of femtosecond optical vortices with multiple (two and five) singularities directly from a laser oscillator. The average powers and pulse durations of the resulting vortex pulses are several hundred milliwatts and less than 300 fs, respectively. This work represents an innovate way for obtaining femtosecond multi-vortices, opening the way to the further studies of optical vortex crystals and their applications.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Direct prediction and compensation of atmospheric turbulence for free-space integer and fractional order OAM multiplexed transmission links

Atmospheric turbulence has an adverse impact on orbital angular momentum (OAM) beam transmission, resulting in power fluctuations and mode crosstalk. These challenges are particularly pronounced in OAM multiplexing links. In this paper, we propose and demonstrate a novel network architecture that integrates convolutional layers and residual structures to address the issue of turbulence phase compensation. By harnessing the local feature learning capability of convolutional layers and the information-preserving function of residual structures, we aim to mitigate the adverse effects of network depth on information loss. By employing the proposed network, we compensate the turbulence phase directly using the received intensity distributions for free space multiplexed integer and fractional order OAM links, respectively. The obtained results show that the received optical power can be improved for more than 10 dB for integer order OAM multiplexed FSO links under weak to strong turbulence conditions, while 9 dB for fractional-order OAM multiplexed FSO links. Moreover, mode crosstalk can be reduced for about 10 dB under 4 OAM modes multiplexed links under turbulence strength D/r0=5. The proposed deep learning based atmospheric turbulence compensation method can predict phase screens rapidly and accurately, thus enhancing the dependability of future OAM multiplexing technology.

Topologically crafted spatiotemporal vortices in acoustics

Vortices in fluids and gases have piqued the human interest for centuries. Development of classical-wave physics and quantum mechanics highlighted wave vortices characterized by phase singularities and topological charges. In particular, vortex beams have found numerous applications in modern optics and other areas. Recently, optical spatiotemporal vortex states exhibiting the phase singularity both in space and time have been described. Here, we report the topologically robust generation of acoustic spatiotemporal vortex pulses. We utilize an acoustic meta-grating with broken mirror symmetry which exhibits a topological phase transition with a pair of phase singularities with opposite topological charges emerging in the momentum-frequency domain. We show that these vortices are topologically robust against structural perturbations of the meta-grating and can be employed for the generation of spatiotemporal vortex pulses. Our work paves the way for studies and applications of spatiotemporal structured waves in acoustics and other wave systems.

Optical vortices shape optical tornados

We demonstrate that by seeding an accelerating ring-Airy beam with a finite number of off-axis optical vortices, it transforms into a tornado wave (ToW) upon propagation. Using numerical simulations, we show that both the spiraling high-intensity lobes and the optical vortices exhibit angular acceleration and follow interwinding braid-like trajectories. Likewise, we study the effect of the number, position, and topological charge of the vortices on the propagation dynamics and reveal the connection between optical vortices and optical tornados.

Defect Contrast with 4D-STEM: Understanding Crystalline Order with Virtual Detectors and Beam Modification

Material properties strongly depend on the nature and concentration of defects. Characterizing these features may require nano- to atomic-scale resolution to establish structure-property relationships. 4D-STEM, a technique where diffraction patterns are acquired at a grid of points on the sample, provides a versatile method for highlighting defects. Computational analysis of the diffraction patterns with virtual detectors produces images that can map material properties. Here, using multislice simulations, we explore different virtual detectors that can be applied to the diffraction patterns that go beyond the binary response functions that are possible using ordinary STEM detectors. Using graphene and lead titanate as model systems, we investigate the application of virtual detectors to study local order and in particular defects. We find that using a small convergence angle with a rotationally varying detector most efficiently highlights defect signals. With experimental graphene data, we demonstrate the effectiveness of these detectors in characterizing atomic features, including vacancies, as suggested in simulations. Phase and amplitude modification of the electron beam provides another process handle to change image contrast in a 4D-STEM experiment. We demonstrate how tailored electron beams can enhance signals from short-range order and how a vortex beam can be used to characterize local symmetry.

Quantum Interference between Fundamentally Different Processes Is Enabled by Shaped Input Wavefunctions

This work presents a general framework for quantum interference between processes that can involve different fundamental particles or quasi-particles. This framework shows that shaping input wavefunctions is a versatile and powerful tool for producing and controlling quantum interference between distinguishable pathways, beyond previously explored quantum interference between indistinguishable pathways. Two examples of quantum interference enabled by shaping in interactions between free electrons, bound electrons, and photons are presented: i) the vanishing of the zero-loss peak by destructive quantum interference when a shaped electron wavepacket couples to light, under conditions where the electron's zero-loss peak otherwise dominates; ii) quantum interference between free electron and atomic (bound electron) spontaneous emission processes, which can be significant even when the free electron and atom are far apart, breaking the common notion that a free electron and an atom must be close by to significantly affect each other's processes. Conclusions show that emerging quantum wave-shaping techniques unlock the door to greater versatility in light-matter interactions and other quantum processes in general.

Generation of Perfect Electron Vortex Beam with a Customized Beam Size Independent of Orbital Angular Momentum

The electron vortex beam (EVB)-carrying quantized orbital angular momentum (OAM) plays an essential role in a series of fundamental research. However, the radius of the transverse intensity profile of a doughnut-shaped EVB strongly depends on the topological charge of the OAM, impeding its wide applications in electron microscopy. Inspired by the perfect vortex in optics, herein, we demonstrate a perfect electron vortex beam (PEVB), which completely unlocks the constraint between the beam size and the beam's OAM. We design nanoscale holograms to generate PEVBs carrying different quanta of OAM but exhibiting almost the same beam size. Furthermore, we show that the beam size of the PEVB can be readily controlled by only modifying the design parameters of the hologram. The generation of PEVB with a customized beam size independent of the OAM can promote various in situ applications of free electrons carrying OAM in electron microscopy.

Tunable photon-induced spatial modulation of free electrons

Spatial modulation of electron beams is an essential tool for various applications such as nanolithography and imaging, yet its conventional implementations are severely limited and inherently non-tunable. Conversely, proposals of light-driven electron spatial modulation promise tunable electron wavefront shaping, for example, using the mechanism of photon-induced near-field electron microscopy. Here we present tunable photon-induced spatial modulation of electrons through their interaction with externally controlled surface plasmon polaritons (SPPs). Using recently developed methods of shaping SPP patterns, we demonstrate a dynamic control of the electron beam with a variety of electron distributions and verify their coherence through electron diffraction. Finally, the nonlinearity stemming from energy post-selection provides us with another avenue for controlling the electron shape, generating electron features far below the SPP wavelength. Our work paves the way to on-demand electron wavefront shaping at ultrafast timescales, with prospects for aberration correction, nanofabrication and material characterization.

Entangling free electrons and optical excitations

The inelastic interaction between flying particles and optical nanocavities gives rise to entangled states in which some excitations of the latter are paired with momentum changes in the former. Specifically, free-electron entanglement with nanocavity modes opens appealing opportunities associated with the strong interaction capabilities of the electrons. However, the achievable degree of entanglement is currently limited by the lack of control over the resulting state mixtures. Here, we propose a scheme to generate pure entanglement between designated optical-cavity excitations and separable free-electron states. We shape the electron wave function profile to select the accessible cavity modes and simultaneously associate them with targeted electron scattering directions. This concept is exemplified through theoretical calculations of free-electron entanglement with degenerate and nondegenerate plasmon modes in silver nanoparticles and atomic vibrations in an inorganic molecule. The generated entanglement can be further propagated through its electron component to extend quantum interactions beyond existing protocols.

High purity orbital angular momentum of light

We present a novel technique for generating beams of light carrying orbital angular momentum (OAM) that increases mode purity and decreases singularity splitting by orders of magnitude. This technique also works to control and mitigate beam divergence within propagation distances less than the Rayleigh length. Additionally, we analyze a tunable parameter of this technique that can change the ratio of beam purity to power to fit desired specifications. Beam generation via this technique is achievable using only phase-modulating optical elements, which reduces experimental complexity and beam energy loss.

Ultrafast Transverse Modulation of Free Electrons by Interaction with Shaped Optical Fields

Spatiotemporal electron-beam shaping is a bold frontier of electron microscopy. Over the past decade, shaping methods evolved from static phase plates to low-speed electrostatic and magnetostatic displays. Recently, a swift change of paradigm utilizing light to control free electrons has emerged. Here, we experimentally demonstrate arbitrary transverse modulation of electron beams without complicated electron-optics elements or material nanostructures, but rather using shaped light beams. On-demand spatial modulation of electron wavepackets is obtained via inelastic interaction with transversely shaped ultrafast light fields controlled by an external spatial light modulator. We illustrate this method for the cases of Hermite-Gaussian and Laguerre-Gaussian modulation and discuss their use in enhancing microscope sensitivity. Our approach dramatically widens the range of patterns that can be imprinted on the electron profile and greatly facilitates tailored electron-beam shaping.

Twisted Magnon Frequency Comb and Penrose Superradiance

Quantization effects of the nonlinear magnon-vortex interaction in ferromagnetic nanodisks are studied. We show that the circular geometry twists the spin-wave fields with spiral phase dislocations carrying quantized orbital angular momentum (OAM). Meanwhile, the confluence and splitting scattering of twisted magnons off the gyrating vortex core (VC) generates a frequency comb consisting of discrete and equally spaced spectral lines, dubbed as twisted magnon frequency comb (TMFC). It is found that the mode spacing of the TMFC is equal to the gyration frequency of the VC and the OAM quantum numbers between adjacent spectral lines differ by one. By applying a magnetic field perpendicular to the plane of a thick nanodisk, we observe a magnonic Penrose superradiance inside the cone vortex state, which mimics the amplification of particles scattered from a rotating black hole. It is demonstrated that the higher-order modes of TMFC are significantly amplified while the lower-order ones are trapped within the VC gyrating orbit which manifests as the ergoregion. These results suggest a promising way to generate twisted magnons with large OAM and to drastically improve the flatness of the magnon comb.

The Longitudinal Plasma Modes of κ-Deformed Kaniadakis Distributed Plasmas Carrying Orbital Angular Momentum

Based on plasma kinetic theory, the dispersion and Landau damping of Langmuir and ion-acoustic waves carrying finite orbital angular momentum (OAM) were investigated in the κ-deformed Kaniadakis distributed plasma system. The results showed that the peculiarities of the investigated subjects relied on the deformation parameter κ and OAM parameter η. For both Langmuir and ion-acoustic waves, dispersion was enhanced with increased κ, while the Landau damping was suppressed. Conversely, both the dispersion and Landau damping were depressed by OAM. Moreover, the results coincided with the straight propagating plane waves in a Maxwellian plasma system when κ=0 and η→∞. It was expected that the present results would give more insight into the trapping and transportation of plasma particles and energy.

Tailoring electron beams with high-frequency self-assembled magnetic charged particle micro optics

Tunable electromagnets and corresponding devices, such as magnetic lenses or stigmators, are the backbone of high-energy charged particle optical instruments, such as electron microscopes, because they provide higher optical power, stability, and lower aberrations compared to their electric counterparts. However, electromagnets are typically macroscopic (super-)conducting coils, which cannot generate swiftly changing magnetic fields, require active cooling, and are structurally bulky, making them unsuitable for fast beam manipulation, multibeam instruments, and miniaturized applications. Here, we present an on-chip microsized magnetic charged particle optics realized via a self-assembling micro-origami process. These micro-electromagnets can generate alternating magnetic fields of about ±100 mT up to a hundred MHz, supplying sufficiently large optical power for a large number of charged particle optics applications. That particular includes fast spatiotemporal electron beam modulation such as electron beam deflection, focusing, and wave front shaping as required for stroboscopic imaging.

Electron beam manipulation is important for their application in microscopes, lithography instruments, and colliders. Here the authors report a wafer scale, self-assembled, microcoil electrically-driven magnetic charge particle optic device that can be implemented into different configurations for controlling of electron beams.

Molecular Free Electron Vortices in Photoionization by Polarization-Tailored Ultrashort Laser Pulses

Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.

Nuclear Excitation by Electron Capture in Excited Ions

A nuclear excitation following the capture of an electron in an empty orbital has been recently observed for the first time. So far, the evaluation of the cross section of the process has been carried out widely using the assumption that the ion is in its electronic ground state prior to the capture. We show that by lifting this restriction new capture channels emerge resulting in a boost of more than three orders of magnitude to the electron capture resonance strength.

Dynamical Control of Nuclear Isomer Depletion via Electron Vortex Beams

Some nuclear isomers are known to store a large amount of energy over long periods of time, with a very high energy-to-mass ratio. Here, we describe a protocol to achieve the external control of the isomeric nuclear decay by using electron vortex beams whose wave function has been especially designed and reshaped on demand. Recombination of these electrons into the isomer's atomic shell can lead to the controlled release of the stored nuclear energy. On the example of ^{93m}Mo, we show theoretically that the use of tailored electron vortex beams increases the depletion by 4 orders of magnitude compared to the spontaneous nuclear decay of the isomer. Furthermore, specific orbitals can sustain an enhancement of the recombination cross section for vortex electron beams by as much as 6 orders of magnitude, providing a handle for manipulating the capture mechanism. These findings open new prospects for controlling the interplay between atomic and nuclear degrees of freedom, with potential energy-related and high-energy radiation source applications.

Principles of electron wave front modulation with two miniature electron mirrors

We have analyzed the possibilities of wave front shaping with miniature patterned electron mirrors through the WKB approximation. Based on this, we propose a microscopy scheme that uses two miniature electron mirrors on an auxiliary optical axis that is in parallel with the microscope axis. A design for this microscopy scheme is presented for which the two axes can be spatially separated by as little as 1 mm. We first provide a mathematical relationship between the electric potential and the accumulated phase modulation of the reflected electron wave front using the WKB approximation. Next, we derive the electric field in front of the mirror, as a function of a topographic or pixel wise excited mirror pattern. With this, we can relate the effect of a mirror pattern onto the near-field phase, or far field intensity distribution and use this to provide a first optical insight into the functioning of the patterned mirror. The equations can only be applied numerically, for which we provide a description of the relevant numerical methods. Finally, these methods are applied to find mirror patterns for controlled beam diffraction efficiency, beam mode conversion, and an arbitrary phase and amplitude distribution. The successful realization of the proposed methods would enable arbitrary shaping of the wave front without electron-matter interaction, and hence we coin the term virtual phase plate for this design. The design may also enable the experimental realization of a Mach-Zehnder interferometer for electrons, as well as interaction-free measurements of radiation sensitive specimen.

SEM Nano: An Electron Wave Optical Simulation for the Scanning Electron Microscope

The simulation program “SEM Nano” is introduced to explain and visualize probe formation in field-emission scanning electron microscopes (SEMs). The program offers an easy and intuitive graphical user interface (GUI) to provide input in terms of understandable SEM parameters and visualization of the output. The simulations are based on wave optics treatment of the electron beam in the SEM column. Based on input parameters provided by the user, the spatial intensity distribution of electrons is calculated at the specimen by incorporating the effects of diffraction, aberrations, coherence, and noise. Given the specimen structure signal (So), the program has the capability to produce an image of the specimen using the electron probe intensity distribution. Finally, a feature is provided to reconstruct the electron probe intensity from the noisy image using a Wiener filter-based deconvolution.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Shaping of Electron Beams Using Sculpted Thin Films

Electron beam shaping by sculpted thin films relies on electron-matter interactions and the wave nature of electrons. It can be used to study physical phenomena of special electron beams and to develop technological applications in electron microscopy that offer new and improved measurement techniques and increased resolution in different imaging modes. In this Perspective, we review recent applications of sculpted thin films for electron orbital angular momentum sorting, improvements in phase contrast transmission electron microscopy, and aberration correction. For the latter, we also present new results of our work toward correction of the spherical aberration of Lorentz scanning transmission electron microscopes and suggest a method to correct chromatic aberration using thin films. This review provides practical insight for researchers in the field and motivates future progress in electron microscopy.

Parameterization of magnetic vector potentials and fields for efficient multislice calculations of elastic electron scattering

The multislice method, which simulates the propagation of the incident electron wavefunction through a crystal, is a well established method for analysing the multiple scattering effects that an electron beam may undergo. The inclusion of magnetic effects into this method proves crucial towards simulating enhanced magnetic interaction of vortex beams with magnetic materials, calculating magnetic Bragg spots or searching for magnon signatures, to name a few examples. Inclusion of magnetism poses novel challenges to the efficiency of the multislice method for larger systems, especially regarding the consistent computation of magnetic vector potentials A and magnetic fields B over large supercells. This work presents a tabulation of parameterized magnetic (PM) values for the first three rows of transition metal elements computed from atomic density functional theory (DFT) calculations, allowing for the efficient computation of approximate A and B across large crystals using only structural and magnetic moment size and direction information. Ferromagnetic b.c.c. (body-centred cubic) Fe and tetragonal FePt are chosen to showcase the performance of PM values versus directly obtaining A and B from the unit-cell spin density by DFT. The magnetic fields of b.c.c. Fe are well described by the PM approach while for FePt the PM approach is less accurate due to deformations in the spin density. Calculations of the magnetic signal, namely the change due to A and B of the intensity of diffraction patterns, show that the PM approach for both b.c.c. Fe and FePt is able to describe the effects of magnetism in these systems to a good degree of accuracy.

Making the Most of your Electrons: Challenges and Opportunities in Characterizing Hybrid Interfaces with STEM

Inspired by the unique architectures composed of hard and soft materials in natural and biological systems, synthetic hybrid structures and associated soft-hard interfaces have recently evoked significant interest. Soft matter is typically dominated by fluctuations even at room temperature, while hard matter (which often serves as the substrate or anchor for the soft component) is governed by rigid mechanical behavior. This dichotomy offers considerable opportunities to leverage the disparate properties offered by these components across a wide spectrum spanning from basic science to engineering insights with significant technological overtones. Such hybrid structures, which include polymer nanocomposites, DNA functionalized nanoparticle superlattices and metal organic frameworks to name a few, have delivered promising insights into the areas of catalysis, environmental remediation, optoelectronics, medicine, and beyond. The interfacial structure between these hard and soft phases exists across a variety of length scales and often strongly influence the functionality of hybrid systems. While scanning/transmission electron microscopy (S/TEM) has proven to be a valuable tool for acquiring intricate molecular and nanoscale details of these interfaces, the unusual nature of hybrid composites presents a suite of challenges that make assessing or establishing the classical structure-property relationships especially difficult. These include challenges associated with preparing electron-transparent samples and obtaining sufficient contrast to resolve the interface between dissimilar materials given the dose sensitivity of soft materials. We discuss each of these challenges and supplement a review of recent developments in the field with additional experimental investigations and simulations to present solutions for attaining a nano or atomic-level understanding of these interfaces. These solutions present a host of opportunities for investigating and understanding the role interfaces play in this unique class of functional materials.

Structuring total angular momentum of light along the propagation direction with polarization-controlled meta-optics

Recent advances in wavefront shaping have enabled complex classes of Structured Light which carry spin and orbital angular momentum, offering new tools for light-matter interaction, communications, and imaging. Controlling both components of angular momentum along the propagation direction can potentially extend such applications to 3D. However, beams of this kind have previously been realized using bench-top setups, requiring multiple interaction with light of a fixed input polarization, thus impeding their widespread applications. Here, we introduce two classes of metasurfaces that lift these constraints, namely: i) polarization-switchable plates that couple any pair of orthogonal polarizations to two vortices in which the magnitude and/or sense of vorticity vary locally with propagation, and ii) versatile plates that can structure both components of angular momentum, spin and orbital, independently, along the optical path while operating on incident light of any polarization. Compact and integrated devices of this type can advance light-matter interaction and imaging and may enable applications that are not accessible via other wavefront shaping tools.

Creating complex forms of structured light typically requires bulky optics and multiple interactions with incident light. Here the authors demonstrate versatile control over light’s polarization and orbital angular momentum along the propagation direction with a single metasurface.

Experimental realization of a π/2 vortex mode converter for electrons using a spherical aberration corrector

In light optics, beams with orbital angular momentum (OAM) can be produced by employing a properly-tuned two-cylinder-lens arrangement, also called π/2 mode converter. It is not possible to convey this concept directly to the beam in an electron microscope due to the non-existence of cylinder lenses in commercial transmission electron microscopes (TEMs). A viable work-around are readily-available electron optical elements in the form of quadrupole lenses. In a proof-of-principle experiment in 2012, it has been shown that a single quadrupole in combination with a Hilbert phase-plate produces a spatially-confined, transient vortex mode. Here, an analogue to an optical π/2 mode converter is realized by repurposing a CEOS DCOR probe corrector in an aberration corrected TEM in a way that it resembles a dual cylinder lens using two quadrupoles. In order to verify the presence of OAM in the output beam, a fork dislocation grating is used as an OAM analyser. The possibility to use magnetic quadrupole fields instead of, e.g., prefabricated fork dislocation gratings to produce electron beams carrying OAM enhances the beam brightness by almost an order of magnitude and delivers switchable high-mode purity vortex beams without unwanted side-bands.

A semi-classical theory of magnetic inelastic scattering in transmission electron energy loss spectroscopy

The feasibility of detecting magnetic excitations using monochromated electron energy loss spectroscopy in the transmission electron microscope is examined. Inelastic scattering cross-sections are derived using a semi-classical electrodynamic model, and applied to AC magnetic susceptibility measurements and magnon characterization. Consideration is given to electron probes with a magnetic moment, such as vortex beams, where additional inelastic scattering can take place due to the change in magnetic potential energy of the incident electron in a non-uniform magnetic field. This so-called 'Stern-Gerlach' energy loss can be used to enhance the strength of the scattering by increasing the orbital angular momentum of the vortex beam, and enables separation of magnetic from non-magnetic (i.e. dielectric) energy losses, thus providing a promising experimental route for detecting magnons. AC magnetic susceptibility measurements are however not feasible using Stern-Gerlach energy losses for a vortex beam.

Imprinting the quantum statistics of photons on free electrons

[Figure: see text].

Vortex beams of atoms and molecules

[Figure: see text].

Single-particle cryo-EM: alternative schemes to improve dose efficiency

Imaging of biomolecules by ionizing radiation, such as electrons, causes radiation damage which introduces structural and compositional changes of the specimen. The total number of high-energy electrons per surface area that can be used for imaging in cryogenic electron microscopy (cryo-EM) is severely restricted due to radiation damage, resulting in low signal-to-noise ratios (SNR). High resolution details are dampened by the transfer function of the microscope and detector, and are the first to be lost as radiation damage alters the individual molecules which are presumed to be identical during averaging. As a consequence, radiation damage puts a limit on the particle size and sample heterogeneity with which electron microscopy (EM) can deal. Since a transmission EM (TEM) image is formed from the scattering process of the electron by the specimen interaction potential, radiation damage is inevitable. However, we can aim to maximize the information transfer for a given dose and increase the SNR by finding alternatives to the conventional phase-contrast cryo-EM techniques. Here some alternative transmission electron microscopy techniques are reviewed, including phase plate, multi-pass transmission electron microscopy, off-axis holography, ptychography and a quantum sorter. Their prospects for providing more or complementary structural information within the limited lifetime of the sample are discussed.

Automated and Autonomous Experiments in Electron and Scanning Probe Microscopy

Machine learning and artificial intelligence (ML/AI) are rapidly becoming an indispensable part of physics research, with domain applications ranging from theory and materials prediction to high-throughput data analysis. In parallel, the recent successes in applying ML/AI methods for autonomous systems from robotics to self-driving cars to organic and inorganic synthesis are generating enthusiasm for the potential of these techniques to enable automated and autonomous experiments (AE) in imaging. Here, we aim to analyze the major pathways toward AE in imaging methods with sequential image formation mechanisms, focusing on scanning probe microscopy (SPM) and (scanning) transmission electron microscopy ((S)TEM). We argue that automated experiments should necessarily be discussed in a broader context of the general domain knowledge that both informs the experiment and is increased as the result of the experiment. As such, this analysis should explore the human and ML/AI roles prior to and during the experiment and consider the latencies, biases, and prior knowledge of the decision-making process. Similarly, such discussion should include the limitations of the existing imaging systems, including intrinsic latencies, non-idealities, and drifts comprising both correctable and stochastic components. We further pose that the role of the AE in microscopy is not the exclusion of human operators (as is the case for autonomous driving), but rather automation of routine operations such as microscope tuning, etc., prior to the experiment, and conversion of low latency decision making processes on the time scale spanning from image acquisition to human-level high-order experiment planning. Overall, we argue that ML/AI can dramatically alter the (S)TEM and SPM fields; however, this process is likely to be highly nontrivial and initiated by combined human-ML workflows and will bring challenges both from the microscope and ML/AI sides. At the same time, these methods will enable opportunities and paradigms for scientific discovery and nanostructure fabrication.

Three-Dimensional Measurement of Magnetic Moment Vectors Using Electron Magnetic Chiral Dichroism at Atomic Scale

Here we have developed an approach of three-dimensional (3D) measurement of magnetic moment vectors in three Cartesian directions using electron magnetic chiral dichroism (EMCD) at atomic scale. Utilizing a subangstrom convergent electron beam in the scanning transmission electron microscopy (STEM), beam-position-dependent chiral electron energy-loss spectra (EELS), carrying the EMCD signals referring to magnetization in three Cartesian directions, can be obtained during the scanning across the atomic planes. The atomic resolution EMCD signals from all of three directions can be separately obtained simply by moving the EELS detector. Moreover, the EMCD signals can be remarkably enhanced using a defocused electron beam, relieving the issues of low signal intensity and signal-to-noise-ratio especially at atomic resolution. Our proposed method is compatible with the setup of the widely used atomic resolution STEM-EELS technique and provides a straightforward way to achieve 3D magnetic measurement at atomic scale on newly developing magnetic-field-free TEM.

Rotational Doppler shift from a rotating rod

This Letter reports on a rotational Doppler effect obtained from a rotating rod illuminated by a fundamental Gaussian laser beam. More specifically, we decompose the transmitted light behind the rotating rod into Laguerre-Gaussian modes and investigate the associated frequency shifts. The main contributing modes correspond to modes having the same rotational symmetry as the rotating object. Furthermore, their shifts equal the topological charge of the beam times the rotational frequency of the object. Potential applications in pattern recognition and rotation identification are then considered.

Quantum Wave-Particle Duality in Free-Electron-Bound-Electron Interaction

We present a comprehensive relativistic quantum-mechanical theory for interaction of a free electron with a bound electron in a model, where the free electron is represented as a finite-size quantum electron wave packet (QEW) and the bound electron is modeled by a quantum two-level system (TLS). The analysis reveals the wave-particle duality nature of the QEW, delineating the point-particle-like and wavelike interaction regimes and manifesting the physical reality of the wave function dimensions when interacting with matter. This QEW size dependence may be used for interrogation and coherent control of superposition states in a TLS and for enhancement of cathodoluminescence and electron energy-loss spectroscopy in electron microscopy.

Spatiotemporal Vortex Pulses: Angular Momenta and Spin-Orbit Interaction

Recently, spatiotemporal optical vortex pulses carrying a purely transverse intrinsic orbital angular momentum were generated experimentally [Optica 6, 1547 (2019)OPTIC82334-253610.1364/OPTICA.6.001547; Nat. Photonics 14, 350 (2020)NPAHBY1749-488510.1038/s41566-020-0587-z]. However, an accurate theoretical analysis of such states and their angular-momentum properties remains elusive. Here, we provide such analysis, including scalar and vector spatiotemporal Bessel-type solutions as well as description of their propagational, polarization, and angular-momentum properties. Most importantly, we calculate both local densities and integral values of the spin and orbital angular momenta, and predict observable spin-orbit interaction phenomena related to the coupling between the transverse spin and orbital angular momentum. Our analysis is readily extended to spatiotemporal vortex pulses of other natures (e.g., acoustic).