Experimental Demonstration of an Electrostatic Orbital Angular Momentum Sorter for Electron Beams

Abstract: The implementation of log-pol transformation has recently introduced a new boost in electron optics with charged matter vortices, allowing to map conformally between linear and orbital angular momentum (OAM) states and to measure them. That coordinate change belongs to the general framework of Hossack's transformations and it has been recently realized efficiently by means of electrostatic elements. In this letter we show that it is a general property of those conformal transformations to be produced by harmonic phase elements and therefore to admit an electrostatic implementation in the electron optics scenario. We consider a new kind of conformal mapping, the circular-sector transformation, which has been recently introduced for OAM multiplication and division in optics, and discuss how it represents a general solution of Laplace's equation, showing the analogy of the generating phase elements with projected multipole fields and linear charge distributions. Moreover, we demonstrate its capability to perform the sorting of multipole wavefronts, discovering a novel and effective method to measure the strength and orientation of a dipole field in a fast, compact and direct way.

Abstract: In this paper we prove that any conformal transformation of a wave can be produced via a suitably arranged cascade of two, or at most four, discrete phase elements satisfying Laplace's equation. Although this result is of general applicability, in the case of charged-matter waves it implies that such transformations can be exactly obtained by employing only electrostatic or magnetostatic phase elements. Furthermore, we illustrate how a basis for such generating phase elements is given by integer and fractional charge multipoles, proving that these transformations can be used to perform the efficient sorting of multipole-induced quantum states. This provides a fast, compact, and direct method to measure the strength and orientation of dipole systems and of astigmatism. It thus adds a further observable to the four whose spectrum can already be directly measured via spatial separation on the detector, i.e., position, momentum, energy, and orbital angular momentum. The results hold true in optics and for all kinds of charged-particle beams of sufficient coherence.

Abstract: The spatial features of ultrafast changes in magnetic textures carry detailed information on microscopic couplings and energy transport mechanisms. Electrons excel in imaging such picosecond or shorter processes at nanometer length scales. We review the range of physical interactions that produce ultrafast magnetic contrast with electrons, and specifically highlight the recent emergence of ultrafast Lorentz transmission electron microscopy. From the fundamental processes involved in demagnetization at extremely short timescales to skyrmion-based devices, we show that ultrafast electron imaging will be a vital tool in solving pressing problems in magnetism and magnetic materials where nanoscale inhomogeneity, microscopic field measurement, non-equilibrium behavior or dynamics are involved.

Abstract: •A deep convolutional neural network is used to evaluate and correct the alignment of an orbital angular momentum sorter.•The convolutional neural network automatically analyses OAM spectra at a rate of 50 ms/spectrum, allowing for real time implementation.•The method is easily transferable to any programmable beam shaping technique. A convolutional neural network is used to align an orbital angular momentum sorter in a transmission electron microscope. The method is demonstrated using simulations and experiments. As a result of its accuracy and speed, it offers the possibility of real-time tuning of other electron optical devices and electron beam shaping configurations.

Abstract: Modern nanotechnology techniques offer new opportunities for fabricating structures and devices at the micron and sub-micron level. Here, we use focused ion beam techniques to realize drift tube Zernike phase plates for electrons, whose operation is based on the presence of contact potentials in Janus bimetallic cylinders, in a similar manner to the electrostatic Aharonov-Bohm effect in bimetallic wires. We use electron Fraunhofer interference to demonstrate that such bimetallic pillar structures introduce phase shifts that can be tuned to desired values by varying their dimensions, in particular their heights.

Abstract: Radiation damage is the main problem which prevents the determination of the structure of a single biological macromolecule at atomic resolution using any kind of microscopy. This is true whether neutrons, electrons or X-rays are used as the illumination. For neutrons, the cross-section for nuclear capture and the associated energy deposition and radiation damage could be reduced by using samples that are fully deuterated and 15N-labelled and by using fast neutrons, but single molecule biological microscopy is still not feasible. For naturally occurring biological material, electrons at present provide the most information for a given amount of radiation damage. Using phase contrast electron microscopy on biological molecules and macromolecular assemblies of approximately 10(5) molecular weight and above, there is in theory enough information present in the image to allow determination of the position and orientation of individual particles: the application of averaging methods can then be used to provide an atomic resolution structure. The images of approximately 10,000 particles are required. Below 10(5) molecular weight, some kind of crystal or other geometrically ordered aggregate is necessary to provide a sufficiently high combined molecular weight to allow for the alignment. In practice, the present quality of the best images still falls short of that attainable in theory and this means that a greater number of particles must be averaged and that the molecular weight limitation is somewhat larger than the predicted limit. For X-rays, the amount of damage per useful elastic scattering event is several hundred times greater than for electrons at all wavelengths and energies and therefore the requirements on specimen size and number of particles are correspondingly larger. Because of the lack of sufficiently bright neutron sources in the foreseeable future, electron microscopy in practice provides the greatest potential for immediate progress.

Abstract: One of the biggest obstacles in improving the resolution of the electron microscope has always been the blurring of the image caused by lens aberrations. Here we report a solution to this problem for a medium-voltage electron microscope which gives a stunning enhancement of image quality.

Abstract: We present a method to efficiently sort orbital angular momentum (OAM) states of light using two static optical elements. The optical elements perform a Cartesian to log-polar coordinate transformation, converting the helically phased light beam corresponding to OAM states into a beam with a transverse phase gradient. A subsequent lens then focuses each input OAM state to a different lateral position. We demonstrate the concept experimentally by using two spatial light modulators to create the desired optical elements, applying it to the separation of eleven OAM states.

Abstract: The rapid development of electron tomography, in particular the introduction of novel tomographic imaging modes, has led to the visualization and analysis of three-dimensional structural and chemical information from materials at the nanometre level. In addition, the phase information revealed in electron holograms allows electrostatic and magnetic potentials to be mapped quantitatively with high spatial resolution and, when combined with tomography, in three dimensions. Here we present an overview of the techniques of electron tomography and electron holography and demonstrate their capabilities with the aid of case studies that span materials science and the interface between the physical sciences and the life sciences.

Abstract: It has been possible to produce photon vortex beams — optical beams with spiralling wavefronts — for some time, and they have found widespread application as optical tweezers, in interferometry and in information transfer, for example. The production of vortex beams of electrons was demonstrated earlier this year ( http://go.nature.com/4H2xWR ) in a procedure involving the passage of electrons through a spiral stack of graphite thin films. The ability to generate such beams reproducibly in a conventional electron microscope would enable many new applications. Now Jo Verbeeck and colleagues have taken a step towards that goal. They describe a versatile holographic technique for generating these twisted electron beams, and demonstrate their potential use as probes of a material's magnetic properties. It was demonstrated recently that passing electrons through a spiral stack of graphite thin films generates an electron beam with orbital angular momentum — analogous to the spiralling wavefronts that can be introduced in photon beams and which have found widespread application. Here, a versatile holographic technique for generating these twisted electron beams is described. Moreover, a demonstration is provided of their potential use in probing a material's magnetic properties. Vortex beams (also known as beams with a phase singularity) consist of spiralling wavefronts that give rise to angular momentum around the propagation direction. Vortex photon beams are widely used in applications such as optical tweezers to manipulate micrometre-sized particles and in micro-motors to provide angular momentum1,2, improving channel capacity in optical3 and radio-wave4 information transfer, astrophysics5 and so on6. Very recently, an experimental realization of vortex beams formed of electrons was demonstrated7. Here we describe the creation of vortex electron beams, making use of a versatile holographic reconstruction technique in a transmission electron microscope. This technique is a reproducible method of creating vortex electron beams in a conventional electron microscope. We demonstrate how they may be used in electron energy-loss spectroscopy to detect the magnetic state of materials and describe their properties. Our results show that electron vortex beams hold promise for new applications, in particular for analysing and manipulating nanomaterials, and can be easily produced.