Nondestructive Measurement of Orbital Angular Momentum for an Electron Beam

Automatic Alignment of an Orbital Angular Momentum Sorter in a Transmission Electron Microscope Using a Convolutional Neural Network

We report on the automatic alignment of a transmission electron microscope equipped with an orbital angular momentum sorter using a convolutional neural network. The neural network is able to control all relevant parameters of both the electron-optical setup of the microscope and the external voltage source of the sorter without input from the user. It can compensate for mechanical and optical misalignments of the sorter, in order to optimize its spectral resolution. The alignment is completed over a few frames and can be kept stable by making use of the fast fitting time of the neural network.

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

The component of orbital angular momentum (OAM) in the propagation direction is one of the fundamental quantities of an electron wave function that describes its rotational symmetry and spatial chirality. Here, we demonstrate experimentally an electrostatic sorter that can be used to analyze the OAM states of electron beams in a transmission electron microscope. The device achieves postselection or sorting of OAM states after electron-material interactions, thereby allowing the study of new material properties such as the magnetic states of atoms. The required electron-optical configuration is achieved by using microelectromechanical systems technology and focused ion beam milling to control the electron phase electrostatically with a lateral resolution of 50 nm. An OAM resolution of 1.5ℏ is realized in tests on controlled electron vortex beams, with the perspective of reaching an optimal OAM resolution of 1ℏ in the near future.

Exploring the Spatial Features of Electronic Transitions in Molecular and Biomolecular Systems by Swift Electrons

We devise a new kind of experiment that extends the technology of electron energy loss spectroscopy to probe (supra-)molecular systems: by using an electron beam in a configuration that avoids molecular damage and a very recently introduced electron optics setup for the analysis of the outcoming electrons, one can obtain information on the spatial features of the investigated excitations. Physical insight into the proposed experiment is provided by means of a simple but rigorous model to obtain the transition rate and selection rule. Numerical simulations of DNA G-quadruplexes and other biomolecular systems, based on time dependent density functional theory calculations, point out that the conceived new technique can probe the multipolar components and even the chirality of molecular transitions, superseding the usual optical spectroscopies for those cases that are problematic, such as dipole-forbidden transitions, at a very high spatial resolution.

Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region

In this paper, ultra-thin metalenses are proposed to generate converging and non-diffractive vortex beam carrying orbital angular momentum (OAM) in microwave region. Phase changes are introduced to the transmission cross-polarized wave by tailoring spatial orientation of Pancharatnam-Berry phase unit cell. Based on the superposition of phase profile of spiral phase plate and that of a converging lens or an axicon, vortex beam carrying OAM mode generated by the metalens can also exhibit characteristics of a focusing beam or a Bessel beam. Measured field intensities and phase distributions at microwave frequencies verify the theoretical design procedure. The proposed method provides an efficient approach to control the radius of vortex beam carrying OAM mode in microwave wireless applications for medium-short range distance.

Nonuniform Currents and Spins of Relativistic Electron Vortices in a Magnetic Field

We present a relativistic description of electron vortex beams in a homogeneous magnetic field. Including spin from the beginning reveals that spin-polarized electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exists a set of vortex beams with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. The well-defined phase structure of these beams is analogous to simpler scalar vortex beams, owing to the protection by the Zeeman effect. For states that do show spin-orbit mixing, the spin polarization across the beam is nonuniform rendering the spin and orbital degrees of freedom inherently inseparable.

Relativistic Electron Wave Packets Carrying Angular Momentum

There are important differences between the nonrelativistic and relativistic description of electron beams. In the relativistic case the orbital angular momentum quantum number cannot be used to specify the wave functions and the structure of vortex lines in these two descriptions is completely different. We introduce analytic solutions of the Dirac equation in the form of exponential wave packets and we argue that they properly describe relativistic electron beams carrying angular momentum.