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Plasmonics, the science and technology of the interaction of light with metallic objects, is fundamentally changing the way we can detect, generate and manipulate light. Although the field is progressing swiftly, thanks to the availability of nanoscale manufacturing and analysis methods, fundamental properties such as the plasmonic excitations' symmetries cannot be accessed directly, leading to a partial, sometimes incorrect, understanding of their properties. Here we overcome this limitation by deliberately shaping the wave function of an electron beam to match a plasmonic excitations' symmetry in a modified transmission electron microscope. We show experimentally and theoretically that this offers selective detection of specific plasmon modes within metallic nanoparticles, while excluding modes with other symmetries. This method resembles the widespread use of polarized light for the selective excitation of plasmon modes with the advantage of locally probing the response of individual plasmonic objects and a far wider range of symmetry selection criteria.

Recent theoretical and experimental developments in the field of electron vortex beam physics have raised questions on what exactly this novelty in the field of electron microscopy (and other fields, such as particle physics) really provides. An important part in the answer to those questions lies in scattering theory. The present investigation explores various aspects of inelastic quantum scattering theory for cylindrically symmetric beams with orbital angular momentum. The model system of Coulomb scattering on a hydrogen atom provides the setting to address various open questions: How is momentum transferred? Do vortex beams selectively excite atoms, and how can one employ vortex beams to detect magnetic transitions? The analytical approach presented here provides answers to these questions. OAM transfer is possible, but not through selective excitation; rather, by pre- and post-selection one can filter out the relevant contributions to a specific signal.

The phase problem can be considered as one of the cornerstones of quantum mechanics intimately connected to the detection process and the uncertainty relation. The latter impose fundamental limits on the manifold phase reconstruction schemes invented to date in particular at small magnitudes of the quantum wave. Here, we show that a rigorous solution of the Transport of Intensity Reconstruction (TIE) scheme in terms of a linear elliptic partial differential equation for the phase provides reconstructions even in the presence of wave zeros if particular boundary conditions (BCs) are given. We furthermore discuss how partial coherence hampers phase reconstruction and show that a modified version of the TIE reconstructs the curl-free current density at arbitrary (in-)coherence. This opens the way for a large variety of new applications in fields as diverse as astrophysics, geophysics, photonics, acoustics, and electron microscopy, where zeros in the respective wave field are a ubiquitous feature., Comment: 5 pages, 3 figures, includes correction as in https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.199902

We investigate topological aspects of sub-nm electron vortex beams upon elastic propagation through atomic scattering potentials. Two main aspects can be distinguished: (i) Significantly reduced delocalization compared to a similar non-vortex beam if the beam centers on an atomic column and (ii) site symmetry dependent splitting of higher-order vortex beams. Furthermore, the results provide insight into the complex vortex line fabric within the elastically scattered wave containing characteristic vortex loops predominantly attached to atomic columns and characteristic twists of vortex lines around atomic columns., Comment: 10 pages, 6 figures

The recent demonstration of electron vortex beams has opened up the new possibility of studying orbital angular momentum (OAM) in the interaction between electron beams and matter. To this aim, methods to analyze the OAM of an electron beam are fundamentally important and a necessary next step. We demonstrate the measurement of electron beam OAM through a variety of techniques. The use of forked holographic masks, diffraction from geometric apertures, diffraction from a knife-edge and the application of an astigmatic lens are all experimentally demonstrated. The viability and limitations of each are discussed with supporting numerical simulations., Comment: 5 pages, 4 figurse

By considering a cylindrically symmetric generalization of a plane wave, the first Born approximation of screened Coulomb scattering unfolds two new dimensions in the scattering problem: transverse momentum and orbital angular momentum of the incoming beam. In this paper, the elastic Coulomb scattering amplitude is calculated analytically for incoming Bessel beams. This reveals novel features occurring for wide angle scattering when the incoming beam is correctly prepared. The result successfully generalizes the well known Rutherford formula, incorporating transverse and orbital angular momentum into the formalism., Comment: 9 pages, 5 figures

Kirchhoff's scalar diffraction theory is applied throughout photon and electron optics. It is based on the stationary electromagnetic or Schr\"odinger wave equation, and is useful in describing interference phenomena for both light and matter waves. Here, Kirchhoff's diffraction theory is derived from the relativistic Dirac equation, thus reformulated to work on Dirac spinors. The parallels with the "classic" scalar theory are highlighted, and a basic interpretation of the result obtained for the Fraunhofer diffraction limit is given. The goal of this paper is to emphasize the similarity between the two equations on the most fundamental level.

The recent experimental realization of electron vortex beams opens up a wide research domain previously unexplored. The present paper explores the relativistic properties of these electron vortex beams, and quantifies deviations from scalar wave theory. It is common in electron optics to use the Schr\"odinger equation neglecting spin. The present paper investigates the role of spin and the total angular momentum Jz and how it pertains to the vortex states. As an application, we also investigate if it is possible to use holographic reconstruction to create novel total angular momentum eigenstates in a Transmission Electron Microscope. It is demonstrated that relativistic spin coupling effects disappear in the paraxial limit, and spin effects in holographically created electron vortex beams can only be exploited by using specialized magnetic apertures., Comment: 6 pages, 2 figures

Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, hen passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behaviour is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions., Comment: 5 pages, 5 figures

We examine the propagation of the recently-discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as non-diffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Remarkably, the non-rotating superpositions reproduce stable multi-vortex configurations that appear in rotating superfluids. Our results open up an avenue for the direct electron-microscopy observation of fundamental properties of free quantum electron states in magnetic fields., Comment: 21 pages, 10 figures, 1 table, to appear in Phys. Rev. X