“Theory and applications of free-electron vortex states”. Bliokh KY, Ivanov IP, Guzzinati G, Clark L, Van Boxem R, Béché, A, Juchtmans R, Alonso MA, Schattschneider P, Nori F, Verbeeck J, Physics reports 690, 1 (2017). http://doi.org/10.1016/j.physrep.2017.05.006
Abstract: Both classical and quantum waves can form vortices: with helical phase fronts and azimuthal current densities. These features determine the intrinsic orbital angular momentum carried by localized vortex states. In the past 25 years, optical vortex beams have become an inherent part of modern optics, with many remarkable achievements and applications. In the past decade, it has been realized and demonstrated that such vortex beams or wavepackets can also appear in free electron waves, in particular, in electron microscopy. Interest in free-electron vortex states quickly spread over different areas of physics: from basic aspects of quantum mechanics, via applications for fine probing of matter (including individual atoms), to high-energy particle collision and radiation processes. Here we provide a comprehensive review of theoretical and experimental studies in this emerging field of research. We describe the main properties of electron vortex states, experimental achievements and possible applications within transmission electron microscopy, as well as the possible role of vortex electrons in relativistic and high-energy processes. We aim to provide a balanced description including a pedagogical introduction, solid theoretical basis, and a wide range of practical details. Special attention is paid to translate theoretical insights into suggestions for future experiments, in electron microscopy and beyond, in any situation where free electrons occur.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 17.425
Times cited: 210
DOI: 10.1016/j.physrep.2017.05.006
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“Electron vortex beams in a magnetic field : a new twist on Landau levels and Aharonov-Bohm states”. Bliokh KY, Schattschneider P, Verbeeck J, Nori F, Physical review X 2, 041011 (2012). http://doi.org/10.1103/PhysRevX.2.041011
Abstract: 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 nondiffracting 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. Interestingly, the nonrotating superpositions reproduce stable multivortex configurations that appear in rotating superfluids. Our results open an avenue for the direct electron-microscopy observation of fundamental properties of free quantum-electron states in magnetic fields.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 12.789
Times cited: 130
DOI: 10.1103/PhysRevX.2.041011
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“Roadmap on structured waves”. Bliokh KY, Karimi E, Padgett MJ, Alonso MA, Dennis MR, Dudley A, Forbes A, Zahedpour S, Hancock SW, Milchberg HM, Rotter S, Nori F, Ozdemir SK, Bender N, Cao H, Corkum PB, Hernandez-Garcia C, Ren H, Kivshar Y, Silveirinha MG, Engheta N, Rauschenbeutel A, Schneeweiss P, Volz J, Leykam D, Smirnova DA, Rong K, Wang B, Hasman E, Picardi MF, Zayats AV, Rodriguez-Fortuno FJ, Yang C, Ren J, Khanikaev AB, Alu A, Brasselet E, Shats M, Verbeeck J, Schattschneider P, Sarenac D, Cory DG, Pushin DA, Birk M, Gorlach A, Kaminer I, Cardano F, Marrucci L, Krenn M, Marquardt F, Journal of optics 25, 103001 (2023). http://doi.org/10.1088/2040-8986/ACEA92
Abstract: Structured waves are ubiquitous for all areas of wave physics, both classical and quantum, where the wavefields are inhomogeneous and cannot be approximated by a single plane wave. Even the interference of two plane waves, or of a single inhomogeneous (evanescent) wave, provides a number of nontrivial phenomena and additional functionalities as compared to a single plane wave. Complex wavefields with inhomogeneities in the amplitude, phase, and polarization, including topological----- structures and singularities, underpin modern nanooptics and photonics, yet they are equally important, e.g. for quantum matter waves, acoustics, water waves, etc. Structured waves are crucial in optical and electron microscopy, wave propagation and scattering, imaging, communications, quantum optics, topological and non-Hermitian wave systems, quantum condensed-matter systems, optomechanics, plasmonics and metamaterials, optical and acoustic manipulation, and so forth. This Roadmap is written collectively by prominent researchers and aims to survey the role of structured waves in various areas of wave physics. Providing background, current research, and anticipating future developments, it will be of interest to a wide cross-disciplinary audience.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 2.1
Times cited: 7
DOI: 10.1088/2040-8986/ACEA92
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“Observation of the Larmor and Gouy rotations with electron vortex beams”. Guzzinati G, Schattschneider P, Bliokh KY, Nori F, Verbeeck J, Physical review letters 110, 093601 (2013). http://doi.org/10.1103/PhysRevLett.110.093601
Abstract: Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused by 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, when 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 behavior 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.
Keywords: A1 Journal article; Electron microscopy for materials research (EMAT)
Impact Factor: 8.462
Times cited: 91
DOI: 10.1103/PhysRevLett.110.093601
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