Measuring the Orbital Angular Momentum of Electron Vortex Beams Using a Forked Grating

Saitoh, Koh; Hasegawa, Yuya; Hirakawa, Kazuma; Tanaka, Nobuo; Uchida, Masaya

doi:10.1103/physrevlett.111.074801

Cited by 84 publications

(56 citation statements)

References 21 publications

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“…A hologram mask can be used to determine the topological charge of the beam Saitoh et al, 2013). In this method, a forked grating structure, formed from the interference of a plane wave and a vortex wave of topological charge of l grating , is used as a beam analyser.…”

Section: Di↵ractionmentioning

confidence: 99%

Electron vortices: Beams with orbital angular momentum

et al. 2017

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The recent prediction and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years had elapsed since the recognition of the physical significance and potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free space propagation of optical beams and the time-independent Schrödinger equation governing freely propagating electron vortex beams. There are, however, key di↵erences in the properties of the two kinds of vortex beams. This review is concerned primarily with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution as well as the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analysed, including nanoparticle manipulation and the mechanisms of orbital angular momentum transfer in the electron vortex interaction with matter.

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Section: Di↵ractionmentioning

confidence: 99%

Electron vortices: Beams with orbital angular momentum

et al. 2017

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“…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. Introduction.-Recent advances in experiments with relativistic (100-300 keV) electron beams [1][2][3][4][5][6][7][8][9] carrying orbital angular momentum call for a mathematical description based on the Dirac equation. The generally used Schrödinger equation gives an inadequate description because the differences between the nonrelativistic and relativistic wave functions are essential.…”

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confidence: 99%

Relativistic Electron Wave Packets Carrying Angular Momentum

Bialynicki‐Birula

Bialynicka‐Birula

2017

Phys. Rev. Lett.

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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. Introduction.-Recent advances in experiments with relativistic (100-300 keV) electron beams [1-9] carrying orbital angular momentum call for a mathematical description based on the Dirac equation. The generally used Schrödinger equation gives an inadequate description because the differences between the nonrelativistic and relativistic wave functions are essential. It is not only the problem of relativistic corrections, which for 300 keV electrons may amount to about 60%. A more important difference is in the use of the orbital angular momentum quantum number l in the description of electronic states. In the nonrelativistic case both the orbital angular momentum and the total angular momentum are separately conserved while in the relativistic case only the total angular momentum has this property. This has already been pointed out by Dirac who in his first paper on the theory of the electron wrote "This makes a difference between the present theory and the previous spinning electron theory, in which m 2 is constant." Directly related to the problem of orbital angular momentum is a different structure of vortex lines in the two cases.

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“…Unlike the case for light, isolation of inelastically scattered electrons can be challenging, so non-interferometric methods to measure OAM may be necessary for inelastic scattering experiments with electron vortex beams. Three different non-interferometric methods have been demonstrated: diffraction grating-based phase flattening [63,64], measurements using apertures [63] and mode transformation with cylindrical lenses [61,63], yet none of these techniques are suitable for measuring mixtures of OAM in scattered electrons. Two new proposed techniques for sorting electrons based on OAM include magnetic lens-based on-axis sorting [65], and electrostatic off-axis sorting [66,67].…”

Section: Experiments and Demonstrations Of Free Electron Vorticesmentioning

confidence: 99%