Normal modes and mode transformation of pure electron vortex beams

G. Thirunavukkarasu, M. Mousley, M. Babiker, J. Yuan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Electron vortex beams constitute the first class of matter vortex beams which are currently routinely produced in the laboratory. Here, we briefly review the progress of this nascent field and put forward a natural quantum basis set which we show is suitable for the description of electron vortex beams. The normal modes are truncated Bessel beams (TBBs) defined in the aperture plane or the Fourier transform of the transverse structure of the TBBs (FT-TBBs) in the focal plane of a lens with the said aperture. As these modes are eigenfunctions of the axial orbital angular momentum operator, they can provide a complete description of the two-dimensional transverse distribution of the wave function of any electron vortex beam in such a system, in analogy with the prominent role Laguerre- Gaussian (LG) beams played in the description of optical vortex beams. The characteristics of the normal modes of TBBs and FT-TBBs are described, including the quantized orbital angular momentum (in terms of the winding number l) and the radial index p> 0. We present the experimental realization of such beams using computer-generated holograms. The mode analysis can be carried out using astigmatic transformation optics, demonstrating close analogy with the astigmatic mode transformation between LG and Hermite-Gaussian beams.

Original languageEnglish
Article number20150438
Pages (from-to)1
Number of pages12
Journal Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Volume375
Issue number2087
Early online date9 Jan 2017
DOIs
Publication statusPublished - 28 Feb 2017

Bibliographical note

© 2017 The Authors.

Keywords

  • Electron vortex, normal mods, eigenstates
  • beam shaping
  • MMC2017/EMAG2017

    Yuan, J. (Organiser)

    3 Jul 20176 Jul 2017

    Activity: Participating in or organising an eventConference participation

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