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.This article is part of the themed issue 'Optical orbital angular momentum'.
Highlights
The ground-breaking work by Allen et al [1] was a profound development which led physicists to a new understanding of the physics of light
We demonstrate the production of the normal modes of electron vortex beams based on FT-truncated Bessel beams (TBBs) possessing both well-defined azimuthal index l and radial index p
Our results show that the normal modes of the electron vortex beams have LG-like qualities with the number p + 1 of ‘bright’ rings related to the radial index
Summary
The ground-breaking work by Allen et al [1] was a profound development which led physicists to a new understanding of the physics of light. The transverse, in-plane, radial structure of electron vortex beams has not received much attention, with work concentrating so far mainly on doughnut-type modes which display only azimuthal dependence in ring-like intensity distributions. We anticipate that in the context of electron vortices our results pave the way towards the complete control of the quantum state of matter vortex beams This could provide the basis for the quantum manipulation of electron vortex beams, with potential applications in various quantum technologies such as quantum imaging or quantum information processing and in possible super-resolution microscopy
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