Electron vortices: Beams with orbital angular momentum

Abstract

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.

Semiclassical probability of radiation of twisted photons in the ultrarelativistic limit

“…2). We found estimate (82) for the number of twisted photons with large projections of the total angular momentum produced in the forward radiation. We also described the effect of blossoming out rose [9] in the radiation of twisted photons by electrons evolving in strong laser waves with circular polarization and wigglers (see Fig.…”

Relativistic quantum-mechanical description of twisted paraxial electron and photon beams

“…We predict the new property of twisted particles consisting in a quantization of the group velocity and following from Eqs. (18) and (19). We suppose that this quantization can be observed because the modes n and l are measurable [79].…”

“…At present, twisted photon and electron beams are objects of intensive studies and have many practical applications (see Refs. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein). The most important kind of such beams is a paraxial (Laguerre-Gauss) wave beam [1,18,21] satisfying the paraxial approximation (p ⊥ << p).…”

“…However, the twisted electron can also be regarded as the centroid with the velocity v z given by Eq. (19) and with the mass equal to…”

Coiling free electron matter waves

“…Recent work with diffractive electron optics in transmission electron microscopes (TEMs) has allowed for the reliable creation and study of structured electron beams [1]. One such structure is a freely-propagating electron matter wave with a helical phase f ℓ e i , where ℓ is an integer and f is the azimuthal coordinate, winding about the azimuth, called an electron vortex [2][3][4]. The phase vortex has an associated quantized orbital angular momentum (OAM).…”