Electron vortex beams subject to static magnetic fields (original) (raw)

Electron vortices: Beams with orbital angular momentum

Reviews of Modern Physics

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. List of Symbols and Abbreviations 39 References 41 I. INTRODUCTION Electron vortex beams are a new member of an expanding class of experimentally realisable freely propa

Electron vortex beams in a magnetic field and spin filter

We investigate the propagation of electron vortex beams in a magnetic field. It is pointed out that when electron vortex beams carrying orbital angular momentum propagate in a magnetic field, the Berry curvature associated with the scalar electron moving in a cyclic path around the vortex line is modified from that in free space. This alters the spin-orbit interaction, which affects the propagation of nonparaxial beams. The electron vortex beams with tilted vortices lead to a spin Hall effect in free space. In the presence of a magnetic field in time-space we have spin filtering such that either positive or negative spin states emerge in spin Hall currents with clustering of spin 1/2 states.

Relativistic electron vortex beams in a laser fi eld

The orbital angular momentum Hall e ffect and spin Hall eff ect of electron vortex beams (EVB) have been studied for the EVBs interacting with laser field. In the scenario of paraxial beam, the cumulative e ffect of the orbit-orbit interaction of EVBs and laser fields drives the orbital Hall e ffect, which in turn produces a shift of the center of the beam from that of the fi eld-free case towards the polarization axis of photons. Besides, for non-paraxial beams one can also perceive a similar shift of the center of the beam owing to spin Hall eff ect involving spin-orbit interaction. Our analysis suggests that the shift in the paraxial beams will always be larger than that in non-paraxial beams.

Relativistic Electron Vortex Beams: Angular Momentum and Spin-Orbit Interaction

2011

Motivated by the recent discovery of electron vortex beams carrying orbital angular momentum (AM), we construct exact Bessel-beam solutions of the Dirac equation. They describe relativistic and nonparaxial corrections to the scalar electron beams. We describe the spin and orbital AM of the electron with Berry-phase corrections and predict the intrinsic spin-orbit coupling in free space. This can be observed as a spin-dependent probability distribution of the focused electron vortex beams. Moreover, the magnetic moment is calculated, which shows different g-factors for spin and orbital AM and also contains the Berry-phase correction.

Propagation of vortex electron wave functions in a magnetic field

Physical Review A, 2012

The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodingers equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent prefactor. Hence adding OAM and propagating can in this case be replaced by first propagating then adding OAM. Also, the results shown provide an explicit illustration of the fact that the gyromagnetic ratio for OAM is unity. We also propose a novel version of the Bohm-Aharonov effect using vortex electron beams.

Observation of the Larmor and Gouy Rotations with Electron Vortex Beams

Physical Review Letters, 2013

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 ...

Orbital angular momentum of mixed vortex beams

SPIE Proceedings, 2007

The orbital angular momentum (OAM) of the single vortex beam depends on its power and wavefront helicity. In the paper, this relation is generalized for mixed vortex beams composed of several coaxial vortices with different topological charges. The presented interference law indicates interference effects of the OAM resulting in local spatial gradients of the OAM density. Description of the OAM of mixed vortex beams is used for demonstration of a possibility to tune the OAM density of a composite vortex field without changing topological charges or intensity distribution. Experimental realization of the OAM tuning is discussed for interference of two focused vortex beams generated by means of a spiral phase mask.