Normal modes and mode transformation of pure electron vortex beams

Thirunavukkarasu, G.; Mousley, Michael; Babiker, M.; Yuan, Jun

doi:10.1098/rsta.2015.0438

Cited by 17 publications

(20 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, in which case the wavefunction locally becomes a sinc function of the radial coordinate. Thirunavukkarasu et al (2017) This can also be understood by regarding the original mask as the product of the unobstructed Bessel beam and a top-hat mask function. The transverse structures of the vortex beam at the focal plane can be considered as the convolution of the Fourier transform of the Bessel function (whose transverse structure is a ring with a radius controlled by the radial size of the first dark zone in the mask) and that of the top-hat mask (which is the well known Airy pattern with side band ring structures).…”

Section: Bandwidth-limited Vortex Beamsmentioning

confidence: 99%

“…To represent the waveform of the arbitrary beam in similar bandwidth-limited situations, an orthonormal basis set characterised by orbital angular momentum has recently been reported for vortex beams (Thirunavukkarasu et al, 2017), including both the azimuthal and radial quantum numbers l and p, respectively. It is based on describing the normal modes of the transverse wavefront confined to a finite radius at the pupil or aperture plane by an orthonormal set of truncated Bessel functions, much like the solutions of the allowed normal modes of surface vibrations on a drum surface:…”

Section: Bandwidth-limited Vortex Beamsmentioning

confidence: 99%

“…The details of the experimental realization of the FT-TBB beams can be found in ref. (Thirunavukkarasu et al, 2017) The FT-TBB set of beams is one of the bandwidthlimited vortex beams whose spatial frequency is determined by the aperture size. As this FT-TBB set of modes forms a complete orthonormal set, it can be used to describe any such bandwidth-limited vortex beam.…”

Section: Bandwidth-limited Vortex Beamsmentioning

confidence: 99%

See 2 more Smart Citations

Electron vortices: Beams with orbital angular momentum

et al. 2017

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Bandwidth-limited Vortex Beamsmentioning

confidence: 99%

Section: Bandwidth-limited Vortex Beamsmentioning

confidence: 99%

Section: Bandwidth-limited Vortex Beamsmentioning

confidence: 99%

See 1 more Smart Citation

Electron vortices: Beams with orbital angular momentum

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…The study of orbital angular momentum has had an impact beyond the field of optics and an issue devoted to OAM would not be complete without papers looking beyond optics. We have two discussing the existence of electron vortices and their angular momentum properties [57,58].…”

Section: Recent Developments and This Theme Issuementioning

confidence: 99%

Optical orbital angular momentum

Barnett

Babiker

Padgett

2017

Phil. Trans. R. Soc. A.

117

View full text Add to dashboard Cite

We present a brief introduction to the orbital angular momentum of light, the subject of our theme issue and, in particular, to the developments in the 13 years following the founding paper by Allen et al. (Allen et al. 1992 Phys. Rev. A 45 , 8185 ( doi:10.1103/PhysRevA.45.8185 )). The papers by our invited authors serve to bring the field up to date and suggest where developments may take us next. This article is part of the themed issue ‘Optical orbital angular momentum’.

show abstract

“…A useful alternative would be the complete set of the Fourier transforms of the truncated Bessel (FT-TBB) functions [32]. We consider here the use of the LG set and write …”

Section: Pacsmentioning

confidence: 99%

Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams

et al. 2017

Self Cite

View full text Add to dashboard Cite

A general orbital angular momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of spiral zone plate holograms and suggesting that naturally occurring rotationally symmetric patterns could be inadvertent sources of vortex beams, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric binary amplitude chiral sieve masks. 42.50.Tx Vortices are common to all wave phenomena [1], including tornadoes at the large scale and superfluid helium at the small scale. The prototypical example of these is the optical vortex beam [2], followed recently by the electron vortex beam [3][4][5] and there are early studies of neutron [6] and atom vortex beams [7]. Vortex beams are characterized by a phase singularity described by an exp ℓ azimuthal phase factor, where θ is the azimuthal angle and ℓ stands for the winding number and is also called the topological charge. Vortex beams are of special interest because of their quantized OAM of ℓħ per particle [1] and have led to various applications in the contexts of super-resolution microscopy [8], nano-manipulation [9], astronomy [10] and crystallography [11]. In contrast to the intrinsic (spin) angular momentum, OAM can be very large and, as such, vortex beams can lead to new physics [12,13] and have potential in multiplex free-space communication [14] and quantum information [15]. PACS:The establishment of a toolbox for flexible vortex beam generation is the key to the development of science and technology involving vortex beams. If the vortex beam wavefunctions are known exactly, they can be generated either by direct phase manipulation (or wavefront shaping) [16] using, for example, spiral phase plates [3,6,17], spinto-orbital angular momentum convertors [18], and by phase encoding techniques through diffraction involving computer-generated holograms (CGHs) [19], including fork grating [4,5] and spiral zone plates [20][21][22]. Other techniques require case by case analysis to identify the nature of the vortex beams produced, as in the case involving the Aharonov-Bohm effect experienced by a charged particle in a suitable magnetic field [23,24]. More recent methods make use of photon sieves [25][26][27] and Vogel spiral arrays [28,29] as diffractive elements for vortex beam generation.Here we put forward a general principle for vortex beam generation in rotationally symmetric systems. We examine the role of rotational symmetry, not only for the purpose of generating a specific vortex wavefunction, but also for the essential symmetry elements that must be possessed by any vortex-related state by virtue of its characteristic azimuthal phase factor exp ℓ . The principle would enable us to understand, in a novel deconstructive manner, the generation of individual pure vorte...

show abstract

Normal modes and mode transformation of pure electron vortex beams

Abstract: One contribution of 14 to a theme issue 'Optical orbital angular momentum' .

Cited by 17 publications

References 57 publications

Electron vortices: Beams with orbital angular momentum

Electron vortices: Beams with orbital angular momentum

Optical orbital angular momentum

Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams

Contact Info

Product

Resources

About