Robust and adjustable C-shaped electron vortex beams

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

doi:10.1088/1367-2630/aa6e3c

Cited by 8 publications

(6 citation statements)

References 53 publications

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“…As L z commutes with the Hamiltonian H, the orbital angular momentum is conserved about the beam axis, with its value proportional to azimuthal index l [10]. Consistent with this, we have shown for TBBs defined in the structured aperture plane of an electron lens that the corresponding wave functions observable at the focal plane of the electron lens are the Fourier transform of TBBs, which can be written as [4] Ψ FT-TBB pl (10) and are eigenfunctions of orbital angular momentum with eigenvalue l .…”

Section: Cylindrically Symmetric Quantum Basismentioning

confidence: 99%

Even-odd effect in higher-order holographic production of electron vortex beams with nontrivial radial structures

et al. 2019

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Structured electron beams carrying orbital angular momentum are currently of considerable interest, both from a fundamental point of view and for application in electron microscopy and spectroscopy. Until recently, most studies have focused on the azimuthal structure of electron vortex beams with well-defined orbital angular momentum. To unambiguously define real electron-beam states and realise them in the laboratory, the radial structure must also be specified. Here we use a specific set of orthonormal modes of electron (vortex) beams to describe both the radial and azimuthal structures of arbitrary electron wavefronts. The specific beam states are based on truncated Bessel beams localised within the lens aperture plane of an electron microscope. We show that their Fourier transform set of beams can be realised at the focal planes of the probe-forming lens using a binary computer generated electron hologram. Using astigmatic transformation optics, we demonstrate that the azimuthal indices of the diffracted beams scale with the order of the diffraction through phase amplification. However, their radial indices remain the same as those of the encoding beams for all the odd diffraction orders or are reduced to the zeroth order for the even-order diffracted beams. This simple even-odd rule can also be explained in terms of the phase amplification of the radial profiles. We envisage that the orthonormal cylindrical basis set of states could lead to new possibilities in phase contrast electron microscopy and spectroscopy using structured electron beams.

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Section: Cylindrically Symmetric Quantum Basismentioning

confidence: 99%

Even-odd effect in higher-order holographic production of electron vortex beams with nontrivial radial structures

et al. 2019

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“…Power-exponent [6] and modified [1] helico-conical beams create the adjustable spiral-like curves with the openings. A designed opening is created by an electron vortex with a C shape [28]. However, these methods cannot produce the light-arm beams.…”

Section: Introductionmentioning

confidence: 99%

A modified multiplexed vortex helico-conical petal-like zone plate

Xia¹,

Cheng²,

Xie³

et al. 2021

Phys. Scr.

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A modified multiplexed vortex helico-conical petal-like zone plate (MMVHPZP) is proposed to generate a polygon-like beam or light-arm beam with an adjustable opening. The MMVHPZP consists of the modified helico-conical petal-like zone plate (MHPZP) with the topological charge l and exponent n, and the multiplexed vortex spiral phase plate (MVSPP) with the inner topological charge l 1 and outer topological charge l 2. Moreover, when l 1 is equal or unequal to l 2, the MMVHPZP has the adjustable polygon-like beam or light-arm beam, respectively. In addition, when n is small or large, the number of arms is equal to the absolute difference between l 1 and l 2 or the sum of one and the absolute difference between l 1 and l 2, respectively. Furthermore, for the different l 1 or l 2, the opening is constant. With the increase of the n or l, the opening is larger. When l 1 is greater or less than l 2, the rotation direction of arms is the anticlockwise or clockwise direction, respectively.

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“…Thereafter, several approaches, such as employing holographic masks 16−19 , magnetic lens aberrations 20 and magnetic needles 21 , are reported to generate EVBs. Because EVB can effectively interact with matter as well as with external electric and magnetic fields, it is now starting to find applications as nanoscale magnetic probes for characterizing materials 22,23 .…”

mentioning

confidence: 99%

“…To better understand the physical picture of structured EVB, we further investigate the probability current density in quantum electron states, defined as , where is mass of a nonrelativistic electron and wave function can be described by amplitude and phase 23 . According to its definition, the probability current density can reflect the local phase gradient in an arbitrary electron field, and thus is very suitable to characterize the angular momentum property of a free-space electron wave function.…”

mentioning

confidence: 99%

Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography

Huo,

Yu,

Liu

et al. 2024

OEA

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An electron vortex beam (EVB) carrying orbital angular momentum (OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.

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Robust and adjustable C-shaped electron vortex beams

Cited by 8 publications

References 53 publications

Even-odd effect in higher-order holographic production of electron vortex beams with nontrivial radial structures

Even-odd effect in higher-order holographic production of electron vortex beams with nontrivial radial structures

A modified multiplexed vortex helico-conical petal-like zone plate

Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography

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