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Huo PC, Yu RX, Liu MZ et al. Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography. Opto-Electron Adv 7, 230184 (2024). doi: 10.29026/oea.2024.230184
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Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography
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Abstract
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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References
[1] Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A 45, 8185–8189 (1992). doi: 10.1103/PhysRevA.45.8185 [2] Pu MB, Li X, Ma XL, Wang YQ, Zhao ZY et al. Catenary optics for achromatic generation of perfect optical angular momentum. Sci Adv 1, e1500396 (2015). doi: 10.1126/sciadv.1500396 [3] Shen YJ, Wang XJ, Xie ZW, Min CJ, Fu X et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light Sci Appl 8, 90 (2019). doi: 10.1038/s41377-019-0194-2 [4] Fang XY, Ren HR, Li KY, Luan HT, Hua YL et al. Nanophotonic manipulation of optical angular momentum for high-dimensional information optics. Adv Opt Photonics 13, 772–833 (2021). doi: 10.1364/AOP.414320 [5] Guo YH, Zhang SC, Pu MB, He Q, Jin JJ et al. Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation. Light Sci Appl 10, 63 (2021). doi: 10.1038/s41377-021-00497-7 [6] Zhang YX, Liu XF, Lin H, Wang D, Cao ES et al. Ultrafast multi-target control of tightly focused light fields. Opto-Electron Adv 5, 210026 (2022). doi: 10.29026/oea.2022.210026 [7] Porfirev A, Khonina S, Ustinov A, Ivliev N, Golub I. Vectorial spin-orbital Hall effect of light upon tight focusing and its experimental observation in azopolymer films. Opto-Electron Sci 2, 230014 (2023). doi: 10.29026/oes.2023.230014 [8] Paterson L, MacDonald MP, Arlt J, Sibbett W, Bryant PE et al. Controlled rotation of optically trapped microscopic particles. Science 292, 912–914 (2001). doi: 10.1126/science.1058591 [9] Grier DG. A revolution in optical manipulation. Nature 424, 810–816 (2003). doi: 10.1038/nature01935 [10] Willig KI, Rizzoli SO, Westphal V, Jahn R, Hell SW. STED-microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis. Nature 440, 935–939 (2006). doi: 10.1038/nature04592 [11] Luo XG. Principles of electromagnetic waves in metasurfaces. Sci China Phys, Mech Astron 58, 594201 (2015). doi: 10.1007/s11433-015-5688-1 [12] Nicolas A, Veissier L, Giner L, Giacobino E, Maxein D et al. A quantum memory for orbital angular momentum photonic qubits. Nat Photonics 8, 234–238 (2014). doi: 10.1038/nphoton.2013.355 [13] Ren HR, Li XP, Zhang QM, Gu M. On-chip noninterference angular momentum multiplexing of broadband light. Science 352, 805–809 (2016). doi: 10.1126/science.aaf1112 [14] Fang XY, Ren HR, Gu M. Orbital angular momentum holography for high-security encryption. Nat Photonics 14, 102–108 (2020). doi: 10.1038/s41566-019-0560-x [15] Uchida M, Tonomura A. Generation of electron beams carrying orbital angular momentum. Nature 464, 737–739 (2010). doi: 10.1038/nature08904 [16] Verbeeck J, Tian H, Schattschneider P. Production and application of electron vortex beams. Nature 467, 301–304 (2010). doi: 10.1038/nature09366 [17] McMorran BJ, Agrawal A, Anderson IM, Herzing AA, Lezec HJ et al. Electron vortex beams with high quanta of orbital angular momentum. Science 331, 192–195 (2011). doi: 10.1126/science.1198804 [18] Grillo V, Gazzadi GC, Mafakheri E, Frabboni S, Karimi E et al. Holographic generation of highly twisted electron beams. Phys Rev Lett 114, 034801 (2015). doi: 10.1103/PhysRevLett.114.034801 [19] Yuan XY, Xu Q, Lang YH, Jiang XH, Xu YH et al. Tailoring spatiotemporal dynamics of plasmonic vortices. Opto-Electron Adv 6, 220133 (2023). doi: 10.29026/oea.2023.220133 [20] Petersen TC, Weyland M, Paganin DM, Simula TP, Eastwood SA et al. Electron vortex production and control using aberration induced diffraction catastrophes. Phys Rev Lett 110, 033901 (2013). doi: 10.1103/PhysRevLett.110.033901 [21] Béché A, Van Boxem R, Van Tendeloo G, Verbeeck J. Magnetic monopole field exposed by electrons. Nat Phys 10, 26–29 (2014). doi: 10.1038/nphys2816 [22] Harris J, Grillo V, Mafakheri E, Gazzadi GC, Frabboni S et al. Structured quantum waves. Nat Phys 11, 629–634 (2015). doi: 10.1038/nphys3404 [23] Bliokh KY, Ivanov IP, Guzzinati G, Clark L, Van Boxem R et al. Theory and applications of free-electron vortex states. Phys Rep 690, 1–70 (2017). doi: 10.1016/j.physrep.2017.05.006 [24] Mousley M, Thirunavukkarasu G, Babiker M, Yuan J. Robust and adjustable C-shaped electron vortex beams. New J Phys 19, 063008 (2017). doi: 10.1088/1367-2630/aa6e3c [25] Yang YQ, Forbes A, Cao LC. A review of liquid crystal spatial light modulators: devices and applications. Opto-Electron Sci 2, 230026 (2023). doi: 10.29026/oes.2023.230026 [26] Freund I. Optical vortices in Gaussian random wave fields: statistical probability densities. J Opt Soc Am A 11, 1644–1652 (1994). [27] Freund I, Freilikher V. Parameterization of anisotropic vortices. J Opt Soc Am A 14, 1902–1910 (1997). doi: 10.1364/JOSAA.14.001902 [28] Nye JF, Berry MV. Dislocations in wave trains. Proc Roy Soc A Math Phys Eng Sci 336, 165–190 (1974). [29] Harvey TR, Pierce JS, Agrawal AK, Ercius P, Linck M et al. Efficient diffractive phase optics for electrons. New J Phys 16, 093039 (2014). doi: 10.1088/1367-2630/16/9/093039 [30] Grillo V, Karimi E, Gazzadi GC, Frabboni S, Dennis MR et al. Generation of nondiffracting electron Bessel beams. Phys Rev X 4, 011013 (2014). [31] Polman A, Kociak M, Javier García de Abajo F. Electron-beam spectroscopy for nanophotonics. Nat Mater 18, 1158–1171 (2019). doi: 10.1038/s41563-019-0409-1 [32] Yu RX, Huo PC, Liu MZ, Zhu WQ, Agrawal A et al. Generation of perfect electron vortex beam with a customized beam size independent of orbital angular momentum. Nano Lett 23, 2436–2441 (2023). doi: 10.1021/acs.nanolett.2c03822 [33] Verbeeck J, He T, Van Tendeloo G. How to manipulate nanoparticles with an electron beam. Adv Mater 25, 1114–1117 (2013). doi: 10.1002/adma.201204206 [34] Lloyd S, Babiker M, Yuan J. Quantized orbital angular momentum transfer and magnetic dichroism in the interaction of electron vortices with matter. Phys Rev Lett 108, 074802 (2012). doi: 10.1103/PhysRevLett.108.074802 [35] Ugarte D, Ducati C. Controlling multipolar surface Plasmon excitation through the azimuthal phase structure of electron vortex beams. Phys Rev B 93, 205418 (2016). doi: 10.1103/PhysRevB.93.205418 [36] Guzzinati G, Béché A, Lourenço-Martins H, Martin J, Kociak M et al. Probing the symmetry of the potential of localized surface plasmon resonances with phase-shaped electron beams. Nat Commun 8, 14999 (2017). doi: 10.1038/ncomms14999 [37] Clark CW, Barankov R, Huber MG, Arif M, Cory DG et al. Controlling neutron orbital angular momentum. Nature 525, 504–506 (2015). doi: 10.1038/nature15265 [38] Madan I, Vanacore GM, Gargiulo S, LaGrange T, Carbone F. The quantum future of microscopy: wave function engineering of electrons, ions, and nuclei. Appl Phys Lett 116, 230502 (2020). doi: 10.1063/1.5143008 [39] Lembessis VE, Ellinas D, Babiker M, Al-Dossary O. Atom vortex beams. Phys Rev A 89, 053616 (2014). doi: 10.1103/PhysRevA.89.053616 [40] Luski A, Segev Y, David R, Bitton O, Nadler H et al. Vortex beams of atoms and molecules. Science 373, 1105–1109 (2021). doi: 10.1126/science.abj2451 -
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Huo PC, Yu RX, Liu MZ et al. Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography. Opto-Electron Adv 7, 230184 (2024). doi: 10.29026/oea.2024.230184
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Figure 1.
Schematic of the generation of structured EVBs. The binary holographic phase masks can be engineered with the generalized spiral phase to shape the incident free electrons to generate structured EVBs with customizable intensity patterns. The phase mask is composed of nanoscale forked gratings fabricated on 100 nm-thick silicon nitride membranes.
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Figure 2.
Theoretical construction of structured EVBs. (a–c) Three parameterized azimuth gradients
$ {\text{f}}_{\text{1}}{{'}}\left(\text{θ} \right) $ $ {\text{f}}_{\text{2}}{{'}}\left(\text{θ} \right) $ $ {\text{f}}_{\text{3}}{{'}}\left(\text{θ}\right) $ $ {\text{\varphi} }_{\text{1}} $ $ {\text{\varphi} }_{\text{2}} $ $ {\text{\varphi} }_{\text{3}} $ -
Figure 3.
Experimental generation of structured EVBs using nanoscale holographic phase masks with fork dislocations. (a–c) The scanning electron microscope (SEM) images of phase masks for three EVBs. Scale bars: 4 μm. Insets are the enlarged middle portions of phase masks. Scale bars: 1 μm. (d–f) Experimentally recorded far-field intensity distributions and (g–i) Phase profiles retrieved by the transmission iterative algorithm. (j–l) Calculated far-field intensity distributions and (m–o) phase profiles. Scale bars of (d–o): 3 μrad. (p–r) In-plane components of the probability current density vectors of three EVBs extracted from experimental measurements. The red arrows indicate the direction of the probability current of electron. The lengths of the red arrows are given in arbitrary unit normalized to the maximum value. Scale bars of (p–r): 3 μrad.
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Figure 4.
Modal decomposition of EVBs. The OAM spectral distributions of three structured EVBs extracted from the experimental results. The blue, green and red histograms correspond to clover, spiral and arrowhead EVBs, respectively.
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Figure 5.
Coherent superposition of structured EVBs. (a–c) The SEM images of fabricated phase masks to generate superposition states of topological charge l1 = 30 and l2 = 33, corresponding to three structured EVBs. Scale bars: 4 μm. Insets are the enlarged middle portions of phase masks. Scale bars: 1 μm. (d–f) Experimentally recorded interference patterns of the superposition states. (g–i) Simulated interference patterns of superposition states. Scale bars of (d–i): 3 μrad.
