Generation of electron beams carrying orbital angular momentum

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Abstract

All forms of waves can contain phase singularities1,2,3,4. In the case of optical waves, a light beam with a phase singularity carries orbital angular momentum, and such beams have found a range of applications in optical manipulation, quantum information and astronomy3,4,5,6,7,8,9. Here we report the generation of an electron beam with a phase singularity propagating in free space, which we achieve by passing a plane electron wave through a spiral phase plate constructed naturally from a stack of graphite thin films. The interference pattern between the final beam and a plane electron wave in a transmission electron microscope shows the ‘Y’-like defect pattern characteristic of a beam carrying a phase singularity with a topological charge equal to one. This fundamentally new electron degree of freedom could find application in a number of research areas, as is the case for polarized electron beams.

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Figure 1: Conversion from a plane wave to a spiral-type wave using a spiral phase plate.
Figure 2: Phase distributions and simulated interference patterns for the spiral and spiral-like linear phase plates.
Figure 3: Spiral-like phase plate composed of graphite thin films and the phase singularity in the electron interference pattern.

References

  1. 1

    Nye, J. F. & Berry, M. V. Dislocations in wave trains. Proc. R. Soc. Lond. A 336, 165–190 (1974)

    ADS  MathSciNet  Article  Google Scholar 

  2. 2

    Nye, J. F. Natural Focusing and Fine Structure of Light (Institute of Physics Publishing, 1999)

    Google Scholar 

  3. 3

    Allen, L., Barnett, S. M. & Padgett, M. J. eds. Optical Angular Momentum (Taylor & Francis, 2003)

    Google Scholar 

  4. 4

    Padgett, M., Courtial, J. & Allen, L. Light’s orbital angular momentum. Phys. Today 57 (5). 35–40 (2004)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian modes. Phys. Rev. A 45, 8185–8190 (1992)

    ADS  CAS  Article  Google Scholar 

  6. 6

    He, H., Friese, M. E. J., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 75, 826–829 (1995)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Paterson, M. et al. Controlled rotation of optically trapped microscopic particles. Science 292, 912–914 (2001)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Mair, A., Vaziri, A., Weihs, G. & Zeilinger, A. Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Molina-Terriza, G., Torres, J. P. & Torner, L. Twisted photons. Nature Phys. 3, 305–310 (2007)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Fukuhara, A., Shinagawa, K., Tonomura, A. & Fujiwara, H. Electron holography and magnetic specimens. Phys. Rev. B 27, 1839–1843 (1983)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Tonomura, A. Applications of electron holography. Rev. Mod. Phys. 59, 639–669 (1987)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Allen, L. J., Faulkner, H. M. L., Oxley, M. P. & Paganin, D. Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy. Ultramicroscopy 88, 85–97 (2001)

    CAS  Article  Google Scholar 

  13. 13

    Bliokh, K. Y., Bliokh, Y. P., Savel’ev, S. & Nori, F. Semiclassical dynamics of electron wave packet states with phase vortices. Phys. Rev. Lett. 99, 190404 (2007)

    ADS  Article  Google Scholar 

  14. 14

    Beijersbergen, M. W., Allen, L., van der Veen, H. E. L. O. & Woerdman, J. P. Astigmatic laser mode converters and transfer of orbital momentum. Opt. Commun. 96, 123–132 (1993)

    ADS  Article  Google Scholar 

  15. 15

    Khonina, S. N., Kotlyar, V. V., Shinkaryev, M. V., Soifer, V. A. & Uspleniev, G. V. The phase rotor filter. J. Mod. Opt. 39, 1147–1154 (1992)

    ADS  Article  Google Scholar 

  16. 16

    Beijersbergen, M. W., Coerwinkel, R. P. C., Kristensen, M. & Woerdman, J. P. Helical-wavefront laser beams produced with a spiral phaseplate. Opt. Commun. 112, 321–327 (1994)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Kotlyar, V. V. et al. Diffraction of a plane, finite-radius wave by a spiral phase plate. Opt. Lett. 31, 1597–1599 (2006)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Bazhenov, V., Yu, Vasnetsov, M. V. & Soskin, M. S. Laser beams with screw dislocations in their wavefronts. Sov. JETP Lett. 52, 429–431 (1990)

    Google Scholar 

  19. 19

    Heckenberg, H. R., McDuff, R., Smith, C. P. & White, A. G. Generation of optical phase singularities by computer-generated holograms. Opt. Lett. 17, 221–223 (1992)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Basistiy, I., Bazhenov, V., Yu, Soskin, M. S. & Vasnetsov, M. V. Optics of light beams with screw dislocations. Opt. Commun. 103, 422–428 (1993)

    ADS  Article  Google Scholar 

  21. 21

    Angelsky, O. V., Besaha, R. N. & Mokhun, I. I. Appearance of wave front dislocations under interference among beams with simple wave fronts. Opt. Appl. 27, 273–278 (1997)

    Google Scholar 

  22. 22

    Kim, G. H. et al. Optical vortices produced with a nonspiral phase plate. Appl. Opt. 36, 8614–8621 (1997)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Uchida, M., Onose, Y., Matsui, Y. & Tokura, Y. Real-space observation of helical spin order. Science 311, 359–361 (2006)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Tonomura, A. Electron Holography (Springer, 1999)

    Google Scholar 

  25. 25

    Völkl, E., Allard, L. F. & Frost, B. J. A software package for the processing and reconstruction of electron holograms. Microscopy 180, 39–50 (1995)

    Article  Google Scholar 

  26. 26

    Leach, J., Yao, E. & Padgett, M. J. Observation of the vortex structure of a non-integer vortex beam. N. J. Phys. 6, 71 (2004)

    Article  Google Scholar 

  27. 27

    Fürhapter, S., Jesacher, A., Bernet, S. & Ritsch-Marte, M. Spiral phase contrast imaging in microscopy. Opt. Express 13, 689–694 (2005)

    ADS  Article  Google Scholar 

  28. 28

    Majorovits, E. et al. Optimizing phase contrast in transmission electron microscopy with an electrostatic (Boersch) phase plate. Ultramicroscopy 107, 213–226 (2007)

    CAS  Article  Google Scholar 

  29. 29

    Schattschneider, P. Exchange of angular momentum in EMCD experiments. Ultramicroscopy 109, 91–95 (2008)

    CAS  Article  Google Scholar 

  30. 30

    Sánchez, A. & Ochando, M. A. Calculation of the mean inner potential. J. Phys. C 18, 33–41 (1985)

    ADS  Article  Google Scholar 

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Acknowledgements

Discussions with F. Nori, H. Ichinose and K. Sawada of RIKEN are acknowledged.

Author Contributions M.U. had the idea of doing this experiment, fabricated the phase plate, performed the TEM experiments, analysed and interpreted the data, simulated the interference patterns, and wrote the manuscript; A.T. coordinated the work on the TEM.

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Correspondence to Masaya Uchida.

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The authors declare no competing financial interests.

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Uchida, M., Tonomura, A. Generation of electron beams carrying orbital angular momentum. Nature 464, 737–739 (2010). https://doi.org/10.1038/nature08904

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