Generation of electron beams carrying orbital angular momentum



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.


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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) doi:10.1038/nature08904

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