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Chin. Phys. B, 2020, Vol. 29(8): 084102    DOI: 10.1088/1674-1056/ab96a9

Electromagnetic field of a relativistic electron vortex beam

Changyong Lei(雷长勇)1, Guangjiong Dong(董光炯)1,2
1 State Key Laboratory of Precision Spectroscopy, School of Physics and Electronics, East China Normal University, Shanghai 200241, China;
2 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
Abstract  Electron vortex beams (EVBs) have potential applications in nanoscale magnetic probes of condensed matter and nanoparticle manipulation as well as radiation physics. Recently, a relativistic electron vortex beam (REVB) has been proposed[Phys. Rev. Lett. 107 174802 (2011)]. Compared with EVBs, except for orbital angular momentum, an REVB has intrinsic relativistic effect, i.e., spin angular momentum and spin-orbit coupling. We study the electromagnetic field of an REVB analytically. We show that the electromagnetic field can be separated into two parts, one is only related to orbital quantum number, and the other is related to spin-orbit coupling effect. Exploiting this separation property, the difference between the electromagnetic fields of the REVB in spin-up and spin-down states can be used as a demonstration of the relativistic quantum effect. The linear momentum and angular momentum of the generated electromagnetic field have been further studied and it is shown that the linear momentum is weakly dependent on the spin state; while the angular momentum is evidently dependent on the spin state and linearly increases with the topological charge of electron vortex beam. The electromagnetic and mechanical properties of the REVB could be useful for studying the interaction between REVBs and materials.
Keywords:  relativistic electron vortex beam      electromagnetic vortex field      spin-orbit coupling      orbital angular momentum  
Received:  25 February 2020      Revised:  05 April 2020      Published:  05 August 2020
PACS:  41.85.-p (Beam optics)  
  42.50.Tx (Optical angular momentum and its quantum aspects)  
  03.65.Pm (Relativistic wave equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11574085, 91536218, and 11834003), the 111 Project, China (Grant No. B12024), the National Key Research and Development Program of China (Grant No. 2017YFA0304201), and the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 2019-01-07-00-05-E00079).
Corresponding Authors:  Guangjiong Dong     E-mail:

Cite this article: 

Changyong Lei(雷长勇), Guangjiong Dong(董光炯) Electromagnetic field of a relativistic electron vortex beam 2020 Chin. Phys. B 29 084102

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