Singularities in the flying electromagnetic doughnuts

Apostolos Zdagkas, Nikitas Papasimakis, Vassili Savinov, Mark Dennis, Nikolay I. Zheludev

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
152 Downloads (Pure)


Flying doughnuts (FDs) are exact propagating solutions of Maxwell equations in the form of single-cycle, space-time non-separable toroidal pulses. Here we review their properties and reveal the existence of a complex and robust fine topological structure. In particular, the electric and magnetic fields of the FD pulse vanish across a number of planes, spherical shells and rings, and display a number of point singularities including saddle points and vortices. Moreover, the instantaneous Poynting vector of the field exhibits a large number of singularities, which are often accompanied by extended areas energy backflow.
Original languageEnglish
Pages (from-to)1379-1385
Number of pages7
Issue number8
Publication statusPublished - 22 Jun 2019


  • flying doughnut
  • singularities
  • topology
  • toroidal electrodynamics
  • toroidal pulse
  • vortex


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