Singularities in the flying electromagnetic doughnuts

Research output: Contribution to journalArticlepeer-review


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

Colleges, School and Institutes


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


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