Singularities in the flying electromagnetic doughnuts

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.