Space-time nonseparable pulses: Constructing isodiffracting donut pulses from plane waves and single-cycle pulses

Abstract

Maxwell's equations can be satisfied not only by plane electromagnetic waves, but also by more exotic space-time nonseparable electromagnetic pulses which cannot be represented as a product of time- and space-dependent functions. A family of such pulses with finite energy was identified by Ziolkowski [Phys. Rev. A 39, 2005 (1989)]. Later, Hellwarth and Nouchi [Phys. Rev. E 54, 889 (1996)] highlighted a subset of Ziolkowski's pulses, now known as flying donuts, a formation of polarization singularities of toroidal topology traveling at the speed of light. Spurred by recent advances in ultrafast and topological optics, space-time nonseparable electromagnetic excitations are now becoming the focus of growing experimental efforts as they hold promise for topological information transfer, probing and inducing transient excitations in matter such as anapole and toroidal modes. Here we demonstrate that the flying donut can be constructed from an ensemble of monochromatic plane waves with continuous spatial and frequency spectrum and hence can be generated by converting broadband conventional transverse electromagnetic pulses.