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 non-separable 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 R. Ziolkowski in 1985. Later R. W. Hellwarth and P. Nouchi 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 non-separable 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. Many practical questions are yet to be answered regarding their generation, detection and light-matter interactions. Here we demonstrate that the Flying Donut is bandwidth limited and 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.

Space-time wave packets

“…Viewed from a different viewpoint, each position in the toroidal-pulse wave front is associated with a prescribed temporal spectrum. Therefore, one pathway to synthesizing such a wave packet is to exploit a metasurface in which each point on the surface provides a resonance response that filters the required spectrum for the toroidal pulse at that point from a plane-wave pulse [372,376,377]; Fig. 51(b).…”

Nonseparable states of light: From quantum to classical

“…The crucial characteristic induced by the space-time nonseparable pulse is the isodiffraction nature, whereby the spatial distribution of different spectral components in the transverse plane does not suffer distortion upon propagation. [96,97], as demonstrated by the map of colored lines in Fig. 3l.…”

“…As discussed in Section 3.2, the isodiffracting single-cycle pulses can be expressed as high-dimensional Bell state with two DoFs (space and time). The class of isodiffractin pulses includes pancakelike pulses [93,96] and doughnut-like pulses [94,97]. The focused pancake pulse is linearly polarised, while the doughnut-like pulse presents a can perform complex structure of cylindrically polarized vector fields, including the azimuthal (for transverse electric modes) [136] and radial polarized fields (for transverse magnetic mode) [137] (the vector structure of transverse electric mode is depicted in Fig.…”

Nonseparable States of Light: From Quantum to Classical

“…This family of pulses includes both linearly polarized pulses, termed "focused pancakes", [95] as well as pulses of toroidal symmetry, termed "flying doughnuts", [96] which were experimentally generated very recently. [79] The crucial characteristic induced by the space-time nonseparable pulse is the isodiffraction nature, whereby the spatial distribution of different spectral components in the transverse plane does not suffer distortion upon propagation, [97,98] as demonstrated by the map of colored lines in Figure 3l. Recently, a quantum-analogue method to characterize space-time (or -frequency) nonseparability was proposed, highlighting the link between isodiffracting pulses and highdimensional Bell states.…”