Singularities in the flying electromagnetic doughnuts

Abstract

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.

Supertoroidal light pulses: Propagating electromagnetic skyrmions in free space

“…Energy backflow and Poynting vector singularities -The singularities of the electric and magnetic fields are linked to the complex topological behavior for the energy flow as represented by the Poynting vector S = E × H. An interesting effect for the fundamental TLP is the presence of energy backflow: the Poynting vector at certain regions is oriented against the prorogation direction (blue arrows in Fig. 4a) [27]. Such energy backflow effects have been predicted and discussed in the context of singular superpositions of waves [1,37], superoscillatory light fields [9,38], and plasmonic nanostructures [39].…”

“…While a large body of work on topological properties of structured continuous light beams may be found in literatures, works on the topology of the time-dependent electromagnetic excitations and pulses only start to appear. For instance, the "Flying Doughnut" pulses, or toroidal light pulses (TLPs) first described in 1996 by Hellwarth and Nouchi [26], with unique spatiotemporal topology predicted recently [27], have only very recently observed experimentally [28].…”

Toroidal Metaphotonics and Metadevices

“…[1][2][3][4][5] This integration can be attained by considering the data processing and waveguiding characteristics at more basic level, and the only possible way of overcoming those challenges is employing the concepts of metamaterials and metadevices based on structuring artificial matter at the subwavelength scales. [6][7][8] Optical magnetism, [9][10][11] asymmetric transmission, [12][13][14] hyperbolic dispersion, [15][16][17][18] epsilon near-zero (ENZ), [19][20][21][22] topological states, [23][24][25][26][27] arbitrary control of light's trajectories and cloaking, [28,29] excitation of toroidal fields and charge-current configurations, [30][31][32][33] and generation of flying doughnuts [34,35] are some of the fundamental discoveries that are allowed by metamaterials.…”

“…[53] While there have been extensive studies to develop subwavelength systems capable of multipolar toroidal moments [54] and high-order multiloop supertoroidal currents, [55,56] of particular interest is the dynamic toroidal dipole that can be optically driven and recognized as a ring-shaped head-to-tail configuration of magnetic dipoles, intensely squeezed within a tiny spot. [30][31][32][33][34][35][55][56][57][58][59][60][61][62] Theoretically, the dynamic toroidal dipole offers physically substantial nonzero contributions to both the fundamental properties of matter and scattered radiation. [63,64] Up to now, dynamic toroidal charge-current configurations with different qualities have been excited in both planar (2D) and 3D architectures, as well as cavity oligomers from visible to IR, terahertz (THz), and microwave frequencies.…”

“…[ 53 ] While there have been extensive studies to develop subwavelength systems capable of multipolar toroidal moments [ 54 ] and high‐order multiloop supertoroidal currents, [ 55,56 ] of particular interest is the dynamic toroidal dipole that can be optically driven and recognized as a ring‐shaped head‐to‐tail configuration of magnetic dipoles, intensely squeezed within a tiny spot. [ 30–35,55–62 ] Theoretically, the dynamic toroidal dipole offers physically substantial nonzero contributions to both the fundamental properties of matter and scattered radiation. [ 63,64 ]…”