Electromagnetic toroidal excitations in matter and free space

Abstract

The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristics of matter including absorption, dispersion, and optical activity. Toroidal excitations also exist in free-space as spatially and temporally localized electromagnetic pulses propagating at the speed of light and interacting with matter. We review recent experimental observations of resonant toroidal dipole excitations in metamaterials and the discovery of anapoles, non-radiating current configurations involving toroidal dipoles. While certain fundamental and practical aspects of toroidal electrodynamics remain open for the moment, we envision that exploitation of toroidal response can have important implications for the fields of photonics, sensing, energy and information. IntroductionThe interactions of electromagnetic radiation with matter underpin some of the most important technologies today -from telecommunications to information processing and data storage; from spectroscopy and imaging to light-assisted manufacturing. Our understanding and description of the electromagnetic properties of matter traditionally involves the concept of electric and magnetic dipoles, as well as their more complex combinations, known as multipoles. Introduced by Maxwell and Lorentz and later refined by Jackson and Landau, this framework, termed the multipole expansion, is central in physics and is being routinely applied in the study of optical, condensed matter, atomic, nuclear phenomena and beyond 1 . Within this framework, electromagnetic media can be represented by a set of point-like multipole sources [2][3][4][5] . The commonly used set of multipoles comprises the electric and magnetic families, which can be represented by oscillating charges and loop currents respectively. Dynamic toroidal multipoles constitute a third independent family of elementary electromagnetic sources, rather than an alternative multipole expansion or higher-order corrections to the conventional electric and magnetic multipoles (see tutorial inset I).Introduced in 1958 by Y. B. Zeldovich, toroidal moments have been considered in systems of toroidal topology (see Fig. 1) and studied in the context of nuclear 6 , atomic 7 , and molecular physics 8 , classical electrodynamics 9,10 , and solid state physics 3 . In the field of electromagnetism, in particular, a number of works have led to the development of a complete theoretical framework for toroidal electrodynamics [11][12][13][14][15] and the prediction of exotic effects, including dynamic non-radiating charge current configurations 10 and non-reciprocal interactions 9 . Following recent experimental observations of toroidal contributions in the response of materials across the electromagnetic spectrum, dyn...

Suppression of scattering for small dielectric particles: anapole mode and invisibility

“…Previously it was shown that such type of interference, the socalled anapole mode 31,32 , could be observed in Si nanodisks. For nanodisks, this anapole mode can be achieved at a specific wavelength and for some fixed ratio of the disk height to its diameter.…”

Metamaterials at the University of Southampton and beyond

“…Our group reported the observation of the dynamic anapole in a microwave metamaterial in 2013 [125]. The observation of a resonant toroidal response in metamaterials has enabled the systematic study of toroidal electrodynamics [126]. Despite the recent stream of experimental and theoretical works, however, the field is still in its infancy, with many questions to be resolved and applications to be explored.…”

Exciting dynamic anapoles with electromagnetic doughnut pulses

“…FD pulses can be seen as propagating counterparts of the localized toroidal dipole excitations in matter [11]. The toroidal dipole is distinct from the conventional electric and magnetic dipoles [12,13] and have attracted significant interest in recent years as important contributors to the electromagnetic properties of media with non-local response or elements of toroidal symmetry [11,[14][15][16][17][18][19][20][21]. Superposition of dynamic electric and toroidal dipoles leads to anapoles which, through destructive interference, exhibit vanishing radiated fields outside the source [20,22].…”

“…They are necessarily few-cycle, wideband electromagnetic perturbations with toroidal field topology that can exist in transverse electric (TE) and transverse magnetic (TM) configurations [1,10]. FD pulses can be seen as propagating counterparts of the localized toroidal dipole excitations in matter [11]. The toroidal dipole is distinct from the conventional electric and magnetic dipoles [12,13] and have attracted significant interest in recent years as important contributors to the electromagnetic properties of media with non-local response or elements of toroidal symmetry [11,[14][15][16][17][18][19][20][21].…”