Abstract:

Toroidal multipoles are fundamental electromagnetic excitations, which cannot be represented in terms of the standard multipole expansion and therefore are missing in standard textbooks on electrodynamics [1]. They were first considered by Zel’dovich back in 1957 [2], but only recently have become the subject of growing interest in optics and electrodynamics owing to their peculiar electromagnetic properties. Electromagnetic interactions with toroidal currents were predicted to disobey such widely accepted principle as the action-reaction equality. Toroidal currents can also form charge-current configurations generating vector potential fields in the absence of radiated electromagnetic waves. Although toroidal moments are held responsible for parity violation in nuclear and particle physics, no direct evidence of their importance for classical electrodynamics (and optics, in particular) has been reported until recently. This is because effects associated with toroidal multipoles in naturally available materials are extremely weak and usually masked by much stronger effects due to conventional electric and magnetic dipoles and quadrupoles. A long chase for the elusive dynamic toroidal excitation was concluded by detecting a spectral signature of the toroidal dipolar resonance in the response of a specially designed electromagnetic metamaterial [1], which subsequently gave rise to a whole new research field – toroidal electrodynamics [Nature]. In this tutorial I will give a brief introduction into this (still controversial) field of research and discus the observations of the long sought non-trivial non-radiating charge-current excitation – the so-called dynamic anapole, which provide new ammunition for the discussion on independent physical significance of vector-potential and its role as a new information carrier.

[1] V. M. Dubovik, V. V. Tugushev “Toroid moments in electrodynamics and solid state physics”, Phys. Rep. 187, 145-202 (1990).

[2] Ia .B. Zel’dovich “Electromagnetic interaction with parity violation”, Sov. Phys. JETP 6, 1184-1186 (1958).

[3] T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330, 1510 (2010).

[4] G. N. Afanasiev and Yu. P. Stepanovsky, “The electromagnetic field of elementary time-dependent toroidal sources,” J. Phys. A: Math. Gen. 28, 4565 (1995).

[5] N. Papasimakis, V. Fedotov, V. Savinov, T. A. Raybould, and N. I. Zheludev, “Electromagnetic toroidal excitations in matter and free space,” Nat. Mater. 15, 263 (2016).

Short Bio: 

Prof. Vassili Fedotov is a professor at the Centre for Photonic Science and Engineering where he heads a newly established group, SPARQ lab. Vassili graduated Lomonosov Moscow State University in 1999 with MSc degree in physics, and received PhD degree in laser physics from the University of Southampton (School of Physics and Astronomy) in 2003. Prior to joining Skolkovo Institute of Science and Technology Vassili has held the post of a Principal Research Fellow at Southampton’s Optoelectronics Research Centre. His interest lies in the fields of metamaterials, plasmonics, nanophotonics and toroidal electrodynamics. Prof. Fedotov’s most recent work concerns, in particular, the development of novel hybrid nano-opto-electro-mechanical systems (NOEMS) incorporating liquid crystals for applications in smart nanophotonic devices, re-configurable metamaterials and optical sensors.