Probing the optical response of nanoantennas by vortex electron beams

A new result from a long-standing collaboration with my colleagues from Donostia-San Sebastian: Andrea Konecna (now at Brno University of Technology in Czech Republic), Rainer Hillenbrand, and Javier Aizpurua: in arXiv:2111.08810 we looked at the possiblity of near-field probing of electric and magnetic resonant modes in high-refractive-index nanoantennas with focused electron beams.

Electron microscopy forms a versatile set of tools for interrogating the physical, and chemical properties of nanosystems. In particular, in Electron Energy Loss Spectroscopy (EELS), electron beams are used as broadband sources of electromagnetic waves to map out the optical response of the surroundings (see Fig. 1(a)) – specifically, the electric component of the Local Density of States (e-LDOS).

Over the last decade, the ultra-high spatial resolution offered by EELS was complemented by increasing its spectral resolution, and efficient coupling to electron‑beam‑forming optics [Phys. Rev. Lett. 126, 123901 (2021)]. Another recent innovation in electron microscopy was the introduction of Vortex Electron Beams (VEBs) made up of electrons with large Orbital Angular Momentum [Nature 467, 301 (2010); Rev. Mod. Phys. 89, 035004 (2017)]. In VEBs, the circulating electrons create an effective magnetic current J_m, which can probe the magnetic LDOS, complementing the capabilities of the standard EELS (see Fig. 1(b)).

In this work we introduce a full quantum‑mechanical description of the magnetic EELS. This treatment allows us to account for the considerable spatial extension of the electrons, or the interference between the electric and magnetic currents [Phys. Rev. Lett. 113, 066102 (2014); Opt. Express 20, 15024 (2012)]. We then identify the semi‑classical limit of this problem to build a complete analogy with the EELS technique. Finally, we show how the magnetic EELS can interrogate the magnetic response of several 2D and 3D systems of interest in nanophotonics: dielectric nanoantennas, waveguides, and simple chiral structures.