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Electron beams traversing spherical nanoparticles: Analytic and numerical treatment

P. Elli Stamatopoulou1,*, Wenhua Zhao2,3, Álvaro Rodríguez Echarri3, N. Asger Mortensen1,4, Kurt Busch2,3,†, Christos Tserkezis1, and Christian Wolff1,‡

  • 1POLIMA—Center for Polariton-driven Light-Matter Interactions, University of Southern Denmark, 5230 Odense M, Denmark
  • 2Humboldt-Universität zu Berlin, Institut für Physik, AG Theoretische Optik and Photonik, 12489 Berlin, Germany
  • 3Max-Born-Institut, 12489 Berlin, Germany
  • 4Danish Institute for Advanced Study, University of Southern Denmark, 5230 Odense M, Denmark

  • *elli@mci.sdu.dk
  • †kurt.busch@physik.hu-berlin.de
  • ‡cwo@mci.sdu.dk
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Phys. Rev. Research 6, 013239 – Published 5 March, 2024Erratum Phys. Rev. Research 8, 029002 (2026)

DOI: https://doi.org/10.1103/PhysRevResearch.6.013239

Abstract

We present an analytic, Mie theory-based solution for the energy loss and the photon-emission probabilities in the interaction of spherical nanoparticles with electrons passing nearby and through them, in both cathodoluminescence and electron energy-loss spectroscopies. In particular, we focus on the case of penetrating electron trajectories, for which the complete fully electrodynamic and relativistic formalism has not been reported as yet. We exhibit the efficiency of this method in describing collective excitations in matter through calculations for a dispersive and lossy system, namely a sphere described by a Drude permittivity. Subsequently, we use the analytic solution to corroborate the implementation of electron-beam sources in a state-of-the-art numerical method for problems in electrodynamics, the discontinuous Galerkin time-domain (DGTD) method. We show that the two approaches produce spectra in good mutual agreement, and demonstrate the versatility of DGTD via simulations of spherical nanoparticles characterized by surface roughness. The possibility of simultaneously employing both kinds of calculations (analytic and numerical) facilitates a better understanding of the rich optical response of nanophotonic architectures excited by fast electron beams.

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Erratum

Erratum: Electron beams traversing spherical nanoparticles: Analytic and numerical treatment [Phys. Rev. Research 6, 013239 (2024)]

P. Elli Stamatopoulou, Wenhua Zhao, Álvaro Rodríguez Echarri, N. Asger Mortensen, Kurt Busch, Christos Tserkezis, and Christian Wolff
Phys. Rev. Research 8, 029002 (2026)

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Phys. Rev. Research 6, 013239– Published 5 March, 2024
  • Received 5 September 2023
  • Accepted 7 January 2024
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