Excitation of Nonradiating Anapoles in Dielectric Nanospheres

John A. Parker, Hiroshi Sugimoto, Brighton Coe, Daniel Eggena, Minoru Fujii, Norbert F. Scherer, Stephen K. Gray, and Uttam Manna

Phys. Rev. Lett. 124, 097402 – Published 6 March 2020

Abstract

Although the study of nonradiating anapoles has long been part of fundamental physics, the dynamic anapole at optical frequencies was only recently experimentally demonstrated in a specialized silicon nanodisk structure. We report excitation of the electrodynamic anapole state in isotropic silicon nanospheres using radially polarized beam illumination. The superposition of equal and out-of-phase amplitudes of the Cartesian electric and toroidal dipoles produces a pronounced dip in the scattering spectra with the scattering intensity almost reaching zero—a signature of anapole excitation. The total scattering intensity associated with the anapole excitation is found to be more than 10 times weaker for illumination with radially vs linearly polarized beams. Our approach provides a simple, straightforward alternative path to realizing nonradiating anapole states at the optical frequencies.

Received 14 August 2019
Accepted 27 January 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.097402

Physics Subject Headings (PhySH)

Nanoantennas Nanophotonics Optical materials & elements

Nanoparticles

Optical spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

John A. Parker^2,3, Hiroshi Sugimoto ⁴, Brighton Coe ¹, Daniel Eggena ¹, Minoru Fujii ⁴, Norbert F. Scherer ^2,5, Stephen K. Gray ⁶, and Uttam Manna ^1,*

¹Department of Physics, Illinois State University, Normal, Illinois 61709, USA
²The James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
³Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
⁴Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan
⁵Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
⁶Center for Nanoscale Materials, Argonne National Laboratory, Lemont, Illinois 60439, USA

^*umanna@ilstu.edu

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Issue

Vol. 124, Iss. 9 — 6 March 2020

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Images

Figure 1
Demonstration of the anapole excitation and simulated electric field distributions. (a) Schematic diagram showing excitation of a Si nanosphere ( $d \sim 160 nm$ ) for radially polarized beam excitation. In addition to the z component of the electric resonances ( $P_{z}$ ), the radially polarized beam is expected to generate a z component of the toroidal response ( $T_{z}$ ) produced by the circulating magnetic field ( $H$ ) associated with the poloidal currents ( $J_{p}$ ) flowing in the bulk. (b) Streamlines of the total electric field for radially polarized beam illumination as calculated using generalized Mie theory show that the toroidal current [given by Eq. (3)] is indeed produced within the volume of the nanosphere.
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Figure 2
Scattering spectra of single Si nanospheres under linear and vector beam illumination. The experimental (a),(c) and simulated (b),(d) scattering spectra of single Si nanospheres with diameter 160 (a),(b) and 180 nm (c),(d), respectively, for linearly, radially, and azimuthally polarized beam illuminations. The right insets of (a) and (c) show the SEM images of the exact same nanospheres whose scattering spectra are shown. The white scale bars on the SEM images are 500 nm. The results show that the scattering minima are deepest for radial beam excitation at around 500 nm (the regions of interest is shown in the insets) for $d = 160 nm$ (a),(b), and at around 520 nm for $d = 180 nm$ (c),(d). The simulated spectra were calculated using generalized Mie theory over all the scattering angles, whereas the experimental spectra were measured in the backward direction for the angular range determined by the numerical aperture of the microscope objective.
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Figure 3
Multipolar decomposition of the scattering spectra. The calculated scattering spectra of single Si nanospheres with diameter $d = 160 nm$ for linearly (a), radially (b), and azimuthally (c) polarized beam illuminations. The multipolar decomposition shows that both electric and magnetic modes are excited for linearly polarized beam; whereas only electric (magnetic) modes are excited for radially (azimuthally) polarized beam illumination. The toroidal dipoles are also excited for linearly and radially polarized beam illuminations.
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Figure 4
The amplitude (a) and phase (b) of the Cartesian electric and toroidal dipoles under radially polarized beam illumination for $d = 160 nm$ . The results show that the amplitudes of the Cartesian electric and toroidal dipoles are equal and out of phase at $λ \sim 500 nm$ for $d = 160 nm$ resulting in excitation of the anapole. (c) shows the fraction of the localized vs radiated energy calculated for linear, radial, and azimuthal beam illuminations for $d = 160 nm$ . The stored energy is $\sim 6$ times greater for radial vs linear beam illumination.
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