Anapole states and scattering deflection effects in anisotropic van der Waals nanoparticles

Andrei A. Ushkov, Georgy A. Ermolaev, Andrey A. Vyshnevyy, Denis G. Baranov, Aleksey V. Arsenin, and Valentyn S. Volkov

Phys. Rev. B 106, 195302 – Published 7 November 2022

Abstract

Transition metal dichalcogenides (TMDCs), belonging to the class of van der Waals materials, are promising materials for optoelectronics and photonics. In particular, their giant optical anisotropy may enable important optical effects when employed in nanostructures with finite thickness. In this paper, we theoretically and numerically study light scattering behavior from anisotropic $Mo S_{2}$ nanocylinders, and highlight its distinct features advantageous over the response of conventional silicon particles of the same shape. We establish two remarkable phenomena, appearing in the same $Mo S_{2}$ particle with optimized geometry. The first one is a pure magnetic dipole scattering associated with the excitation of the electric-dipole anapole states. Previously reported in core-shell hybrid (metal/dielectric) systems only, it is now demonstrated in an all-dielectric particle. The second phenomenon is the super deflection in the far-field: the maximum scattering may occur over a wide range of directions, including forward-, backward- and side-scattering depending on the mutual orientation of the $Mo S_{2}$ nanocylinder and the incident wave. In contrast to the well-known Kerker and anti-Kerker effects, which appear in nanoparticles at different frequencies, the super deflection can be achieved by rotating the particle at a constant frequency of incident light. Our results facilitate the development of functional optical devices incorporating nanostructured anisotropic TMDCs and may encourage further research in meta-optics based on highly anisotropic materials.

Received 21 July 2022
Revised 16 October 2022
Accepted 18 October 2022

DOI:https://doi.org/10.1103/PhysRevB.106.195302

Physics Subject Headings (PhySH)

Birefringence Dielectric properties First-principles calculations Nanophotonics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Andrei A. Ushkov ^*, Georgy A. Ermolaev , Andrey A. Vyshnevyy , Denis G. Baranov , Aleksey V. Arsenin , and Valentyn S. Volkov

Center for Photonics & 2D Materials, Moscow Institute of Physics and Technology (MIPT), Dolgoprudny 141700, Russia

^*ushkov.aa@mipt.ru

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Issue

Vol. 106, Iss. 19 — 15 November 2022

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Images

Figure 1
(a)-(b) Schematic view of the studied elliptic-cylinder nanoparticles. A free-standing $Mo S_{2}$ /Si nanoparticle in vacuum is illuminated with TE/TM polarized light in visible and near-IR; the TE/TM polarization is defined with respect to the incidence plane formed by the normal vector n and $d_{1}$ . Optic axis of $Mo S_{2}$ is oriented along the vector n. (c) Optical constants of $Mo S_{2}$ and Si used for numerical simulations.
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Figure 2
Spectral analysis of anapoles and magnetic dipoles in $Mo S_{2}$ and Si particles. (a) Scattering multipole decomposition of $Mo S_{2}$ particle with shape 1 with $d_{1} = d_{2} = 260$ nm, $h = 120$ nm [see Fig. 1 for geometric parameters]. The magnetic scattering occurs at the wavelength 812 nm. Incident light is a linearly polarized plane wave falling vertically on the particle with respect to the inset in (a); (b) Far-field scattering patterns at wavelengths 600 nm, 812 nm, and 1000 nm from left to right, in two mutually orthogonal planes: E plane contains the wave vector and electric field amplitude of the incident light, H plane contains the wave vector and magnetic field amplitude of the incident light. (c) and (d) are analogous to (a) and (b) for the $Mo S_{2}$ particle shape 2 with $d_{1} = 260$ nm, $d_{2} = 140$ nm, and $h = 150$ nm. Electric field of the incident light is oriented along the short axis of the particle ellipse, as shown by orange arrow in the inset; (e) and (g) present scattering multipole decomposition for particles made of Si and $Mo S_{2}$ , with shapes 1 and 2, respectively; (f) and (h) are the corresponding far-field scattering patterns at characteristic wavelengths.
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Figure 3
The spectral distance $| Δ λ_{a m} |$ between the anapole in electric dipole channel and the magnetic dipole resonance as a function of a characteristic particle size $ξ = \sqrt[3]{V_{particle}}$ . Each curve corresponds to the particle of certain shape and material, denoted by the label near the line. The incident light direction and polarization with respect to the particles with shapes 1 and 2 are denoted to the right of the graph.
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Figure 4
Light deflection by $Mo S_{2}$ and Si nanocylinders. The deflection is measured as an angle $θ$ between the incident plane wave $k$ and the direction of maximum scattered radiation in far-field, see the definitions in (b). (a) The deflection $θ$ as a function of incidence angle $α$ for $Mo S_{2}$ and Si nanoparticles and two mutually orthogonal incident polarizations. The “shape 2” particles with dimensions $d_{1} = 260$ nm, $d_{2} = 140$ nm, and $h = 150$ nm are considered [see Fig. 1]. (b) and (c) Schemes illustrating the differences in light deflection by Si and $Mo S_{2}$ particles at different particles rotations. Vectors n and k in (b) denote a normal vector to the particle plane and the incident wave vector, respectively; angles $α$ and $θ$ are defined on the same picture. The axis of particle rotation is normal to the plane with vectors n, k and the longest dimension $d_{1}$ of the particle [see also Fig. 1]; (d) The cross-sections of the far-field radiation pattern in E and H planes for the particles rotations shown in (b) and (c). The incident wavelength is 818 nm.
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Figure 5
Point dipole model of light deflection. (a) The electromagnetic polarization of electric (p) and magnetic (m) linear oscillating dipoles in the far-field; (b) blue curve: the rigorous calculations of the deflection angle $θ$ as a function of incidence angle $α$ , and black curve is the same dependence obtained in the dipole approximation. (c) Visualization of orientations of dipoles p, $m_{eff}$ and $Mo S_{2}$ particle with respect to the incident plane wave with a wave vector k. Three axes $x, y, z$ in red denote a coordinate system, where the particle rotates.
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