Abstract

In the present paper, we propose a coupled multipole model to treat the mutual interactions between nanoparticles aligned in a periodic array, which may be frequently encountered in designing metasurfaces and other functional electromagnetic structures. Our model is comprehensive in that it takes into account the electric and magnetic multipoles both up to the quadrupole order. Working under Cartesian coordinates, this model can readily give the multipole responses of the particles in an infinite array at both normal and oblique incidence. In particular, we work out the analytical expressions of the cross-multipole coupling tensors, which are much more complicated for oblique incidence than normal incidence. We invoke the Ewald method to efficiently and accurately calculate the involved lattice sum whose convergence is otherwise very slow. By quantifying the contributions from the various couplings, we are able to analyze the mechanisms of new resonances that emerge only at oblique incidence. As a prototypical example, we use this method to give physically clear explanations of and show flexible control on the resonance shifts of the multipoles of an array of silicon spheres. The power of this model makes it very promising for dealing with metasurfaces with extended areas or working at large numerical apertures.

© 2023 Optica Publishing Group

Multipole optimization of light focusing by silicon nanosphere structures

Nikita Ustimenko, Kseniia V. Baryshnikova, Roman Melnikov, Danil Kornovan, Vladimir Ulyantsev, Boris N. Chichkov, and Andrey B. Evlyukhin
J. Opt. Soc. Am. B 38(10) 3009-3019 (2021)

Geometric effects on far-field coupling between multipoles of nanoparticles in square arrays

Drew DeJarnette, D. Keith Roper, and Braden Harbin
J. Opt. Soc. Am. B 29(1) 88-100 (2012)

Multiresonant all-dielectric metasurfaces based on high-order multipole coupling in the visible

Izzatjon Allayarov, Andrey B. Evlyukhin, and Antonio Calà Lesina
Opt. Express 32(4) 5641-5658 (2024)

Coupled magnetic dipole resonances in sub-wavelength dielectric particle clusters

Mark S. Wheeler, J. Stewart Aitchison, and Mohammad Mojahedi
J. Opt. Soc. Am. B 27(5) 1083-1091 (2010)

Multipole analysis of light scattering by arbitrary-shaped nanoparticles on a plane surface

Andrey B. Evlyukhin, Carsten Reinhardt, Egor Evlyukhin, and Boris N. Chichkov
J. Opt. Soc. Am. B 30(10) 2589-2598 (2013)