Collective lattice resonances in arrays of dielectric nanoparticles: a matter of size

Kostyukov, Artem S.; Ershov, Alexander E.; Gerasimov, Valeriy S.; Filimonov, Sergey A.; Rasskazov, Ilia L.; et al. Journal Of Quantitative Spectroscopy & Radiative Transfer. DOI: 10.1364/OL.44.005743

Collective lattice resonances (CLRs) in finite-sized $2 D$ arrays of dielectric nanospheres have been studied via the coupled dipole approximation. We show that even for sufficiently large arrays, up to $100 \times 100$

nanoparticles (NPs), electric or magnetic dipole CLRs may differ significantly from the ones calculated for infinite arrays with the same NP sizes and interparticle distances. The discrepancy is explained by the existence of a sufficiently strong cross-interaction between electric and magnetic dipoles induced at NPs in finite-sized lattices, which is ignored for infinite arrays. We support this claim numerically and propose an analytic model to estimate a spectral width of CLRs for finite-sized arrays. Given that most of the current theoretical and numerical researches on collective effects in arrays of dielectric NPs rely on modeling infinite structures, the reported findings may contribute to thoughtful and optimal design of inherently finite-sized photonic devices.