Collective lattice resonances (CLRs) in finite-sized $ 2D $ 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.

Regular arrays of plasmonic nanoparticles have brought significant attention over the last decade due to their ability to support localized surface plasmons (LSPs) and exhibit diffractive grating behavior simultaneously. For a specific set of parameters (i.e., period, particle shape, size, and material), it is possible to generate super-narrow surface lattice resonances (SLRs) that are caused by interference of the LSP and the grating Rayleigh anomaly. In this letter, we propose plasmonic structures based on regular 2D arrays of TiN nanodisks to generate high-Q SLRs in an important telecommunication range, which is quite difficult to achieve with conventional plasmonic materials. The position of the SLR peak can be tailored within the whole telecommunication bandwidth (from ≈ 1.26 μm to ≈ 1.62 μm) by varying the lattice period, while the Q-factor is controlled by changing nanodisk sizes. We show that the Q-factor of SLRs can reach a value of 2 × 10³, which is the highest reported Q-factor for SLRs at telecommunication wavelengths so far. Tunability of optical properties, refractory behavior, and low-cost fabrication of TiN nanoparticles paves the way for manufacturing cheap nanostructures with extremely stable and adjustable electromagnetic response at telecommunication wavelengths for a large number of applications.

Collective lattice resonances in disordered $2D$ arrays of spherical Si nanoparticles (NPs) have been thoroughly studied within the framework of the coupled dipole approximation. Three types of defects have been analyzed: positional disorder, size disorder, and quasi-random disorder. We show that the positional disorder strongly suppresses either the electric dipole (ED) or the magnetic dipole (MD) coupling, depending on the axis along which the NPs are shifted. Contrarily, size disorder strongly affects only the MD response, while the ED resonance can be almost intact, depending on the lattice configuration. Finally, random removing of NPs from an ordered $2D$ lattice reveals a quite surprising result: hybridization of the ED and MD resonances with lattice modes remains observable even in the case of random removing of up to 84% of the NPs from the ordered array. The reported results could be important for rational design and utilization of metasurfaces, solar cells, and other all-dielectric photonic devices.

Collective lattice resonances (CLRs) emerging under oblique incidence in 2D finite-size arrays of Si nanospheres have been studied with the coupled dipole model. We show that hybridization between the Mie resonances localized on a single nanoparticle and angle-dependent grating Wood–Rayleigh anomalies allows for the efficient tuning of CLRs across the visible spectrum. Complex nature of CLRs in arrays of dielectric particles with both electric dipole (ED) and magnetic dipole (MD) resonances paves a way for a selective and flexible tuning of either ED or MD CLR by an appropriate variation of the angle of incidence. The importance of the finite-size effects, which are especially pronounced for CLRs emerging for high diffraction orders under an oblique incidence has been also discussed.