Resonances in finite-size all-dielectric metasurfaces for light trapping and propagation control

We investigate the development and tuning of resonant optical effects in finite-size periodic arrays (metasurfaces) of silicon nanoparticles. By applying Green's tensor formalism and the coupled dipole approximation while incorporating electric and magnetic dipole moments, we outline a theoretical framework to model the optical response of such nanoparticle arrays. We consider the resonant optical response of finite-size arrays as a function of the nanoparticle (unit cell) number in two distinct scenarios of collective resonances: the lattice resonant Kerker effect, which is a complete suppression of the backward scattering, and the quasi-bound state in the continuum. Our developed models and findings provide a pathway for extracting crucial details about the lattice period and the required array size for the experimental observation of collective resonances. These resonances are typically predicted under the assumption of an infinite periodic lattice. By bridging the theoretical predictions with practical considerations, our results contribute to better understanding of specific conditions needed to experimentally observe these collective resonances in finite-size arrays.