Conceptualizing collectivity in lattice resonances of periodic arrays of nanostructures

The use of periodic arrays of nanostructures has become a powerful strategy for enhancing light-matter interactions. These systems support collective modes known as lattice resonances, which are characterized by strong and spectrally narrow optical responses. While all lattice resonances arise from the multiple, coherent scattering among the nanostructures of the array, the particular geometrical characteristics of the system can strongly affect the interaction strength, leading to very distinct optical responses. Despite the extensive research on this topic, a consistent framework for quantifying and comparing these differences remains lacking. In this work, we introduce the degree of collectivity of a lattice resonance, defined as a measure of the interaction strength between the nanostructures in the array, and relate it to the spectral detuning of the lattice resonance-an easily quantifiable metric. This allows us to establish a direct link between the geometrical characteristics of the array and the optical properties of the lattice resonances it supports. Through a combination of theoretical modeling and experimental validation, we investigate how the degree of collectivity affects the robustness of lattice resonances when the system deviates from perfect periodicity. Our results show that lattice resonances with higher degree of collectivity are more sensitive to common experimental imperfections, such as finite array size, positional disorder, and refractive index mismatch between the substrate and the superstrate. The degree of collectivity introduced in this study provides a valuable tool for predicting the performance and experimental feasibility of the lattice resonances supported by periodic arrays of nanostructures, thus paving the way for the development of advanced photonic devices.