Periodic arrays of metallic nanostructures support collective
lattice
resonances, which give rise to optical responses that are, at the
same time, stronger and more spectrally narrow than those of the localized
plasmons of the individual nanostructures. Despite the extensive research
effort devoted to investigating the optical properties of lattice
resonances, the majority of theoretical studies have analyzed them
under plane-wave excitation conditions. Such analysis not only constitutes
an approximation to realistic experimental conditions, which require
the use of finite-width light beams, but also misses a rich variety
of interesting behaviors. Here, we provide a comprehensive study of
the response of periodic arrays of metallic nanostructures when excited
by finite-width light beams under both paraxial and nonparaxial conditions.
We show how as the width of the light beam increases, the response
of the array becomes more collective and converges to the plane-wave
limit. Furthermore, we analyze the spatial extent of the lattice resonance
and identify the optimum values of the light beam width to achieve
the strongest optical responses. We also investigate the impact that
the combination of finite-size effects in the array and the finite
width of the light beam has on the response of the system. Our results
provide a solid theoretical framework to understand the excitation
of lattice resonances by finite-width light beams and uncover a set
of behaviors that do not take place under plane-wave excitation.