Optical response by time-varying plasmonic nanoparticles

The temporal modulation of material parameters enables optical amplification within linear media. Here, we consider a subwavelength metal nanoparticle, the fundamental building block of plasmonics, and study how temporal modulation alters the optical response of these frequency-dispersive, time-varying, nanostructured media. We show that periodic temporal modulation gives rise to Floquet replicas of the localized surface plasmon resonance of the nanoparticle, which can result in light amplification. We propose a model based on a pointlike dipole description of the time-varying frequency-dispersive nanoparticle that fully captures the radiative and amplifying properties of the system in the subwavelength regime. By comparing our simplified model to full Floquet-Mie scattering calculations, we demonstrate that the optical scattering by the nanoparticle is accurately described by an analytical two-band model. This formulation allows us to introduce an effective two-frequency polarizability that fully incorporates the properties of the localized surface plasmon and its amplifying replica, as well as their interaction. In addition, we analyze the emergence of parametric amplification in the modulated nanoparticle, showing that amplification can be obtained in a broad range of parameters.