# Optical Response by Time-Varying Plasmonic Nanoparticles

## TL;DR

This paper investigates how temporal modulation of plasmonic nanoparticles can lead to optical amplification by creating Floquet replicas of surface plasmon resonances, using a simplified analytical model validated by scattering calculations.

## Contribution

It introduces a two-frequency polarizability model for time-modulated nanoparticles, capturing their radiative and amplifying properties with analytical simplicity.

## Key findings

- Floquet replicas enable light amplification in nanoparticles.
- The two-band model accurately predicts scattering behavior.
- Broad parameter range for parametric amplification.

## Abstract

The temporal modulation of material parameters enables optical amplification within linear media. Here we consider the fundamental building block of plasmonics, a subwavelength metal nanoparticle, and study how temporal modulation alters the optical response of the frequency-dispersive scatterers. We show that modulating in time leads 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 point-like 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 allows us to introduce a two-frequency effective 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 the parametric amplification condition for the modulated nanoparticle, showing that amplification can be obtained in a broad range of parameters.