Time-Varying Plasmonic Particles

In this paper, we derive a third-order linear differential equation for describing polarization dynamics of a spherical plasmonic nanoparticle. We entitle such equation, being analogous to the Abraham-Lorentz equation, as the Rüdenberg equation that was initially written in 1907 for elucidating the Hertzian dipole antenna in the receiving regime. Based on this equation, we study the case when the plasma frequency of the nanoparticle material varies in time. Under some assumptions, we find analytical solutions which describe the radiative decay of such time-varying nanoparticle.