High Order Plasmonic Resonances in Time-Varying Media

The optical response of noble-metal nanoparticles in the visible spectrum is characterized by the presence localized surface plasmon resonances. Localized surface plasmons are non-propagating coherent oscillations of free-carriers coupled to the electromagnetic field arising as a consequence of confinement effects in sub-wavelength nanoparticles. Plasmonic nanoparticles in general support an infinite discrete set of orthogonal localized surface plasmon modes, yet in the case of structures of deep-subwavelength dimensions only the lowest order resonances of dipolar nature can be effectively excited by an incident electromagnetic wave. By reciprocity such high-order modes tend to be subradiant and therefore difficult to observe in far-field. Here we discuss the novel localized surface plasmon dynamics that emerge when the electromagnetic properties of the plasmonic particle or of the background medium vary in time. We show in particular that such temporal permittivity variations lift the orthogonality of the localized surface plasmon modes and introduce coupling among different angular momentum states. Exploiting such dynamics we show how surface plasmon amplification of high order resonances can be achieved under the action of a spatially uniform optical pump of appropriate frequency.