A Semi-classical, Time-dependent Approach to Localized Surface Plasmons in Presence of Gain Elements
The study of gain assisted Localized Surface Plasmons (LSP) is of growing interest in different fields of nanotechnology. In fact, the embedding of optical gain is possibly the most promising strategy to compensate the losses they show in visible-range. Moreover, metallic nanostructures with gain elements are nanoscale source of strong optical fields. This intriguing feature, culminating in the conception of the spaser, widened their applicability to nanoscale lithography, probing, microscopy and more. It is possible to demonstrate, through a purely classical and steady state approach, that a single metallic nanoparticle immersed in a gain medium may show new types of optical responses as the gain level is modified, producing amplification and distortions in the spectra.
This classical, steady state approach naturally fails when instable, amplifying regimes are reached. Here we present a time-dependent model, integrating a quantum formalism to describe the gain while the metal is treated classically. This new model does contain previous results as steady state solutions and allows to investigate the system in time domain. By means of this dynamical approach it is possible to describe transient regimes, to study instabilities and to account for the effects of a pulsed pump. Furthermore, the geometrical solidity of the model allows to study the stability of the spasing mode; describing how, in many geometrical configurations, population saturation shifts the most of the energy into parasitic modes, thereby destroying the amplification effect. Being this phenomenon related to the geometrical configuration, our approach can be used to identify the best design possible to enhance the stability of the amplified mode.