Analysis of the Limits of the Optical Response of a Metallic Nanoparticle with Gain

Metallic nanostructures endowed with optical gain are promising building blocks for the development of active nanophotonic devices with enhanced optical responses as well as for exploring novel phenomena such as parity-time symmetry and nonreciprocity. However, despite their potential, the complexity of these systems frequently demands the use of simplified gain models, whose range of applicability is not always clear. Here, tracing our steps toward the basics, we analyze the optical response of a small active metallic nanoparticle using an intuitive, yet accurate, semianalytical model that takes into account the inherent nonlinear nature of the gain. We evaluate the near-and far-field responses of the active nanoparticle as a function of both the pump and the probe field strengths. We show that, under weak probe fields, the optical response of the active nanoparticle is greatly enhanced with increasing pump strength. In contrast, when the probe field is strong enough to deplete the excited-state population of the gain medium, the nanoparticle becomes passive, irrespective of the pump strength. Our results help to delineate the limits of applicability of the linear models used to describe the effect of gain in plasmonic nanostructures, thus paving the way to exploit these systems for the development of new applications.