Self-Quenching Effect of the Decay of Localized Surface Plasmons: Classical and Quantum Perspectives

Abstract

This study presents a self-consistent, quantum-informed model for the decay dynamics of localized surface plasmons (LSPs) in spherical metal nanoparticles (NPs), described as plasmonic quasi-particles (PQPs). By bridging classical electrodynamics description for quasi-normal modes (retardation effects included) with a quantum emitter perspective, this framework provides an analytically tractable description of the damping of the dissipative confined plasmonic systems. In addition to its significance for emission control, the model emphasizes the bosonic characteristics of plasmonic quasi-particles, which are coherent many-electron excitations of the states of quasi-normal modes. Unlike conventional cavity quantum electrodynamics (CQED), where the emitter and cavity exist as separate systems, a plasmonic quasi-particle functions as a quantum emitter embedded within a self-created resonant near-field nano-cavity of confined radial fields, sharing the spectral characteristics of the surface transverse-magnetic (TM) modes, which include nonradiative damping effects resulting from, e.g., ohmic losses in a metal. This work extends Fermi's Golden Rule to include the coupling between the emission process and the self-generated cavity impact. The derived self-consistent formulation offers analytical expressions for the total damping rates, which demonstrate a size-dependent suppression displayed in higher multipolarity modes attributed to the impact of the self-quenching effect resulting from the coaction of radiative and non-radiative channels.