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

TL;DR

The paper develops a quantum-informed, self-consistent framework in which localized surface plasmon excitations of spherical metal nanoparticles are treated as plasmonic quasi-particles (PQPs) that radiate into a self-generated near-field cavity. By unifying classical TM quasi-normal mode theory with a quantum emitter perspective, it derives a self-consistent description of total damping and reveals a self-quenching mechanism where nonradiative losses suppress radiative emission through the emitter–cavity coupling. The model provides analytical expressions for radiative and nonradiative decay rates, demonstrates non-additivity of damping channels, and connects to experimental observations of anomalous damping in nanostructures. This work highlights the bosonic, coherent nature of PQPs and suggests new strategies for emission control and decay engineering in dissipative plasmonic systems at room temperature.

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.

Figures (4)

• Figure 1: Classical and quantum representations of LSP dynamics. (a) Resonant frequencies $\hbar\omega_l(R)$ and damping rates $\hbar\Gamma_l(R)$ of QNMs as a function of radius $R$, including retardation effects kolwas2013damping. (b) Mapping multipolar modes $l$ to energy levels of a quantum plasmonic quasi-particle (PQP), modeled as independent two-level systems $S_l$.
• Figure 2: (a) Total damping rates $\Gamma_l(R)$ (for $l = 1 - 6$) from DR. (b) Close-up view showing that $\Gamma_l(R) \leq \gamma(R)/2$, suggesting non-additivity of radiative and nonradiative terms. Data from kolwas2013damping.
• Figure 3: Conceptual link between the quantum closed cavity-mode model and the plasmonic quasi-particle (PQP) picture. Each TM surface mode of the metal nanoparticle is modeled as a two-level quantum subsystem, with its creation and annihilation operators associated with transitions between ground and excited states.
• Figure 4: a) Classical picture of a metal nanoparticle supporting LSP resonant oscillations embedded in the near-field region, which contains the nonzero component of the electric field $E_l^r$ coupled to surface charge oscillations. The spectral characteristics of the interface and the near field are identical at and near resonance, but are modified in the collisionless electron regime. (b) Corresponding quantum picture: the near-field region is represented by the effective volume $V_l^{eff}$, forming a cavity with a modified LDOS. Plasmon energy is emitted into this self-generated cavity, which is inherently coupled to the emitter.