Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources

TL;DR

This paper analyzes the plasmonic Purcell factor for surface plasmons, deriving expressions for coupling rates and quantifying quality factors and confinement, with implications for enhancing light-matter interactions in nanophotonics.

Contribution

It provides a detailed theoretical analysis of the plasmonic Purcell factor for both SPP and LSP, including closed-form expressions and quantification of key parameters.

Findings

Derived closed-form expressions for coupling rates to surface plasmons.

Quantified quality factors and modal confinement of SPP and LSP.

Demonstrated strongly subwavelength behavior of plasmonic modes.

Abstract

The Purcell factor $F_p$ is a key quantity in cavity quantum electrodynamics (cQED) that quantifies the coupling rate between a dipolar emitter and a cavity mode. Its simple form $F_p\propto Q/V$ unravels the possible strategies to enhance and control light-matter interaction. Practically, efficient light-matter interaction is achieved thanks to either i) high quality factor $Q$ at the basis of cQED or ii) low modal volume $V$ at the basis of nanophotonics and plasmonics. In the last decade, strong efforts have been done to derive a plasmonic Purcell factor in order to transpose cQED concepts to the nanocale, in a scale-law approach. In this work, we discuss the plasmonic Purcell factor for both delocalized (SPP) and localized (LSP) surface-plasmon-polaritons and briefly summarize the expected applications for nanophotonics. On the basis of the SPP resonance shape (Lorentzian or Fano profile), we derive closed form expression for the coupling rate to delocalized plasmons. The quality factor factor and modal confinement of both SPP and LSP are quantified, demonstrating their strongly subwavelength behaviour.