Finite element modeling of spontaneous emission of a quantum emitter at nanoscale proximity to plasmonic waveguides

TL;DR

This paper presents a finite element method to model spontaneous emission of quantum emitters near plasmonic waveguides, enabling precise calculations of energy coupling and emission efficiency at the nanoscale.

Contribution

It introduces a self-consistent finite element approach that handles arbitrary waveguide cross sections and accurately predicts emission coupling and efficiency.

Findings

Coupling to plasmonic modes can be calculated exactly.

Agreement with quasistatic approximation for small nanowires.

Achieved high spontaneous emission factor 0% for rectangular waveguides.

Abstract

We develop a self-consistent finite element method to study spontaneous emission at nanoscale proximity of plasmonic waveguides. In the model, it is assumed that only one guided mode is dominatingly excited by the quantum emitter. With such one dominating mode assumption, the cross section of the plasmonic waveguide can be arbitrary. We apply our numerical method to calculate the coupling of a quantum emitter to a cylindrical nanowire and a rectangular waveguide, and compare the cylindrical nanowire to previous work valid in quasistatic approximation. The fraction of the energy coupled to the plasmonic mode can be calculated exactly, which can be used to determine the single optical plasmon generation efficiency for a quantum emitter. For a gold nanowire we observe agreement with the quasistatic approximation for radii below 20 nm, but for larger radii the total decay rate is up to 10 times larger. For the rectangular waveguide we estimate an optimized value for the spontaneous emission factor \beta of up to 80%.