Critical review of quantum plasmonic models for finite-size media

TL;DR

This paper critically examines quantum plasmonic models for finite media, highlighting discrepancies and issues in common theoretical approaches, especially regarding spontaneous emission calculations.

Contribution

It provides a detailed critique of existing quantum plasmonic models, clarifies the limitations of standard methods, and explores the impact of missing terms in emission calculations.

Findings

Discrepancies in models when coupling approaches vanish

Incomplete identities affect spontaneous emission calculations

Missing terms significantly influence emission rate predictions

Abstract

We provide a critical analysis of some of the commonly used theoretical models to describe quantum plasmons. We summarize the standard approach based on a Fano diagonalization and we show explicit discrepancies in the obtained results by taking the limit of vanishing coupling between the electromagnetic field and the material medium. We then discuss the derivation of spontaneous emission in a plasmonic environment, which usually relies on a Green tensor and is based on an incomplete identity. The effect of the missing terms is calculated in a one-dimensional model.