Abstract
Abstract We provide a critical analysis of some of the commonly used theoretical models to describe quantum plasmons in finite size media. 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.
Highlights
We provide a critical analysis of some of the commonly used theoretical models to describe quantum plasmons in finite size media
We discuss the derivation of spontaneous emission in a plasmonic environment, which usually relies on a Green tensor and is based on an incomplete identity
With the development of quantum sources and singlephoton detectors on one hand, and classical plasmonics on the other hand, new theories have been developed to describe the behavior of light when interacting with dissipative and dispersive media
Summary
With the development of quantum sources and singlephoton detectors on one hand, and classical plasmonics on the other hand, new theories have been developed to describe the behavior of light when interacting with dissipative and dispersive media (typically, metals). It was shown to give a different spectral structure of the diagonalized system and a different expression of the electric field operator Our interpretation of this discrepancy is that the former results [1,2,3,4,5,6,7,8,9,10,11] were obtained under the implicit hypothesis of an infinite bulk medium, it has been extensively extrapolated to finite media in later works. The initial point is the classical Hamiltonian of the system, where the medium is described as an infinite set of harmonic oscillators interacting with the electromagnetic field through a coupling function α. The conclusion is that the ansatz (6) for the diagonalized Hamiltonian is not valid for a finite medium
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