# Description of spontaneous photon emission and local density of states in presence of a lossy polaritonic inhomogenous medium

## TL;DR

This paper develops a comprehensive quantum framework for spontaneous photon emission in lossy, dispersive inhomogeneous media, emphasizing the role of both photonic and material fluctuations to accurately describe local density of states.

## Contribution

It introduces a generalized Huttner-Barnett model that accounts for both fluctuations, justifies previous Langevin noise results, and advances understanding of LDOS in complex environments.

## Key findings

- Unified description of photon emission in lossy media
- Validation of Langevin noise approach
- Insights into local density of states near plasmonic structures

## Abstract

We provide a description of spontaneous emission in a dispersive and dissipative linear inhomogeneous medium based on the generalized Huttner-Barnett model [Phys. Rev. A 46, 4306 (1992)]. Our discussion considers on an equal footing both the photonic and material fluctuations which are necessary to preserve unitarity of the quantum evolution. Within this approach we justify the results obtained in the past using the Langevin noise method that neglects the removal of photonic fluctuations. We finally discuss the concept of local density of states (LDOS) in a lossy and dispersive inhomogeneous environment that provides a basis for theoretical studies of fluorescent emitters near plasmonic and polaritonic antennas.