# Quantized fluctuational electrodynamics for three-dimensional plasmonic structures

## TL;DR

This paper extends the quantized fluctuational electrodynamics (QFED) formalism from one dimension to three dimensions, enabling the analysis of complex plasmonic structures and their local photon properties.

## Contribution

The authors develop a 3D QFED formalism that overcomes previous limitations, allowing detailed study of plasmonic and other three-dimensional nanostructures.

## Key findings

- Demonstrated the formalism on a quantum-well with metallic coating
- Calculated local photon numbers and field temperatures
- Showed applicability to plasmonic structures

## Abstract

We recently introduced a quantized fluctuational electrodynamics (QFED) formalism that provides a physically insightful definition of an effective position-dependent photon-number operator and the associated ladder operators. However, this far the formalism has been applicable only for the normal incidence of the electromagnetic field in planar structures. In this work, we overcome the main limitation of the one-dimensional QFED formalism by extending the model to three dimensions, allowing us to use the QFED method to study, e.g., plasmonic structures. To demonstrate the benefits of the developed formalism, we apply it to study the local steady-state photon numbers and field temperatures in a light-emitting near-surface InGaN quantum-well structure with a metallic coating supporting surface plasmons.