# Quantising the electromagnetic field near two-sided semi-transparent mirrors

## TL;DR

This paper develops a quantum model for electromagnetic fields near semi-transparent mirrors, accounting for energy exchange and mirror images, and validates it through atomic decay rate calculations.

## Contribution

It introduces a novel quantum framework for light scattering at semi-transparent surfaces, incorporating energy exchange and mirror images, extending beyond traditional models.

## Key findings

- Reproduces known decay rates in limiting cases
- Provides a basis for modeling complex light-mirror interactions
- Validates the model with atomic level shift calculations

## Abstract

This paper models light scattering through flat surfaces with finite transmission, reflection and absorption rates, with wave packets approaching the mirror from both sides. While using the same notion of photons as in free space, our model also accounts for the presence of mirror images and the possible exchange of energy between the electromagnetic field and the mirror surface. To test our model, we derive the spontaneous decay rate and the level shift of an atom in front of a semi-transparent mirror as a function of its transmission and reflection rates. When considering limiting cases and using standard approximations, our approach reproduces well-known results but it also paves the way for the modelling of more complex scenarios.