# Light propagation in inhomogeneous media, coupled quantum harmonic oscillators and phase transitions

## TL;DR

This paper models light propagation in inhomogeneous media using classical optics and quantum techniques, revealing phase transitions in the system, and provides exact solutions for coupled quantum harmonic oscillators and quantized fields.

## Contribution

It introduces a classical optics approach to model coupled quantum harmonic oscillators and solves the quantum propagation problem exactly in a specific graded index medium.

## Key findings

- Exact solutions for light propagation in graded index media
- Identification of phase transitions in the system
- Modeling of coupled quantum oscillators using classical optics

## Abstract

This contribution has two main purposes. First, we show using classical optics how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we use quantum mechanical techniques to solve, exactly, the propagation of light through a particular type of graded index medium. In passing, we show that the system presents phase transitions.