Photon Momentum in Linear Dielectric Media

TL;DR

This paper investigates photon momentum in linear dielectrics, proposing a relativistic approach that clarifies the total momentum of polaritons, contributing to the longstanding Abraham--Minkowski controversy.

Contribution

It introduces a relativistic derivation of photon momentum in dielectrics, providing a new perspective on the total momentum of polaritons.

Findings

Total polariton momentum is ${ abla} imes{f B}/c$

Total momentum density is ${f g}_T=n{f E} imes{f B}/c$

Clarifies the relation between photon momentum and electromagnetic field in dielectrics

Abstract

According to the scientific literature, the momentum of a photon in a simple linear dielectric is either $\hbar\omega/(nc)$ or $n\hbar\omega/c$ with a unit vector ${\bf \hat e}_k$ in the direction of propagation. These momentums are typically used to argue the century-old Abraham--Minkowski controversy in which the momentum density of the electromagnetic field in a dielectric is either the Abraham momentum density, ${\bf g}_A={\bf E}\times{\bf H}/c$, or the Minkowski momentum density, ${\bf g}_M={\bf D}\times{\bf B}/c$. The elementary optical excitations, photons, are typically known as polaritions in the particular case of light traveling in a dielectric medium. Applying the relativistic energy formula, we find that the total momentum that is attributable to a polariton in a dielectric is $\hbar\omega{\bf \hat e}_k/c$ corresponding to a total momentum density ${\bf g}_T=n{\bf E}\times{\bf B}/c$.