Wave propagation in linear electrodynamics

TL;DR

This paper derives the Fresnel equation for electromagnetic wave propagation in general linear media, showing how certain conditions simplify the wave surface to the familiar light cone structure, and explores the necessity of these conditions.

Contribution

It provides a general derivation of the Fresnel equation in linear electrodynamics and analyzes conditions for the wave surface to reduce to the light cone.

Findings

Wave normals generally lie on a fourth order surface.

The closure relation simplifies the wave surface to a light cone.

The closure relation is sufficient but not necessarily necessary for this reduction.

Abstract

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.