Non-dissipative electromagnetic medium with a double light cone

TL;DR

This paper classifies all electromagnetic media tensors that are invertible, skewon-free, and birefringent, revealing only three possible classes with explicit local descriptions, thus advancing the understanding of wave propagation in complex media.

Contribution

It provides a complete pointwise classification of birefringent electromagnetic media tensors satisfying specific mathematical conditions, including explicit local coordinate expressions.

Findings

Only three classes of such media exist.

Explicit local coordinate formulas are provided for each class.

The Fresnel surface generalizes the light cone concept in these media.

Abstract

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is modelled by an antisymmetric (2, 2)-tensor kappa with real coefficients. In this setting the Fresnel surface is a fourth order polynomial surface in each cotangent space that acts as a generalisation of the light cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speeds as a function of direction. The contribution of this paper is the complete pointwise description of all electromagnetic medium tensors that satisfy the following conditions: (i) kappa is invertible, (ii) kappa is skewon-free, (iii) kappa is birefringent, that is, the Fresnel surface of kappa is the union of two distinct light cones. We show that there are only three classes of mediums with these properties. Moreover, we give explicit expressions in local coordinates for each class.