The non-birefringent limit of all linear, skewonless media and its unique light-cone structure

TL;DR

This paper characterizes the structure of all skewonless, non-birefringent linear media using a geometric approach, revealing a unique light-cone structure and implications for transformation optics and premetric electrodynamics.

Contribution

It provides a comprehensive geometric representation of such media, showing the constitutive law is determined by an optical metric and additional bivectors and axion, with bivectors vanishing in hyperbolic cases.

Findings

Bivectors vanish for hyperbolic Fresnel equations.

The constitutive law is based on an optical metric plus bivectors and axion.

The structure has applications in transformation optics and premetric electrodynamics.

Abstract

Based on a recent work by Schuller et al., a geometric representation of all skewonless, non-birefringent, linear media is obtained. The derived constitutive law is based on a "core", encoding the optical metric up to a constant. All further corrections are provided by two (anti-)selfdual bivectors, and an "axion". The bivectors are found to vanish if the optical metric has signature (3,1) - that is, if the Fresnel equation is hyperbolic. We propose applications of this result in the context of transformation optics and premetric electrodynamics.