Light propagation in (2+1)-dimensional electrodynamics: the case of linear constitutive laws

TL;DR

This paper investigates light propagation in a three-dimensional electrodynamics setting with linear constitutive laws, deriving the Fresnel equation and effective optical metric using a covariant approach and algebraic geometry.

Contribution

It introduces a covariant framework for analyzing light in 3D electrodynamics with linear response tensors, deriving the Fresnel equation and optical metric.

Findings

Derived the Fresnel equation for the medium

Obtained the effective optical metric

Applied algebraic geometry to analyze light rays

Abstract

In this paper, we turn our attention to light propagation in three-dimensional electrodynamics. More specifically, we investigate the behavior of light rays in a continuous bi-dimensional hypothetical medium living in a three-dimensional ambient spacetime. Relying on a fully covariant approach, we assume that the medium is endowed with a local and linear response tensor which maps field strengths into excitations. In the geometric optics limit, we then obtain the corresponding Fresnel equation and, using well-known results from algebraic geometry, we derive the effective optical metric.