Fresnel analysis of the wave propagation in nonlinear electrodynamics

TL;DR

This paper analyzes wave propagation in nonlinear electrodynamics using Fresnel equations, demonstrating how birefringence arises or is suppressed based on the constitutive tensor's properties, with applications to moving media.

Contribution

It provides a detailed Fresnel analysis for nonlinear electrodynamics, showing how birefringence depends on the constitutive tensor's closure and extending the approach to moving media with skewon and axion effects.

Findings

Birefringence occurs in general nonlinear models due to Fresnel equation factorization.

Closure of the constitutive tensor eliminates birefringence, ensuring a unique light cone.

Nonlinearities induce birefringence in nonmagnetic media, with derived optical metrics.

Abstract

We study the wave propagation in nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of general nonlinear Lagrangian models, we demonstrate how the originally quartic Fresnel equation factorizes, yielding the generic birefringence effect. We show that the closure of the effective constitutive (or jump) tensor is necessary and sufficient for the absence of birefringence, i.e., for the existence of a unique light cone structure. As another application of the Fresnel approach, we analyze the light propagation in a moving isotropic nonlinear medium. The corresponding effective constitutive tensor contains non-trivial skewon and axion pieces. For nonmagnetic matter, we find that birefringence is induced by the nonlinearity, and derive the corresponding optical metrics.