Effects of non-linear vacuum electrodynamics on the polarization plane of light

TL;DR

This paper derives a general law for how the polarization plane of light propagates in nonlinear vacuum electrodynamics theories, considering complex backgrounds and high-frequency limits, with specific examples like Born-Infeld theory.

Contribution

It provides the first derivation of the polarization transport law in Plebański class nonlinear electrodynamics within a general relativistic setting.

Findings

Derived a universal polarization transport law for nonlinear vacuum electrodynamics.

Applied the law to the Born-Infeld theory as an example.

Established a method to analyze high-frequency electromagnetic wave propagation in nonlinear theories.

Abstract

We consider the Pleba{\'n}ski class of nonlinear theories of vacuum electrodynamics, i.e., Lagrangian theories that are Lorentz invariant and gauge invariant. Our main goal is to derive the transport law of the polarization plane in such a theory, on an unspecified general-relativistic spacetime and with an unspecified electromagnetic background field. To that end we start out from an approximate-plane-harmonic-wave ansatz that takes the generation of higher harmonics into account. By this ansatz, the electromagnetic field is written as an asymptotic series with respect to a parameter $\alpha$, where the limit $\alpha \to 0$ corresponds to sending the frequency to infinity. We demonstrate that by solving the generalized Maxwell equations to zeroth and first order with respect to $\alpha$ one gets a unique transport law for the polarization plane along each light ray. We exemplify the general results with the Born-Infeld theory.