Kerr rotation signature of nonlinear Maxwell electrodynamics under a uniform electromagnetic background

TL;DR

This paper explores how nonlinear Maxwell electrodynamics, specifically the ModMax model, affects optical phenomena like Kerr rotation and birefringence under uniform electromagnetic backgrounds, revealing the influence of the model's parameters.

Contribution

It provides a detailed analysis of optical effects in ModMax electrodynamics with external fields, including Kerr rotation, birefringence, and the Goos-Hänchen effect, highlighting the role of the nonlinear parameter and field ratios.

Findings

Kerr rotation and ellipticity depend on the nonlinear parameter and field ratios.

Birefringence phase shifts are derived for plane waves in magnetic backgrounds.

The Goos-Hänchen effect is analyzed at dielectric interfaces governed by ModMax.

Abstract

Nonlinear electrodynamics naturally arises in quantum field theory, where the electromagnetic vacuum behaves as an effective nonlinear optical medium, leading to phenomena such as vacuum birefringence and dichroism. Among the recently proposed models, modified Maxwell electrodynamics (ModMax) stands out as a conformally invariant nonlinear extension of Maxwell theory that preserves the fundamental symmetries of classical electrodynamics while predicting nontrivial optical effects. In this work, we investigate optical effects in ModMax electrodynamics in the presence of an external electromagnetic field. Considering uniform and constant magnetic and electric backgrounds, the solutions for the refractive indices are revisited. Using these results, we obtain the propagating modes and the phase shift (birefringence) for plane wave solutions in the presence of a pure magnetic background field. Afterwards, we investigate the Goos-H\"anchen effect considering the interface between a simple dielectric and a medium whose electromagnetic response tensors are ruled by the ModMax electrodynamics. Further, based on the general reflection problem, we discuss the complex Kerr rotation with both the electric (E) and magnetic (B) background fields, considering two main cases: i) $B > E$ and ii) $E > B$. Our findings indicate that the $\gamma$ parameter and the ratios (B/E) and (E/B) play a central role in describing the Kerr signals (rotation and ellipticity) of systems with optical effects induced by nonlinear electromagnetic interactions.