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

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, the 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 non-trivial 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. Afterward, we investigate the Goos–Hänchen effect considering the interface between a simple dielectric and a medium whose electromagnetic response tensors are ruled by the ModMax electrodynamics. Furthermore, 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) $$B&gt;E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> and ii) $$E&gt;B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> </mml:math> . Our findings indicate that the $$\gamma$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> 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.