Optical effects in modified Maxwell electrodynamics under a uniform electromagnetic background

Abstract

In this work, we investigate optical effects in modified Maxwell electrodynamics (ModMax) 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-Hänchen 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 $γ$ parameter and 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 non-linear electromagnetic effects.

Figures (6)

• Figure 1: Refractive index $n_{2B}$ of Eq. (\ref{['n2B']}) in terms of propagation direction $\theta$. Here, we have set: $\gamma=$ 0.1 (blue), 0.2 (red), 0.4 (magenta), 0.6 (dashed blue). The solid black curve represents the standard case with $\gamma \rightarrow 0$.
• Figure 2: Goos-Hänchen shift $D_{s}$ of Eq. (\ref{['DsVoigt']}) for $s$-polarized incident wave (solid curves) and $D_{p}$ of Eq. (\ref{['DpVoigt']}) (dashed lines) in terms of the incidence angle $\theta_{I}$. Here, we have used: $\epsilon_{1}=1.6$, $\gamma=0$ (usual scenario), $0.01$ (red), $0.05$ (blue), and $0.1$ (magenta). The vertical dashed lines indicate the critical angle, given by Eq. (\ref{['critical-angle-GH-1']}), above which the GH effect takes place.
• Figure 3: Kerr rotation angle $\theta_{K}$ of Eq. (\ref{['kerr-modmax-2']}) in terms of the incidence angle $\theta_{I}$. Here, we have used: $\gamma=0.1$, $\mu_{1}=1$, $\epsilon_{1}=1.6$, and $y=$$1.5$ (red), $2$ (blue), and $3$ (magenta).
• Figure 4: Kerr ellipticity angle $\eta_{K}$ of Eq. (\ref{['kerr-modmax-2']}) in terms of the incidence angle $\theta_{I}$. Here, we have used: $\gamma=0.1$, $\mu_{1}=1$, $\epsilon_{1}=1.6$, and $y=$$1.5$ (red), $2$ (blue), and $3$ (magenta). The vertical dashed lines are given by $\tilde{\theta}_{i}$ of Eq. (\ref{['expression-tilde-theta-1']}) for each example $i=$ 1 (red), 2 (blue), 3 (magenta).
• Figure 5: Kerr rotation angle $\theta_{K}$ of Eq. (\ref{['kerr-modmax-2']}) in terms of the incidence angle $\theta_{I}$. Here, we have used: $\gamma=0.1$, $\mu_{1}=1$, $\epsilon_{1}=1.6$, and $x=$$1.5$ (red), $2$ (blue), and $3$ (magenta).