Double rotatory power reversal, continuous Kerr angle, and enhanced reflectance in bi-isotropic media with anomalous Hall current

TL;DR

This work develops a theoretical framework for bi-isotropic media under the anomalous Hall effect described by axion electrodynamics, deriving four distinct refractive indices and analyzing their implications for circular birefringence and magneto-optical responses. It shows a double sign reversal in the rotatory power and reveals a giant, continuous Kerr rotation without the typical discontinuity, along with anomalous reflectance (R>1) arising from negative refraction. The results highlight unique nonequilibrium optical signatures of chiral, axion-dielectric systems and suggest candidate materials such as Bi2Se3 and related pyrochlores for experimental observation. Overall, the paper identifies novel magnetoelectric optical phenomena enabled by AHE and lays groundwork for further exploration of nonreciprocal light–matter interactions in topological and chiral media.

Abstract

We investigate the optical properties of bi-isotropic materials under the anomalous Hall effect (AHE) of axion electrodynamics. Four refractive indices associated with circularly polarized waves are achieved, implying circular birefringence with rotatory power endowed with double sign reversal, an exotic optical signature for chiral dielectrics. The Kerr rotation and ellipticity are analyzed, with an unusual observation of a giant rotation angle deprived of discontinuity. Anomalous enhanced reflectance (R greater than unity) is also reported, associated with negative refraction stemming from the anomalous transport properties. These effects constitute the singular optical signature of a nonequilibrium bi-isotropic medium with the AHE.

Figures (7)

• Figure 1: Refractive indices $n_{1,\pm}$ of Eq. (\ref{['RCPLCP']}). The red (blue) lines represent $n_{1,+}$ ($n_{1,-}$). The solid (dashed) line indicates the real (imaginary) part of the refractive indices. The solid purple line represents the real parts of $n_{1,+}$ and $n_{1,-}$, lying on top of each other. Here, we have used $\mu=1, \epsilon=3, \alpha^{\prime\prime}=3$ and $b=1$$\mathrm{s}^{-1}$.
• Figure 2: Refractive indices $n_{2,\pm}$ of Eq. (\ref{['RCPLCP']}). The red (blue) line indicates the positive (negative) refractive index ($n_{2,\pm}$), respectively. The horizontal dashed lines are given by Eq. (\ref{['Asymp1']}). Here, we have used $\mu=1, \epsilon=3, \alpha^{\prime\prime}=3$ and $b=1$$\mathrm{s}^{-1}$.
• Figure 3: Rotatory power $\delta_{+,\pm}$ of Eq. (\ref{['RP+pm']}), constructed using the two refractive indices for the RCP wave and $n_{2,+}$. The RP $\delta_{+,+}$ is depicted by the purple-red line, while $\delta_{+,-}$ is demarcated by the purple-blue line, endowed with double sign reversal. Here, we have used $\mu=1, \epsilon=\alpha^{\prime\prime}=3$, and $b=1$$\mathrm{s}^{-1}$.
• Figure 4: Kerr rotation $\theta_{K}^{+,\pm}$ of Eq. (\ref{['thetaK1']}). The red line shows the behavior of $\theta_{K}^{+,+}$, composed by the indices $n_{2,+}$ and $n_{1,+}$. The blue line depicts $\theta_{K}^{+,-}$, constituted with $n_{2,+}$ and $n_{1,-}$. The purple line is defined for the region where both $\theta_{K}^{+,\pm}$ are null. Here, we have used $n_{1}=1$, $\mu_{1}=1$$\mu=1$, $\epsilon=3, \alpha^{\prime\prime}=3$, and $b=1$$\mathrm{s}^{-1}$.
• Figure 5: Kerr rotation $\theta_{K}^{+,+}$ of Eq. (\ref{['thetaK1']}) under the condition (\ref{['condition-for-divergence-Kerr-rotation-1']}). The red and blue lines show $\theta_{K}^{+,+}$ (obtained by using $n_{2,+}$ and $n_{1,+}$) for $n_{1}=1.5$ and $n_{1}=1.9$, respectively. The purple line indicates $\theta_{K}^{+,+} =0$. Here, we have used $\mu_{1}=1$$\mu=1$, $\epsilon=3, \alpha^{\prime\prime}=1$, $b=1$$\mathrm{s}^{-1}$, $n_{1}=1.5$ (red), and $n_{1}=1.9$ (blue).