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.

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• Dielectric properties
• Magneto-dielectric effect
• Magneto-optics
• Permittivity
• Topological insulators