Photon rings in the metamaterial analog of a gravitomagnetic monopole

Abstract

After studying null geodesics in the equatorial plane in NUT spacetime, we show that there are unstable photon rings in this plane. Next we transform the metric of this plane to the isotropic coordinates and introduce its equivalent two-parameter index of refraction. Utilizing the analog gravity concepts, we assign this index of refraction to a metamaterial analog of this plane, and by ray-tracing simulation find its photon rings. Furthermore, we extend our analysis to the charged NUT spacetime and employ wave optics to numerically solve Maxwell's equations for electromagnetic waves within an inhomogeneous medium assigned with this spacetime's three-parameter index of refraction. We investigate the optical properties of such metamaterial analogs for designing enhanced and fine-tuned optical devices.