Ray geodesics and wave propagation on the Beltrami surface: Optics of an optical wormhole

Abstract

This study investigates ray geodesics and wave propagation on the Beltrami surface, with a particular emphasis on the effective potentials governing photon dynamics. We derive the geodesic equations and analyze the Helmholtz equation within this curved geometry, revealing that the resulting potentials are purely repulsive. For ray trajectories, the potential is determined by wormhole parameters such as the throat radius ($\ell$), radial optical distance ($u$), scale parameter ($R$), and the angular momentum of the test field. Near the wormhole throat, the potential remains constant, preventing inward motion below a critical energy threshold, whereas at larger radial distances, it decays exponentially, allowing free propagation. In the context of wave propagation, the potential exhibits a centrifugal barrier along with a constant repulsive term at large $u$. The Beltrami surface, characterized by constant negative Gaussian curvature, serves as a model for graphene sheets and optical wormholes in condensed matter systems. These results allow us to determine the space- and frequency-dependent refractive index of the medium, providing a coherent framework for understanding photon behavior in such systems, with promising implications for material applications.

6 pages, 6 figures

References in corpus (11)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Lensing by Kerr Black Holes
• Light Localization induced by Random Imaginary Permittivities
• An optical wormhole from hollow disclinations
• Negative-curvature spacetime solutions for graphene
• A cosmological model for corrugated graphene sheets
• Vector bosons in the rotating frame of negative curvature wormholes
• Rotational influence on fermions within negative curvature wormholes
• Coupled fermion-antifermion pairs within a traversable wormhole
• Electronic states in a quantum Beltrami surface
• Photonic Modes in Twisted Graphene Nanoribbons

Cited by in corpus (2)

• Optical and Thermodynamic Signatures of Lorentz Symmetry Breaking in Bumblebee AdS Black Holes
• Electromagnetic wave propagation in static black hole spacetimes: an effective refractive index description in Schwarzschild geometry