Light trajectories and wave dynamics in optical wormholes

Abstract: We investigate the optical properties of a wormhole geometry characterized by a constant negative Gaussian curvature. This distinctive optical structure is modeled using the optical metric of the static BTZ black hole, corresponding to the hyperbolic wormhole framework. Within this model, we derive the arbitrary geodesics and the associated effective potential. Our analysis reveals that the effective potential becomes increasingly narrow as the curvature radius of the optical wormhole decreases, with all possible trajectories converging at the optical origin (\rho = 0). We further analyze the wave modes governing light propagation on this curved surface, demonstrating that the effective potential is purely repulsive in both the small and large (\rho) limits. While the potential remains finite in both regimes, its behavior differs markedly. Near the optical origin, the magnetic quantum number ((m)) exerts a significant influence on the effective repulsive potential, particularly for large values of (m), where the potential resembles a typical barrier. However, this effect diminishes with increasing optical distance. Using this framework, we compute the reflection and transmission coefficients for (m \neq 0). Our findings indicate that the optical properties of the background are predominantly governed by the curvature radius of the optical wormhole, highlighting its critical role in shaping light propagation in such geometries.