Ray trajectories and wave optics in a traversable wormhole: Optics of a minimal surface

This study investigates ray trajectories and wave propagation in a static, ( 2 + 1 ) -dimensional, radially symmetric traversable wormhole (TWH) spacetime with a constant redshift function and a radial shape function proportional to 1 / ρ . The spatial geometry forms a minimal surface (a catenoid bridge), enabling a geometric-optical interpretation. An analysis of the ray trajectories reveals how the curvature-induced structure of the wormhole (WH) governs the ray paths, depending on the relative sizes of the radial coordinate ρ and the throat radius ℓ ∘ . Extending the study to wave dynamics, we derive a refractive index n ( ρ , ω ) that explicitly depends on both ρ and the wave frequency ω , identifying a critical frequency that marks the transition between propagation and attenuation. These results demonstrate how the WH's topology distinctly influences wave propagation and may inform future developments in analogue gravity models and advanced optical media.