Ray and wave optics in an optical wormhole

We examine ray trajectories and wave dynamics in an optical wormhole with constant negative Gaussian curvature, analogous to a monolayer graphene sheet or graphene wormholes. Focusing on the elliptic wormhole (EWH), we derive exact solutions for ray trajectories and show that the effective potential is impenetrable at the optical origin u=0, but rapidly vanishes at large distances, allowing trajectories to remain unaffected. By solving the Helmholtz equation on the EWH surface, we find that S-waves ( m=0) are indefinitely trapped at the origin by an infinitely attractive effective potential, whereas modes with m≠0 encounter an infinitely repulsive barrier. Additionally, we determine the spatially and frequency-dependent refractive index characterizing the EWH and discuss the corresponding optical response of the background.