标题： Beltrami曲面上的光线测地线和波传播：光学蠕虫洞的光学特性 显示英文标题

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

摘要： 本研究探讨了贝尔特拉米曲面上的射线测地线和波传播，特别关注控制光子动力学的有效势。 我们推导了测地线方程，并在此弯曲几何中分析了亥姆霍兹方程，揭示出所得到的势完全是排斥的。 对于射线轨迹，势由虫洞参数决定，例如喉半径（$\ell$）、径向光学距离（$u$）、尺度参数（$R$）以及测试场的角动量。 在虫洞喉附近，势保持恒定，阻止低于临界能量阈值的向内运动，而在更大的径向距离处，势呈指数衰减，允许自由传播。 在波传播的背景下，势在大$u$处表现出离心势垒以及常数排斥项。 贝尔特拉米曲面具有恒定负高斯曲率，可用作石墨烯片和凝聚态系统中的光学虫洞模型。 这些结果使我们能够确定介质的空间和频率相关的折射率，为理解此类系统中光子行为提供了一个连贯的框架，对材料应用具有潜在意义。 显示英文摘要

摘要： 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.