A geometrical-optics analogy for gravitational lensing using axicon-type lenses

Abstract

Gravitational lensing is often introduced through the bending of light by mass, but its geometrical nature can be difficult to visualize without invoking the full machinery of general relativity. We present a geometrical-optics analogy in which selected lensing-like image morphologies are generated by ray tracing through axicon-type lenses. In contrast with analogies based on a spatially varying refractive index, the present model uses optical elements with a constant refractive index; the redistribution of rays is produced by the geometry of the refracting surfaces. After deriving the ray-tracing equations for a general two-surface axicon, we apply the model to conical and exponential profiles. Axially symmetric configurations generate ring-like images, misaligned incidence produces partial arcs, and broken axial symmetry leads to four-image patterns reminiscent of an Einstein cross. The model is not intended as a physical substitute for a relativistic lens equation, but as a computational and pedagogical tool for exploring how surface geometry and symmetry control ray deflection, redistribution, and image multiplicity.