Varandian Optics: A Non-Euclidean Formulation of Light Propagation

This article introduces Varandian Optics, a generalization of Euclidean geometric optics to spaces of constant curvature. Employing tools from differential geometry, we derive ray propagation as geodesics in spherical (K > 0) and hyperbolic (K < 0) spaces and formulate new optical laws governing propagation, refraction, reflection, and index–curvature duality. We also demonstrate how appropriately de-signed radial refractive indices can emulate constant-curvature metrics in physical media. This framework not only unifies optics with geometric principles but also suggests potential applications in metamaterials, transformational lenses, and cosmology.