Multi-focal spherical media and geodesic lenses in geometrical optics

TL;DR

This paper introduces a novel method for designing complex isotropic spherical media and geodesic lenses that enable multi-focal imaging and perfect 3D domain imaging in geometrical optics.

Contribution

It presents a general approach linking spherical media with geodesic lenses to design multi-focal gradient-index lenses and absolute instruments.

Findings

Designed multi-focal gradient-index lenses embedded in homogeneous regions

Created multi-focal absolute instruments for perfect 3D imaging

Established a theoretical framework connecting spherical media and geodesic lenses

Abstract

This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the corresponding geodesic lens. We use this approach to design multi-focal gradient- index lenses embedded into an optically homogeneous region and multi-focal absolute instruments that provide perfect imaging of three-dimensional domains.