Algorithm for Lens Calculations in the Geometrized Maxwell Theory

Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is usually not given attention. The aim of this work is to demonstrate the work of the proposed the algorithm in the framework of geometrical approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters. The methods of differential geometry are used for effective metrics construction for isotropic and anisotropic media. For effective metric space ray trajectories are obtained in the form of geodesic curves. The introduced algorithm is applied to well-known objects - Maxwell and Luneburg lenses. The similarity of results obtained by classical and geometric approach is demonstrated.