Advances in the application of Lorentz geometry to nonimaging optics

Lorentz Geometry has been successfully applied to the study of geometrical vector flux J. Recently, has been shown that using Lorentz geometry it is possible to obtain irradiance patterns produced by optical systems with refractive elements. In this paper we advance in the application of Lorentz geometry to nonimaging optics. We provide a solution for the coupled systems of partial differential equations, obtained by the application of Lorentz geometry to a 3D refractive optical system. We also analyze the role of eigenvalues of Gram matrix G obtained by the application of Lorentzian formalism.