Phase-ray coordinate system corresponding to Maxwell’s equations solution

The paper describes the relationship between the solutions of Maxwell's equations and the curvilinear coordinates of geometrical optics. It generalizes the results achieved by Lüneburg, concerning the evolution of surfaces of electromagnetic fields discontinuities. This coordinate system in the future we will call phase-ray coordinate system. In the work, it is proved that field under study can be represented by two scalar functions. It is shown that under certain conditions on variable real coefficients of medium filling in the region under consideration, a phase-ray coordinate system that describes the laws of geometrical optics in this region can be constructed. There exist solutions of Maxwell's equations, which take in this coordinate system the simplest canonical form. A pair of quasi-wave equations gives this canonical form of the Maxwell's equations. The work also specify the necessary and sufficient conditions for the existence of a coordinate system, generated by the solution of Maxwell's equations with the holonomic field of the Poynting vector. It is shown that the class of solutions of Maxwell's equations includes monochromatic polarized waves, and the HilbertCourant solutions and their generalizations.