A new formulation for the Maxwell equations written in arbitrary curvilinear coordinates

The Maxwell equations for complex field-vector amplitudes written for an arbitrary inhomogeneous and anisotropic absorbing medium are considered. It is shown that, using an arbitrary system of curvilinear coordinates, it is possible to choose three bases (frames) for describing the desired field vectors and specified permittivity and permeability tensors such that corresponding scalar field equations can be treated as obtained in the Cartesian coordinate system for some equivalent (fictitious) magnetodielectric medium.