Ray series for electromagnetic waves in static heterogeneous bianisotropic dielectric media

We consider generally bianisotropic dielectric media. We consider the linear constitutive relations for bianisotropic media in the Boys-Post representation without spatial dispersion. We propose the high-frequency asymptotic ray series in terms of the magnetic vector potential. For the sake of simplicity, we assume that the media are static (do not change with time). In this case we can work in frequency domain, apply 3-D spatial rays, and avoid 4-D space-time rays. We assume that the media are so smoothly heterogeneous that we can apply the high-frequency ray-theory approximation. We assume the Weyl gauge (zero electric potential), which is best suited for electromagnetic wave fields. We derive the Hamiltonian function which specifies the rays and travel time. We then derive the transport equations for the zero-order and higher-order vectorial amplitudes.