Plane-wave propagation is studied in the most general bianisotropic medium
in which the electromagnetic wave can be split into two eigenwaves with cer
tain polarizations depending on two arbitrary directions in space. Hence th
e whole problem splits into two parts. The dispersion dyadics of the materi
als seen by the eigenwaves are derived and the refractive indices are solve
d for arbitrary direction of propagation. Also, a general expression for th
e eigenpolarizations is found. The theory is applied to some cases Sitting
the requirements of the media.