A Variable Metric Electrodynamics. Plane Waves

Classical electrodynamics can be divided into two parts. In the first one, a need of introducing a plenty of directed quantities occurs, namely multivectors and differential forms but no scalar product is necessary. We call it premetric electrodynamics. In this part, principal equations of the theory can be tackled. The second part concerns solutions of the equations and requires establishing of a scalar product and, consequently, a metric. For anisotropic media two scalar products can be introduced depending on the electric permittivity and magnetic permeability tensors. In the case of plane electromagnetic waves both of them are needed because two constitutive equations are needed: one for the electric fields, the other for the magnetic field. We show which part of the description of plane electromagnetic waves is independent of scalar products, and where they become necessary.