Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in absorbing isotropic media.

We introduce a formalism based on complex unitary vectors for the direction of propagation and for the polarization in order to describe in detail the propagation of inhomogeneous plane waves in absorbing isotropic media. We obtain analytic expressions for the displacement vector, the electric field, the magnetic field, and the Poynting vector, and we study their geometry in terms of the geometrical interpretation of the complex directions of propagation inside the material. We introduce a complex coordinate system based on complex unitary vectors, where the description of the polarization states of the field vectors and the Poynting vector becomes simpler. The physical meaning and the interpretation of the mathematical operations involving these complex unitary vectors is provided.