On the use of duality and complex vectorial space for the orthonormal decomposition of the electromagnetic field in anisotropic media

The electromagnetic fields in arbitrary geometry and in the presence of a homogeneous and anisotropic medium are described. The study has been motivated by the necessity for a comprehensive analysis of the influence on transport properties in plasmas of HF fields, used for heating, confinement, and stabilization. It is shown how the duality properties of the electromagnetic field completed by the 'Clebsch' decomposition of the 'matter current' permits the formulation of the Maxwell equation in a simple way in complex vectorial space. Finally, discussion covers what sort of material relations permit the obtaining of orthonormal solutions of the total field as extension of the usual T.M. and T.E. modes.