Representation of the electromagnetic fields of a dipole above an inhomogeneous half space

The problem of a dipole above an inhomogeneous half space is considered. Both the permittivity and the permeability are assumed to be functions of the longitudinal direction in the inhomogeneous region. The direct field representation in terms of longitudinal or transverse field components is studied. Excitations by vertical magnetic dipoles, vertical electric dipoles, as well as horizontal dipoles, are considered. A particular representation of the transverse field, for horizontal dipole excitation, in Cartesian components is given.