Polarization properties of the freely propagating electromagnetic field of arbitrary spatial and temporal form

The angular spectrum of plane waves representation of the freely propagating electromagnetic field in the halfspace z z of a homogeneous, isotropic, locally linear, temporally dispersive medium is employed to describe the polarization properties of the field throughout the half-space z > z in terms of the polarization behavior of either field vector on the plane at z = z. Both the spatial and the temporal dependence of the initial field vectors on this plane are assumed to be known but are otherwise arbitrary functions of the transverse position vector rT and time t on that plane. The general relationship between the electric and the magnetic polarization ellipses is obtained, along with the general orthogonality relations between the field vectors. Finally, the conditions under which either or both field vectors may be uniformly polarized are described.