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 half-space 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 vec-tors 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 polariza-tion 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. 1. INTRODUCTION Let the field vectors on the plane z = z, denoted by The usual treatment of the polarization properties of the electromagnetic field 4 is restricted to the special case of a time-harmonic plane-wave field. This restriction has, in part, been removed by Nisbet and Wolf ' for the case o