Local properties of radiation in lossy media

In lossless inhomogeneous media the ray-optical description of the propagation and scattering of electromagnetic waves exhibits the local and sequential properties of these phenomena. The extension of ray optics to lossy inhomogeneous media does not exhibit such properties, in general, since the equations defining the paths of rays connecting real source and observation points yield complex values of the space coordinates, i.e., complex rays. The purpose of this paper is to clarify the local and sequential propagation characteristics of fields in an inhomogeneous lossy medium, and to assertain the significance of the complex rays. The simplest configuration suited to this purpose is a planar interface between homogeneous lossless and lossy half-spaces. By studying the shadowing effects produced at an observation point by sampling windows placed in planes crossed by the field, one finds the region through which the field principally propagates to the observation point, and there-from the local and sequential properties. The results give physical meaning to complex rays and should provide a basis for a description of propagation and scattering in lossy media that avoids the use of complex space.