On the optical behavior of the electromagnetic field excited by a semi-infinite electric traveling-wave current

A closed-form solution for the spatial distribution of the electromagnetic field excited by an electric traveling-wave current source is presented. Incomplete Hankel and modified Bessel functions are employed to represent progressive and evanescent wave fields, respectively. It is shown that these fields are expressed in terms of spherical and cylindrical waves exhibiting optical character. Using the properties of the incomplete Hankel and modified Bessel functions, the spatial regions where the fields exist in optical sense are determined. It is shown that different shadow boundaries (SBs), featuring complex shapes, identify discontinuity surfaces for the geometrical optics (GO) field. Three surfaces, one being the well-know Keller´s cone, are found to describe in the general case the SBs for both the progressive and the evanescent wave fields. It is demonstrated that these surfaces collapse to the Keller´s cone surface in the limit of β→∞.