Exact, closed-form representations for the time-domain surface impedances of a homogeneous, lossy half-space

In this paper, we derive exact, closed-form representations for the transverse electric and transverse magnetic time-domain, surface impedances associated with a plane wave that is obliquely incident on a homogeneous, lossy half-space. The time-domain surface impedances are expressed in terms of modified Bessel functions and incomplete Lipschitz-Hankel integrals. The limitations on the validity of a previously published approximate expression are also discussed.