A Second-Order Asymptotic Approximation for the Sommerfeld Half-Space Problem

Investigation is made on the Sommerfeld half-space problem that concerns the spherical-wave fields on the sparser side of a planar interface involving both permittivity and permeability contrasts. For a point current source placed at the interface, the fields are described by a second-order approximation that properly evaluates the asymptotic component having the inverse-square dependence on the distance from the source. The validity of this approximation is demonstrated in the time domain by comparisons with the waveforms of the simpler approximations and the wavenumber-synthetic waveforms.