Consistency Requirements for Integral Representations of Green’s Functions—Part II: An Erroneous Representation

The two requirements set forth in Part I of this paper are used to demonstrate the inadequacy of a recently proposed Green's function for a material half-space. It is shown that the construction carried out with respect to the wavenumber normal to the interface results not only in an incomplete representation but also in nonphysical fields in the conducting medium. By comparing with the Sommerfeld integral representation, which was shown to be complete and exact in Part I, it is demonstrated that the so-constructed Green's function with respect to the vertical wavenumber: 1) has an error in the main contribution (arising from the primary branch cut) and 2) lacks the key ingredients of a surface wave and an additional branch cut contribution in the representation.