On the Electromagnetic Surface Wave of Sommerfeld

Abstract

It is proved that Sommerfeld's well-known electromagnetic surface wave does not exist in the radiation of a Hertzian dipole over a plane earth because it does not fulfill the so-called "radiation condition." The path of integration chosen by Sommerfeld is correct, but there is another saddle-point overlooked by this author which just annuls the surface wave due to the residue. These results are in agreement with Burrow's measurements.