Editing Surface wave (section)

===Sommerfeld–Zenneck surface wave===

The [[Surface plasmon polariton#Animations|Sommerfeld–Zenneck wave]] or [[Zenneck wave]] is a non-radiative guided [[electromagnetic wave]] that is supported by a planar or spherical interface between two homogeneous media having different dielectric constants. This surface wave propagates parallel to the interface and decays exponentially vertical to it, a property known as evanescence. It exists under the condition that the [[permittivity]] of one of the materials forming the interface is negative, while the other one is positive, as for example the interface between air and a lossy conducting medium such as the terrestrial transmission line, below the [[plasma frequency]]. Its electric field strength falls off at a rate of e<sup>-αd</sup>/√d in the direction of propagation along the interface due to two-dimensional geometrical field spreading at a rate of 1/√d, in combination with a frequency-dependent exponential attenuation (α), which is the terrestrial transmission line dissipation, where α depends on the medium’s conductivity. Arising from original analysis by [[Arnold Sommerfeld]] and [[Jonathan Zenneck]] of the problem of wave propagation over a lossy earth, it exists as an exact solution to [[Maxwell's equations]].<ref name="Barlow-Brown_1962">{{cite book |last1=Barlow |first1=H. |last2=Brown |first2=J. |title=Radio Surface Waves |date=1962 |publisher=Oxford University Press |location=London |pages=v, vii |language=en }}</ref> The Zenneck surface wave, which is a non-radiating guided-wave mode, can be derived by employing the Hankel transform of a radial ground current associated with a realistic terrestrial Zenneck surface wave source.<ref name="Corum_2016" /> Sommerfeld-Zenneck surface waves predict that the energy decays as R<sup>−1</sup> because the energy distributes over the circumference of a circle and not the surface of a sphere. Evidence does not show that in radio space wave propagation, Sommerfeld-Zenneck surfaces waves are a mode of propagation as the path-loss exponent is generally between 20&nbsp;dB/dec and 40&nbsp;dB/dec.