Editing Surface wave (section)

==Electromagnetic waves==
{{further|Ground wave}}

''[[Ground wave]]s'' are [[radio waves]] [[Radio propagation|propagating]] parallel to and adjacent to the surface of the Earth, following the [[curvature of the Earth]].  This radiative ground wave is known as '''Norton surface wave''', or more properly '''Norton ground wave''', because ground waves in radio propagation are not confined to the surface.

Another type of surface wave is the non-radiative, bound-mode ''[[Zenneck wave|Zenneck surface wave]]'' or ''Zenneck–Sommerfeld surface wave''.<ref>[https://archive.org/download/bstj16-1-35/bstj16-1-35_text.pdf The Physical Reality of Zenneck's Surface Wave].</ref><ref name="Hill-Wait_1951">Hill, D. A., and J. R. Wait (1978), Excitation of the Zenneck surface wave by a vertical aperture, Radio Sci., 13(6), 969–977, {{doi|10.1029/RS013i006p00969}}.</ref><ref name="Goubau">Goubau, G., [http://www.nedyn.com/Goubau_1951-X.pdf "Über die Zennecksche Bodenwelle," (On the Zenneck Surface Wave)], ''Zeitschrift für Angewandte Physik'', Vol. 3, 1951, Nrs. 3/4, pp. 103–107.</ref><ref name="Barlow-Brown_1962-II">{{cite book |last1=Barlow |first1=H. |last2=Brown |first2=J. |title=Radio Surface Waves |date=1962 |publisher=Oxford University Press |location=London |pages=10–12 |language=en |chapter= II}}</ref><ref name="Corum_2016">Corum, K. L., M. W. Miller, J. F. Corum, "[http://rexresearch.com/corumzenneck/texzon.pdf Surface Waves and the Crucial Propagation Experiment],” Proceedings of the 2016 Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS 2016), Baylor University, Waco, TX, March 31-April 1, 2016, IEEE, MTT-S, {{ISBN|9781509027569}}.</ref> The earth has one refractive index and the atmosphere has another, thus constituting an [[Interface (chemistry)|interface]] that supports the guided Zenneck wave's transmission. Other types of surface wave are the '''trapped surface wave''',<ref name="Wait_1957">Wait, James, "[http://nvlpubs.nist.gov/nistpubs/jres/59/jresv59n6p365_A1b.pdf Excitation of Surface Waves on Conducting, Stratified, Dielectric-Clad, and Corrugated Surfaces]," ''Journal of Research of the National Bureau of Standards'' Vol. 59, No.6, December 1957.</ref> the '''gliding wave''' and '''[[Dyakonov surface waves]]''' (DSW) propagating at the interface of transparent materials with different symmetry.<ref name=DSW>{{cite journal| last = Dyakonov| first = M. I.| title = New type of electromagnetic wave propagating at an interface| journal =Soviet Physics JETP| volume =67|issue =4| pages =714|date =April 1988| bibcode = 1988JETP...67..714D|url = http://jetp.ac.ru/cgi-bin/e/index/e/67/4/p714?a=list}}</ref><ref>{{cite journal|author=Takayama, O.|title=Dyakonov Surface Waves: A Review. |journal=Electromagnetics|volume=28 |pages=126–145 |date=2008|last2=Crasovan, L. C. |first2=Johansen, S. K. |last3=Mihalache, D |first3=Artigas, D. |last4=Torner, L. |issue=3 |doi=10.1080/02726340801921403 |s2cid=121726611 }}</ref><ref>{{cite journal|author=Takayama, O.|title=Observation of Dyakonov surface waves. |journal=Physical Review Letters|volume=102 |pages=043903 |date=2009|last2=Crasovan, L. C. |first2=Artigas, D. |last3=Torner, L. |issue=4 |doi=10.1103/PhysRevLett.102.043903 |pmid=19257419 |bibcode=2009PhRvL.102d3903T |s2cid=14540394 }}</ref><ref>{{cite journal|author=Takayama, O.|title=Lossless directional guiding of light in dielectric nanosheets using Dyakonov surface waves. |journal=Nature Nanotechnology|volume=9 |pages=419–424 |date=2014|last2=Artigas, D. |first2=Torner, L. |issue=6 |doi=10.1038/nnano.2014.90 |pmid=24859812 |bibcode=2014NatNa...9..419T }}</ref>  Apart from these, various types of surface waves have been studied for optical wavelengths.<ref>{{cite journal|author=Takayama, O.|title=Photonic surface waves on metamaterial interfaces. |journal=Journal of Physics: Condensed Matter|volume=29 |pages=463001 |date=2017|last2= Bogdanov, A. A. |first2=Lavrinenko, A. V. |issue=46 |doi=10.1088/1361-648X/aa8bdd |pmid=29053474 |bibcode=2017JPCM...29T3001T }}</ref>

===Microwave field theory===
Within microwave field theory, the interface of a dielectric and conductor supports "surface wave transmission". Surface waves have been studied as part of [[transmission line]]s and some may be considered as [[single-wire transmission line]]s.

Characteristics and utilizations of the electrical surface wave phenomenon include:
* The [[field (physics)|field]] components of the wave diminish with distance from the interface.
* Electromagnetic energy is not converted from the surface wave field to another form of energy (except in leaky or lossy surface waves)<ref>{{cite journal| last1= Liu |first1= Hsuan-Hao |last2=Chang |first2=Hung-Chun |title=Leaky Surface Plasmon Polariton Modes at an Interface Between Metal and Uniaxially Anisotropic Materials. |journal=IEEE Photonics Journal |volume=5 |issue=6 |pages=4800806 |date=2013 | bibcode=2013IPhoJ...500806L |doi=10.1109/JPHOT.2013.2288298 | doi-access=free }}</ref> such that the wave does not transmit power normal to the interface, i.e. it is evanescent along that dimension.<ref>Collin, R. E., ''Field Theory of Guided Waves'', Chapter 11 "Surface Waveguides". New York: Wiley-IEEE Press, 1990.</ref> 
* In [[coaxial cable]] in addition to the TEM mode there also exists a transverse-magnetic (TM) mode<ref>{{cite web|url=http://www.corridor.biz/FullArticle.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.corridor.biz/FullArticle.pdf |archive-date=2022-10-09 |url-status=live|title=(TM) mode|website=corridor.biz|access-date=4 April 2018}}</ref> which propagates as a surface wave in the region around the central conductor. For coax of common impedance this mode is effectively suppressed but in high impedance coax and on a single central conductor without any outer shield, low attenuation and very broadband propagation is supported. Transmission line operation in this mode is called [[single-wire transmission line|E-Line]].

===Surface plasmon polariton===

[[File:SPP silver-air interface 10um.gif|thumb|255px|right|The [[Electric field|E-field]] of a [[surface plasmon polariton]] at a silver–air interface, at a frequency corresponding to a free-space wavelength of 10μm. At this frequency, the silver behaves approximately as a [[perfect electric conductor]], and the SPP is called a Sommerfeld–Zenneck wave, with almost the same wavelength as the free-space wavelength. <!--The permittivity of silver at this frequency is {{nowrap|(−2700 + 1400i)}}. The picture is {{nowrap|(0.6 × 10μm)}} across horizontally.-->]]

The [[surface plasmon polariton]] (SPP) is an [[electromagnetic wave|electromagnetic surface wave]] that can travel along an interface between two media with different dielectric constants. It exists under the condition that the [[permittivity]] of one of the materials <ref name="Corum_2016"/> forming the interface is negative, while the other one is positive, as is the case for the interface between air and a lossy conducting medium below the [[plasma frequency]]. The wave propagates parallel to the interface and decays exponentially vertical to it, a property called evanescence. Since the wave is on the boundary of a lossy conductor and a second medium, these oscillations can be sensitive to changes to the boundary, such as the adsorption of molecules by the conducting surface.<ref>{{cite journal|author=S. Zeng|title=Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications |journal=Chemical Society Reviews|volume=43 |pages=3426–3452 |date=2014|doi=10.1039/C3CS60479A|last2= Baillargeat|first2= Dominique|last3=Ho|first3=Ho-Pui|last4=Yong|first4=Ken-Tye |pmid=24549396 |issue=10 |hdl=10220/18851 |url=https://www.researchgate.net/publication/260252810|hdl-access=free}}</ref>

===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.