physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, a surface wave is a

mechanical wave In physics, a mechanical wave is a wave that is an oscillation of matter, and therefore transfers energy through a medium. While waves can move over long distances, the movement of the medium of transmission—the material—is limited. Therefor ...

that propagates along the

interface Interface or interfacing may refer to: Academic journals * ''Interface'' (journal), by the Electrochemical Society * '' Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics'' * '' Int ...

between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at the interface between two fluids with different densities. Elastic surface waves can travel along the surface of solids, such as '' Rayleigh'' or ''

Love Love encompasses a range of strong and positive emotional and mental states, from the most sublime virtue or good habit, the deepest interpersonal affection, to the simplest pleasure. An example of this range of meanings is that the love o ...

'' waves.

Electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...

s can also propagate as "surface waves" in that they can be guided along with a

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...

gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...

or along an interface between two media having different dielectric constants. In

radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmi ...

transmission, a ''

ground wave Ground waves are radio waves propagating parallel to and adjacent to the surface of the Earth, following the curvature of the Earth. This radiation is known as Norton surface wave, or more properly Norton ground wave, because ground waves in rad ...

'' is a guided wave that propagates close to the surface of the

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

Mechanical waves

seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...

, several types of surface waves are encountered. Surface waves, in this mechanical sense, are commonly known as either ''

Love wave In elastodynamics, Love waves, named after Augustus Edward Hough Love, are horizontally polarized surface waves. The Love wave is a result of the interference of many shear waves ( S-waves) guided by an elastic layer, which is ''welded'' to ...

s'' (L waves) or ''

Rayleigh wave Rayleigh waves are a type of surface acoustic wave that travel along the surface of solids. They can be produced in materials in many ways, such as by a localized impact or by piezo-electric transduction, and are frequently used in non-destructi ...

s''. A

seismic wave A seismic wave is a wave of acoustic energy that travels through the Earth. It can result from an earthquake, volcanic eruption, magma movement, a large landslide, and a large man-made explosion that produces low-frequency acoustic energy ...

is a wave that ''travels through the Earth, often as the result of an earthquake or explosion.'' Love waves have

transverse Transverse may refer to: *Transverse engine, an engine in which the crankshaft is oriented side-to-side relative to the wheels of the vehicle *Transverse flute, a flute that is held horizontally * Transverse force (or ''Euler force''), the tangen ...

motion (movement is perpendicular to the direction of travel, like light waves), whereas Rayleigh waves have both

longitudinal Longitudinal is a geometric term of location which may refer to: * Longitude ** Line of longitude, also called a meridian * Longitudinal engine, an internal combustion engine in which the crankshaft is oriented along the long axis of the vehicl ...

(movement parallel to the direction of travel, like sound waves) and transverse motion. Seismic waves are studied by seismologists and measured by a seismograph or seismometer. Surface waves span a wide frequency range, and the period of waves that are most damaging is usually 10 seconds or longer. Surface waves can travel around the globe many times from the largest earthquakes. Surface waves are caused when P waves and S waves come to the surface. Examples are the

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...

s at the surface of

water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...

and

air The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...

(

ocean surface wave In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction o ...

s). Another example is

internal wave Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change (continuously or discontinuously) with depth/height due to changes, for example, in ...

s, which can be transmitted along the interface of two water masses of different densities. In theory of hearing physiology, the traveling wave (TW) of

Von Bekesy The term ''von'' () is used in German language surnames either as a nobiliary particle indicating a noble patrilineality, or as a simple preposition used by commoners that means ''of'' or ''from''. Nobility directories like the ''Almanach de Go ...

, resulted from an acoustic surface wave of the

basilar membrane The basilar membrane is a stiff structural element within the cochlea of the inner ear which separates two liquid-filled tubes that run along the coil of the cochlea, the scala media and the scala tympani. The basilar membrane moves up and down ...

into the

cochlear duct The cochlear duct (bounded by the scala media) is an endolymph filled cavity inside the cochlea, located between the tympanic duct and the vestibular duct, separated by the basilar membrane and the vestibular membrane (Reissner's membrane) re ...

. His theory purported to explain every feature of the auditory sensation owing to these passive mechanical phenomena. Jozef Zwislocki, and later David Kemp, showed that that is unrealistic and that active feedback is necessary.

Electromagnetic waves

Ground wave Ground waves are radio waves propagating parallel to and adjacent to the surface of the Earth, following the curvature of the Earth. This radiation is known as Norton surface wave, or more properly Norton ground wave, because ground waves in rad ...

s'' are

radio waves Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz ( GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (s ...

propagating parallel to and adjacent to the surface of the Earth, following the

curvature of the Earth Spherical Earth or Earth's curvature refers to the approximation of figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. ...

. 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 surface wave'' or ''Zenneck–Sommerfeld surface wave''.Hill, D. A., and J. R. Wait (1978), Excitation of the Zenneck surface wave by a vertical aperture, Radio Sci., 13(6), 969–977, .Goubau, G.
"Über die Zennecksche Bodenwelle," (On the Zenneck Surface Wave)
''Zeitschrift für Angewandte Physik'', Vol. 3, 1951, Nrs. 3/4, pp. 103–107.Corum, K. L., M. W. Miller, J. F. Corum,
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, . The earth has one refractive index and the atmosphere has another, thus constituting an

that supports the guided Zenneck wave's transmission. Other types of surface wave are the trapped surface wave,Wait, James,
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. the gliding wave and Dyakonov surface waves (DSW) propagating at the interface of transparent materials with different symmetry. Apart from these, various types of surface waves have been studied for optical wavelengths.

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 In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmi ...

s and some may be considered as single-wire transmission lines. Characteristics and utilizations of the electrical surface wave phenomenon include: * The

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

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) such that the wave does not transmit power normal to the interface, i.e. it is evanescent along that dimension. * In

optical fiber An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass ( silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a mea ...

transmission,

evanescent waves In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source (oscillati ...

are surface waves. * In coaxial cable in addition to the TEM mode there also exists a transverse-magnetic (TM) mode 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 E-Line.

Surface plasmon polariton

The surface plasmon polariton (SPP) is an electromagnetic surface wave that can travel along an interface between two media with different dielectric constants. It exists under the condition that the

permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...

of one of the materials 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 Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability i ...

. 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.

Sommerfeld–Zenneck surface wave

The Sommerfeld–Zenneck wave or

Zenneck wave The Zenneck wave, Zenneck surface wave or Sommerfeld-Zenneck surface wave is a longitudinal, inhomogeneous or non-uniform electromagnetic plane wave incident at the complex Brewster's angle onto a planar or spherical boundary interface between tw ...

is a non-radiative guided

electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...

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

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

. Its electric field strength falls off at a rate of e^-αd/√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 Jonathan Adolf Wilhelm Zenneck (15 April 1871 – 8 April 1959) was a German physicist and electrical engineer who contributed to researches in radio circuit performance and to the scientific and educational contributions to the literature of t ...

of the problem of wave propagation over a lossy earth, it exists as an exact solution to

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...

. 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. Sommerfeld-Zenneck surface waves predict that the energy decays as R⁻¹ 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 dB/dec and 40 dB/dec.

References

* Barlow, H.M., and Brown, J., "Radio Surface Waves", Oxford University Press 1962. * Budden, K. G., "''Radio waves in the ionosphere; the mathematical theory of the reflection of radio waves from stratified ionised layers''". Cambridge, Eng., University Press, 1961. LCCN 61016040 /L/r85 * Budden, K. G., "''The wave-guide mode theory of wave propagation''". London, Logos Press; Englewood Cliffs, N.J., Prentice-Hall, c1961. LCCN 62002870 /L * Budden, K. G., "'' The propagation of radio waves : the theory of radio waves of low power in the ionosphere and magnetosphere''". Cambridge (Cambridgeshire); New York : Cambridge University Press, 1985. LCCN 84028498 * Collin, R. E., "''Field Theory of Guided Waves''". New York: Wiley-IEEE Press, 1990. * Foti, S., Lai, C.G., Rix, G.J., and Strobbia, C., "“Surface Wave Methods for Near-Surface Site Characterization”", CRC Press, Boca Raton, Florida (USA), 487 pp., , 2014 * Sommerfeld, A., "Partial Differential Equations in Physics" (English version), Academic Press Inc., New York 1949, chapter 6 – "Problems of Radio". * Polo, Jr., J. A., Mackay, T. G., and Lakhtakia, A., "''Electromagnetic Surface Waves: A Modern Perspective''". Waltham, MA, USA: Elsevier, 2013 . * Rawer, K.,"''Wave Propagation in the Ionosphere''", Dordrecht, Kluwer Acad.Publ. 1993. * Sommerfeld, A., "Partial Differential Equations in Physics" (English version), Academic Press Inc., New York 1949, chapter 6 – "Problems of Radio". * Weiner, Melvin M., "''Monopole antennas''" New York, Marcel Dekker, 2003. * Wait, J. R., "''Electromagnetic Wave Theory''", New York, Harper and Row, 1985. * Wait, J. R., "''The Waves in Stratified Media''". New York: Pergamon, 1962. * Waldron, Richard Arthur, "''Theory of guided electromagnetic waves''". London, New York, Van Nostrand Reinhold, 1970. LCCN 69019848 //r86 * Weiner, Melvin M., "''Monopole antennas''" New York, Marcel Dekker, 2003.

Journals and papers

;Zenneck, Sommerfeld, Norton, and Goubau * J. Zenneck, (translators: P. Blanchin, G. Guérard, É. Picot), "''Précis de télégraphie sans fil : complément de l'ouvrage : Les oscillations électromagnétiques et la télégraphie sans fil''", Paris : Gauthier-Villars, 1911. viii, 385 p. : ill. ; 26 cm. (''Tr''. "Precisions of wireless telegraphy: complement of the work: Electromagnetic oscillations and wireless telegraphy.") * J. Zenneck, "''Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie''"
Annalen der Physik, vol. 23, pp. 846–866, Sept. 1907
(''Tr''. "About the propagation of electromagnetic plane waves along a conductor plane and their relationship to wireless telegraphy.") * J. Zenneck, "''Elektromagnetische Schwingungen und drahtlose Telegraphie''", gart, F. Enke, 1905. xxvii, 1019 p. : ill. ; 24 cm. (Tr''. "Electromagnetic oscillations and wireless telegraphy.") * J. Zenneck, (translator: A.E. Seelig) "''Wireless telegraphy,''", New York tc.McGraw-Hill Book Company, inc., 1st ed. 1915. xx, 443 p. illus., diagrs. 24 cm. LCCN 15024534 (''ed''. "Bibliography and notes on theory" pp. 408–428.) * A. Sommerfeld, "''Über die Fortpflanzung elektrodynamischer Wellen längs eines Drahtes''"
Ann. der Physik und Chemie, vol. 67, pp. 233–290, Dec 1899
(''Tr''. "Propagation of electro-dynamic waves along a cylindric conductor.") * A. Sommerfeld, "''Über die Ausbreitung der Wellen in der drahtlosen Telegraphie''"
Annalen der Physik, Vol. 28, pp. 665–736, March 1909
(''Tr''. "About the Propagation of waves in wireless telegraphy.") * A. Sommerfeld, "''Propagation of waves in wireless telegraphy''," Ann. Phys., vol. 81, pp. 1367–1153, 1926. * K. A. Norton, "''The propagation of radio waves over the surface of the earth and in the upper atmosphere''," Proc. IRE, vol. 24, pp. 1367–1387, 1936. * K. A. Norton, "''The calculations of ground wave field intensity over a finitely conducting spherical earth''," Proc. IRE, vol. 29, pp. 623–639, 1941. * G. Goubau, "''Surface waves and their application to transmission lines''," J. Appl. Phys., vol. 21, pp. 1119–1128; November,1950. * G. Goubau, “Über die Zennecksche Bodenwelle,” (''Tr'
"On the Zenneck Surface Wave."
, Zeitschrift für Angewandte Physik, Vol. 3, 1951, Nrs. 3/4, pp. 103–107. ;Wait * Wait, J. R., "''Lateral Waves and the Pioneering Research of the Late Kenneth A Norton''". * Wait, J. R., and D. A. Hill, "''Excitation of the HF surface wave by vertical and horizontal apertures''". Radio Science, 14, 1979, pp 767–780. * Wait, J. R., and D. A. Hill, "''Excitation of the Zenneck Surface Wave by a Vertical Aperture''", Radio Science, Vol. 13, No. 6, November–December, 1978, pp. 969–977. * Wait, J. R., "''A note on surface waves and ground waves''", IEEE Transactions on Antennas and Propagation, Nov 1965. Vol. 13, Issue 6, pp. 996–997 * Wait, J. R., "''The ancient and modern history of EM ground-wave propagation''". IEEE Antennas Propagat. Mag., vol. 40, pp. 7–24, Oct. 1998. * Wait, J. R., "''Appendix C: On the theory of ground wave propagation over a slightly roughned curved earth''", ''Electromagnetic Probing in Geophysics''. Boulder, CO., Golem, 1971, pp. 37–381. * Wait, J. R., "''Electromagnetic surface waves''", ''Advances in Radio Research'', 1, New York, Academic Press, 1964, pp. 157–219. ;Others * R. E. Collin, "''Hertzian Dipole Radiating Over a Lossy Earth or Sea: Some Early and Late 20th-Century Controversies''", Antennas and Propagation Magazine, 46, 2004, pp. 64–79. * F. J. Zucker, "''Surface wave antennas and surface wave excited arrays''", Antenna Engineering Handbook, 2nd ed., R. C. Johnson and H. Jasik, Eds. New York: McGraw-Hill, 1984. * Yu. V. Kistovich, "''Possibility of Observing Zenneck Surface Waves in Radiation from a Source with a Small Vertical Aperture''", Soviet Physics Technical Physics, Vol. 34, No.4, April, 1989, pp. 391–394. * V. I. Baĭbakov, V. N. Datsko, Yu. V. Kistovich, "''Experimental discovery of Zenneck's surface electromagnetic waves''", Sov Phys Uspekhi, 1989, 32 (4), 378–379. * Corum, K. L. and J. F. Corum, "''The Zenneck Surface Wave''", ''Nikola Tesla, Lightning Observations, and Stationary Waves, Appendix II''. 1994. * M. J. King and J. C. Wiltse, "''Surface-Wave Propagation on Coated or Uncoated Metal Wires at Millimeter Wavelengths''". J. Appl. Phys., vol. 21, pp. 1119–1128; November, * M. J. King and J. C. Wiltse, "''Surface-Wave Propagation on a Dielectric Rod of Electric Cross-Section.''" Electronic Communications, Inc., Tirnonium: kld. Sci. Rept.'No. 1, AFCKL Contract No. AF 19(601)-5475; August, 1960. * T. Kahan and G. Eckart, "''On the Electromagnetic Surface Wave of Sommerfeld''", Phys. Rev. 76, 406–410 (1949).

Other media

* L.A. Ostrovsky (ed.), "''Laboratory modeling and theoretical studies of surface wave modulation by a moving sphere''", m, Oceanic and Atmospheric Research Laboratories, 2002.

External links

* Eric W. Weisstein, et al., "

'", Eric Weisstein's World of Physics, 2006. * David Reiss, "

'". The Net Advance of Physics: Special Reports, No. 1 * Gary Peterson, "

'". Feed Line No. 4. (''ed''. reproduction available online at 21st Century Books)
3D Waves
by Jesse Nochella based on a program by

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. {{Telecommunications Radio frequency propagation Broadcast engineering Seismology

Mechanical waves

Electromagnetic waves

Microwave field theory

Surface plasmon polariton

Sommerfeld–Zenneck surface wave

See also

References

Further reading

Standards and doctrines

Books

Journals and papers

Other media

External links