Surface wave

Surface wave
Diving grebe creates surface waves

In physics, a surface wave is a mechanical wave that propagates along the interface between differing media, usually two fluids with different densities. A surface wave can also be an electromagnetic wave guided by a refractive index gradient. In radio transmission, a ground wave is a surface wave that propagates close to the surface of the Earth.[1]


Mechanical waves

In seismology, several types of surface waves are encountered. Surface waves, in this mechanical sense, are commonly known as either Love waves (L waves) or Rayleigh waves. A seismic wave is a wave that travels through the Earth, often as the result of an earthquake or explosion. Love waves have transverse motion (movement is perpendicular to the direction of travel, like light waves), whereas Rayleigh waves have both longitudinal (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.

The term "surface wave" can describe waves over an ocean, even when they are approximated by Airy functions and are more properly called creeping waves. Examples are the waves at the surface of water and air (ocean surface waves), or ripples in the sand at the interface with water or air. Another example is internal waves, which can be transmitted along the interface of two water masses of different densities.

Electromagnetic waves

Ground waves refer to the propagation of radio waves close to or at the surface of the Earth. These surface waves are also known loosely as Norton surface waves, Zenneck waves, Sommerfeld waves, or gliding waves.

Radio propagation

Lower frequencies, especially AM broadcasts in the mediumwave (sometimes called "medium frequency") and long wave bands (and other types of radio frequencies below that), travel efficiently as a surface wave. This is because they are more efficiently diffracted by the figure of the Earth due to their low frequencies. Ionospheric reflection is taken into consideration as well. The ionosphere reflects frequencies in a certain band, which often changes due to solar conditions. The Earth has one refractive index and the atmosphere has another, thus constituting an interface that supports the surface wave transmission.

Conductivity of the surface affects the propagation of ground waves, with more conductive surfaces such as water providing better propagation.[2] Increasing the conductivity in a surface results in less dissipation.[3] The refractive indices are subject to spatial and temporal changes. Since the ground is not a perfect electrical conductor, ground waves are attenuated as they follow the earth’s surface.

Most long-distance LF "longwave" radio communication (between 30 kHz and 300 kHz) is a result of groundwave propagation. Mediumwave radio transmissions (frequencies between 300 kHz and 3000 kHz) have the property of following the curvature of the earth (the groundwave) in the majority of occurrences. At low frequencies, ground losses are low and become lower at lower frequencies. The VLF and LF frequencies are mostly used for military communications, especially with ships and submarines.

Surface waves have been used in over-the-horizon radar. In the development of radio, surface waves were used extensively. Early commercial and professional radio services relied exclusively on long wave, low frequencies and ground-wave propagation. To prevent interference with these services, amateur and experimental transmitters were restricted to the higher (HF) frequencies, felt to be useless since their ground-wave range was limited. Upon discovery of the other propagation modes possible at medium wave and short wave frequencies, the advantages of HF for commercial and military purposes became apparent. Amateur experimentation was then confined only to authorized frequencies in the range.

Mediumwave and shortwave reflect off the ionosphere at night, which is known as skywave. During daylight hours, the lower "D" layer of the ionosphere forms and absorbs lower frequency energy. This prevents skywave propagation from being very effective on mediumwave frequencies in daylight hours. At night, when the "D" layer dissipates, mediumwave transmissions travel better by skywave. Ground waves do not include ionospheric and tropospheric waves.

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 lines and some may be considered as single-wire transmission lines.

Characteristics and utilizations of the electrical surface wave phenomena include:

  • The field components of the wave diminish with distance from the interface.[citation needed]
  • 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.[citation needed]
  • In optical fiber transmission, evanescent waves are surface waves.[citation needed]
  • 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.

Energy flow velocity

The energy of surface electromagnetic waves can break the light barrier c because the dispersion relation is corresponding to the energy-momentum equation of a tachyon. In addition, the consequential velocity of a tachyon just equals the energy flow velocity S/w of the field given by classical electrodynamics.[4] It is a good model helpful to study the tachyon and extend special relativity.

See also

  • Arnold Sommerfeld – published the mathematical treatise on the zenneck wave
  • Jonathan Zenneck – Pupil of Sommerfeld; Wireless pioneer; developed the zenneck wave
  • Kenneth Norton
  • John Stone Stone – Wireless pioneer; produced theories on radio propagation
  • Ground constants, the electrical parameters of earth
  • Near and far field, the radiated field that is within one quarter of a wavelength of the diffracting edge or the antenna and beyond.
  • Skin effect, the tendency of an alternating electric current to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core.
  • Green function, a function used to solve inhomogeneous differential equations subject to boundary conditions.

External articles, further readings, and references


  1. ^  This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188).
  2. ^ "Naval Electrical Engineering Training Series", Chapter 2 Radio Wave Propagation, Ground Waves. Integrated publishing.
  3. ^ Antennas and Radio Propagation, TM 11-666, Dept. of the Army, Feb. 1953, pp. 17-23.
  4. ^ Wang, Zhong-Yue (2011). "Superluminal energy transmission in the Goos-Hanchen shift of total reflection". Optics Communications 284 (7): 1747–1751. Bibcode 2011OptCo.284.1747W. doi:10.1016/j.optcom.2010.12.027. 

Web sites


  • U.S. Patent 2,685,068, "Surface wave transmission line". George J. E. Goubau
  • U.S. Patent 2,921,277, "Launching and receiving of surface waves". George J. E. Goubau.
  • U.S. Patent 7,567,154, "Surface wave transmission system over a single conductor having E-fields terminating along the conductor ". Glenn E. Elmore.

Standards and doctrines


  • Collin, R. E., "Field Theory of Guided Waves". New York: Wiley-IEEE Press, 1990.
  • Waldron, Richard Arthur, "Theory of guided electromagnetic waves". London, New York, Van Nostrand Reinhold, 1970. ISBN 0-442-09167-2 LCCN 69019848 //r86
  • Weiner, Melvin M., "Monopole antennas" New York, Marcel Dekker, 2003. ISBN 0-8247-0496-7
  • Wait, J. R., "The Waves in Stratified Media". New York: Pergamon, 1962.
  • Wait, J. R., "Electromagnetic Wave Theory", New York, Harper and Row, 1985.
  • 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. ISBN 0-521-25461-2 LCCN 84028498
  • 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
  • Barlow, H.M., and Brown, J., "Radio Surface Waves", Oxford University Press 1962.
  • Sommerfeld, A., "Partial Differential Equations in Physics" (English version), Academic Press Inc., New York 1949, chapter 6 - "Problems of Radio".
  • Rawer, K.,"Wave Propagation in the Ionosphere", Dordrecht, Kluwer Acad.Publ. 1993.

Journals and papers

Zenneck, Sommerfeld, and Norton
  • 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", Ann. 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 [etc.] McGraw-Hill Book Company, inc., 1st ed. 1915. xx, 443 p. illus., diagrs. 24 cm. LCCN 15024534 (ed. "Bibliography and notes on theory" p. 408-428.)
  • A. Sommerfeld, "Fortpflanzung elektrodynamischer Wellen an einem zylindrischen Leiter", 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 Ausbreitlung der Wellen in der drahtlosen Telegraphie", Annalen der Physik, Vol. 28, March, 1909, pp. 665-736. (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.
  • 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 by a vertical aperture", Radio Science, 13, 1978, pp. 967-977.
  • Wait, J. R., "A note on surface waves and ground waves", IEEE Transactions on Antennas and Propagation, Nov 1965. Vol. 13, Issue 6, pg 996- 997 ISSN 0096-1973
  • 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.
  • 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.
  • Hill, D. and J.R Wait, "Excitation of the Zenneck Surface Wave by a Vertical Aperture", Radio Science, Vol. 13, No. 6, November–December, 1978, pp. 969-977.
  • 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,
  • Georg Goubau, "Surface waves and their application to transmission lines", J. Appl. Phys., vol. 21, pp. 1119–1128; November,1950.
  • 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. OCLC 50325097

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