# Surface wave

In physics, a surface wave is a mechanical wave that propagates along the interface 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 waves. Electromagnetic waves can also propagate as "surface waves" in that they can be guided along with a refractive index gradient or along an interface between two media having different dielectric constants. In radio transmission, a ground wave is a guided wave that propagates close to the surface of the Earth.

## 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. Surface waves are caused when P waves and S waves come to the surface.
Examples are the waves at the surface of water and air (ocean surface waves). Another example is internal waves, 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, resulted from an acoustic surface wave of the basilar membrane into the cochlear duct. 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 waves are radio waves 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 surface wave or Zenneck–Sommerfeld surface wave. The earth has one refractive index and the atmosphere has another, thus constituting an interface that supports the guided Zenneck wave's transmission. Other types of surface wave are the trapped surface wave, 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 lines and some may be considered as single-wire transmission lines.
Characteristics and utilizations of the electrical surface wave phenomenon include:
* The 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) such that the wave does not transmit power normal to the interface, i.e. it is evanescent along that dimension.
* 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 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. 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 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$^{-αd}$/√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 of the problem of wave propagation over a lossy earth, it exists as an exact solution to Maxwell's equations. 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.