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Encyclopedia > Plane wave

In the physics of wave propagation (especially electromagnetic waves), a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant amplitude and phase) are infinite parallel planes normal to the propagation direction. Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ... In geometrical optics, a wave front (or crest of the wave) is defined as the locus of points having the same phase of vibration. ... ...

By extension, the term is also used to describe waves that are approximately plane waves in a localized region of space. For example, a localized source such as an antenna produces a field that is approximately a plane wave in its far-field region. A yagi antenna Most simply, an antenna is an electronic component designed to send or receive radio waves. ... In the study of diffraction and antenna design, the near field is that part of the radiated field that is within a small number of wavelengths of the diffracting edge or antenna. ...

Mathematically, a plane wave is a solution to the wave equation of the following form: The wave equation is an important partial differential equation which generally describes all kinds of waves, such as sound waves, light waves and water waves. ...

where i is the imaginary unit, k is the wave vector, ω is the angular frequency, and a is the (complex) amplitude. (In some conventions, this expression is conjugated.) The physical solution is usually found by taking the real part of this expression. For the vector wave equation of electromagnetism, a is the vector for the electric or magnetic field (and is orthogonal to k, for an isotropic medium). In mathematics, the imaginary unit i allows the real number system to be extended to the complex number system . ... A wave vector is a vector that represents two properties of a wave: the magnitude of the vector represents wavenumber (inversely related to wavelength), and the vector points in the direction of wave propagation. ... Angular frequency is a measure of how fast an object is rotating In physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed) is a scalar measure of rotation rate. ... In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying . ... In physics and engineering, the word vector typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but this...

In this equation, the function ω(k) is the dispersion relation of the medium, with the ratio ω/|k| giving the phase velocity and dω/dk giving the group velocity. For electromagnetism in an isotropic medium with index of refraction n, the phase velocity is c/n (which equals the group velocity only if the index is not frequency-dependent). For the same reason, the ratio of c to the phase velocity is called the effective index and is proportional to the characteristic impedance of the medium. The group velocity of a wave is the velocity with which the overall shape of the waves amplitude (known as the envelope of the wave) propagates through space. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ... The group velocity of a wave is the velocity with which the overall shape of the waves amplitude (known as the envelope of the wave) propagates through space. ... In radio communications, characteristic impedance (acoustic impedance or sound impedance) of a uniform transmission line is the impedance of a circuit that, when connected to the output terminals of a line of arbitrary length, causes the line to appear infinitely long. ...

(The term is used in the same way for telecommunication, e.g. in Federal Standard 1037C and MIL-STD-188.) BlackBerry 7100t Telecommunication is the extension of communication over a distance. ... Federal Standard 1037C entitled Telecommunications: Glossary of Telecommunication Terms is a U.S. Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended. ... MIL-STD-188 is a series of U.S. military standards relating to telecommunications. ...

• J. D. Jackson, Classical Electrodynamics (Wiley: New York, 1998).

Results from FactBites:

 Plane Waves (536 words) The wave vector is normal to the wave fronts and its length is the wavenumber. A plane wave in two or three dimensions is like a sine wave in one dimension except that crests and troughs aren't points, but form lines (2-D) or planes (3-D) perpendicular to the direction of wave propagation. The large arrow is a vector called the wave vector, which defines (1) the direction of wave propagation by its orientation perpendicular to the wave fronts, and (2) the wavenumber by its length.
 Method and apparatus for generating periodic structures in substrates by synthetic wavelength holograph exposure - ... (3871 words) Plane wave vectors k1 and k3 are incident on the surface 10 at angles of incidence,.theta. Plane wave vectors k2 and k4 are incident on the surface 10 at angles of incidence,.phi. Plane wave k1 reflects off of the reflective surface 18 of the mirror 14 to form plane wave k3 which is incident on the photo-sensitive material 11 at an angle of incidence -.theta.
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