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 phase) are infinite parallel planes normal to the phase velocity vector.

Related Topics:
Electromagnetic waves - Wavefronts - Phase - Phase velocity

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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.

Related Topics:
Antenna - Far-field region

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Mathematically, a plane wave is a solution to the wave equation of the following form:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:u(ec{x},t) = a e^{i(ec{k}cdotec{x} - omega t)}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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).

Related Topics:
Imaginary unit - Wave vector - Angular frequency - Complex - Vector

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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.

Related Topics:
Dispersion relation - Phase velocity - Group velocity - Characteristic impedance

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

(The term is used in the same way for telecommunication, e.g. in Federal Standard 1037C and MIL-STD-188.)

Related Topics:
Telecommunication - Federal Standard 1037C - MIL-STD-188

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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