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.

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

In this equation, the function ω(**k**) is the dispersion relation of the medium, with the ratio ω/|**k**| giving the phase velocity and *d*ω/*d***k** 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 the phase velocity to *c* is called the *effective index* and is proportional to the characteristic impedance of the medium.

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

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