Plane Wave

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Plane Wave

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:

:

u(ec{x},t) = a e^{i(ec{k}\cdotec{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).