What is "plane wave"

In the physics of wave propagation, a plane wave (also spelled planewave) is a field $A\left({\vec x}, t\right)$ which takes the form

$$A\left({\vec x}, t\right)=f\left(\frac{\vec n}{c}\cdot{\vec x}-t\right),$$
with an arbitrary ( scalar or vector) function τ ↦ f(τ) and where $|\vec n|=1$ is a fixed unit vector. The solutions in $\vec x$ of

$$\tfrac{\vec n}{c}\cdot{\vec x}-t= const.$$
are comprise the plane with normal vector $\vec n$. Thus, the points of equal field value of $A\left({\vec x}, t\right)$ always form a plane in space. This plane then shifts with time t, along the direction $\vec n$ and with velocity c.

The term is often used to denote the special case where the plane wave is both harmonic and homogeneous. A homogeneous and harmonic plane wave is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector.

It is not possible in practice to have a true plane wave; only a plane wave of infinite extent will propagate as a plane wave. However, many waves 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 far from the antenna in its far-field region. Similarly, if the length scales are much longer than the wave’s wavelength, as is often the case for light in the field of optics, one can treat the waves as light rays which correspond locally to plane waves. __TOC__