Wave Vector

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Definition: a vector indicating the direction of wave propagation and the phase delay per unit length

Category: article belongs to category general optics general optics

DOI: 10.61835/7ok Cite the article: BibTex plain text HTML Link to this page LinkedIn

The wave vector (or <$k$> vector) of a plane wave is a vector which at least in the case of isotropic optical media points in the direction in which the wave propagates. It is always perpendicular to the wavefronts.

The magnitude of the wave vector (with units of m⁻¹) is the wavenumber as defined by

$$k = \frac{{2\pi }}{\lambda }$$

where <$\lambda$> is the wavelength in the medium (not the vacuum wavelength).

In non-isotropic media, the direction of energy flow, which is the direction of the Poynting vector, can somewhat deviate from that of the wave vector, which is always perpendicular to the wavefronts. This phenomenon is called spatial walk-off.

In media with absorption or gain, the wave vector can have complex components. In the case of an evanescent wave, it can even have a purely imaginary component.

More to Learn

Encyclopedia articles:

Questions and Comments from Users

2022-09-11

Is the K vector a covariant or contravariant vector?

The author's answer:

It is contravariant: when using smaller distance units, the vector becomes larger.

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him, e.g. via e-mail.

By submitting the information, you give your consent to the potential publication of your inputs on our website according to our rules. (If you later retract your consent, we will delete those inputs.) As your inputs are first reviewed by the author, they may be published with some delay.