Encyclopedia … combined with a great Buyer's Guide!

Sponsors:     and others

Phase Velocity

Definition: the velocity with which phase fronts propagate in a medium

More general term: velocity of light

German: Phasengeschwindigkeit

Categories: general optics, physical foundations

Units: m/s

Formula symbol: <$v_\textrm{ph}$>


How to cite the article; suggest additional literature

URL: https://www.rp-photonics.com/phase_velocity.html

The phase velocity of light is the velocity with which phase fronts propagate in a medium. It is related to the wavenumber <$k$> and the (angular) optical frequency <$\omega$>:

$${v_{{\rm{ph}}}} = \frac{\omega }{k}$$

In vacuum, the phase velocity is <$c$> = 299 792 458 m/s, independent of the optical frequency, and equals the group velocity. In a medium, the phase velocity is typically smaller by a factor <$n$>, called the refractive index, which is frequency-dependent (→ chromatic dispersion). In the visible spectral region, typical transparent crystals and optical glasses have refractive indices between 1.4 and 2.8. Semiconductors usually have higher values.

In the X-ray region, refractive indices are slightly below 1, corresponding to phase velocities slightly above the vacuum velocity of light. Similar effects can be caused e.g. by optical resonances of atoms in the visible spectral region. However, this does not allow for superluminal transmission of information, or for violating causality.

There are even cases where the phase velocity is directed opposite to the direction of the energy flow. Such phenomena occur in negative-index media, which can be realized as photonic metamaterials.

The phase velocity is usually considered for plane waves, where the wavefronts are simply moving in a direction perpendicular to their orientation. It is interesting to look at the wavefronts of focused laser beams. Due to the Gouy phase shift, these move slightly faster near the focus.

The term wave velocity is vague; it may refer to phase velocity or group velocity, or possibly mean something else.

See also: velocity of light, wavefronts, refractive index, group velocity, dispersion

Questions and Comments from Users

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; we would otherwise delete it soon. (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.

Your question or comment:

Spam check:

  (Please enter the sum of thirteen and three in the form of digits!)

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.


Share this with your friends and colleagues, e.g. via social media:

These sharing buttons are implemented in a privacy-friendly way!

Code for Links on Other Websites

If you want to place a link to this article in some other resource (e.g. your website, social media, a discussion forum, Wikipedia), you can get the required code here.

HTML link on this article:

<a href="https://www.rp-photonics.com/phase_velocity.html">
Article on Phase velocity</a>
in the <a href="https://www.rp-photonics.com/encyclopedia.html">
RP Photonics Encyclopedia</a>

With preview image (see the box just above):

<a href="https://www.rp-photonics.com/phase_velocity.html">
<img src="https://www.rp-photonics.com/previews/phase_velocity.png"
alt="article" style="width:400px"></a>

For Wikipedia, e.g. in the section "==External links==":

* [https://www.rp-photonics.com/phase_velocity.html
article on 'Phase velocity' in the RP Photonics Encyclopedia]