Encyclopedia … combined with a great Buyer's Guide!

The Gouy Phase Shift Speeds Up Light

Posted on 2008-11-25 as part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2008_11_25.html

Author: Dr. Rüdiger Paschotta, RP Photonics AG, RP Photonics AG

Abstract: A kind of superluminal propagation of light occurs simply when a light beam is focused in free space. This results from the Gouy phase shift.

Dr. Rüdiger Paschotta

Ref.: encyclopedia articles on Gouy phase shift, Gaussian beams, superluminal transmission

The Gouy phase shift of Gaussian beams is a well-known phenomenon. Whereas the phase of a plane wave (propagating in <$z$> direction) varies in proportion to <$k z$>, a Gaussian beam has an additional phase term <$-\arctan z / z_\textrm{R}$>, where <$z_\textrm{R}$> is the Rayleigh length.

It is often overlooked that this added term has an interesting consequence: it locally increases the wavelength (i.e., the distance between the phase fronts), and therefore it also increases the local phase velocity. Therefore, you easily obtain a phase velocity above the vacuum velocity of light simply by focusing a beam in free space!

This may be regarded as yet another case of superluminal transmission – not one of the particularly subtle cases, though. Certainly, it is worth to keep in mind that we should not take for granted that the usual rules for plane waves apply to other situations. Quite often, however, we implicitly assume plane waves without being aware of that.


This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

Note that you can also receive the articles in the form of a newsletter or with an RSS feed.

Questions and Comments from Users

{questions_and_comments}

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.

Spam check:

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.

preview

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/spotlight_2008_11_25.html">
Article on The Gouy Phase Shift Speeds up Light</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/spotlight_2008_11_25.html">
<img src="https://www.rp-photonics.com/previews/spotlight_2008_11_25.png"
alt="article" style="width:400px"></a>