RP Photonics logo
RP Photonics
Technical consulting services on lasers, nonlinear optics, fiber optics etc.
Profit from the knowledge and experience of a top expert!
Powerful simulation and design software.
Make computer models in order to get a comprehensive understanding of your devices!
Success comes from understanding – be it in science or in industrial development.
The famous Encyclopedia of Laser Physics and Technology – available online for free!
The ideal place for finding suppliers for many photonics products.
Advertisers: Make sure to have your products displayed here!
… combined with a great Buyer's Guide!
VLib part of the

The Photonics Spotlight

The Gouy Phase Shift Speeds up Light

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 / zR, where zR 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, because its location is permanent. See also the Encyclopedia of Laser Physics and Technology.

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

If you like this article, share it with your friends and colleagues, e.g. via social media: