The Gouy Phase Shift Speeds up Light
Posted on 2008-11-25. Permanent link: http://www.rp-photonics.com/spotlight_2008_11_25.html
Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH
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 send comments and suggestions to RP Photonics Consulting GmbH. You may also link to this page, because its location is permanent. See also the Encyclopedia of Laser Physics and Technology.
