Editing Faster-than-light (section)

===Group velocities above ''c''===
The [[group velocity]] of a wave may also exceed ''c'' in some circumstances.<ref>
{{cite journal
|last1=Wang |first1=L. J.
|last2=Kuzmich |first2=A.
|last3=Dogariu |first3=A.
|year=2000
|title=Gain-assisted superluminal light propagation
|journal=[[Nature (journal)|Nature]]
|volume=406 |issue=6793 |pages=277–279
|doi=10.1038/35018520
|pmid=10917523
|doi-access= |bibcode=2000Natur.406..277W|s2cid=4358601
}}</ref><ref>
{{cite journal
|last1=Bowlan |first1=P.
|last2=Valtna-Lukner |first2=H.
|last3=Lõhmus |first3=M.
|last4=Piksarv |first4=P.
|last5=Saari |first5=P.
|last6=Trebino |first6=R.
|s2cid=122056218
|year=2009
|title=Measurement of the spatiotemporal electric field of ultrashort superluminal Bessel-X pulses
|journal=[[Optics and Photonics News]]
|volume=20 |issue=12 |page=42
|bibcode=2009OptPN..20...42M
|doi=10.1364/OPN.20.12.000042
}}</ref> In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of the envelope of a pulse may travel with a velocity above ''c''. However, even this situation does not imply the propagation of [[signal (information theory)|signals]] with a velocity above ''c'',<ref>
{{cite book |last=Brillouin |first=L. |url=https://archive.org/details/wavepropagationg00bril_0 |title=Wave Propagation and Group Velocity |publisher=[[Academic Press]] |year=1960 |url-access=registration}}</ref> even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind (distortion), the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than ''c'' without this effect.<ref>
{{cite journal
|last1=Withayachumnankul |first1=W.
|last2=Fischer |first2=B. M.
|last3=Ferguson |first3=B.
|last4=Davis |first4=B. R.
|last5=Abbott |first5=D.
|year=2010
|title=A Systemized View of Superluminal Wave Propagation
|url=http://www.eleceng.adelaide.edu.au/personal/dabbott/publications/PIE_withayachumnankul2010.pdf
|journal=[[Proceedings of the IEEE]]
|volume=98 |issue=10 |pages=1775–1786
|doi=10.1109/JPROC.2010.2052910
|s2cid=15100571
}}</ref> However, group velocity [[Gouy phase shift|can exceed]] ''c'' in some parts of a [[Gaussian beam]] in vacuum (without attenuation). The [[diffraction]] causes the peak of the pulse to propagate faster, while overall power does not.<ref>
{{cite journal
|last1=Horváth |first1=Z. L.
|last2=Vinkó |first2=J.
|last3=Bor |first3=Zs.
|last4=von der Linde |first4=D.
|year=1996
|title=Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift
|url=http://www.ilp.physik.uni-essen.de/vonderLinde/Publikationen/APB96_gouy.pdf |archive-url=https://web.archive.org/web/20030403070745/http://www.ilp.physik.uni-essen.de/vonderLinde/Publikationen/APB96_gouy.pdf |archive-date=2003-04-03 |url-status=live
|journal=[[Applied Physics B]]
|volume=63 |issue=5 |pages=481–484
|bibcode=1996ApPhB..63..481H
|doi=10.1007/BF01828944
|s2cid=54757568
}}</ref>