Editing Group velocity (section)

=== Superluminal group velocities ===
Since the 1980s, various experiments have verified that it is possible for the group velocity (as defined above) of [[laser]] light pulses sent through lossy materials, or gainful materials, to significantly exceed the [[speed of light in vacuum]] {{mvar|c}}. The peaks of wavepackets were also seen to move faster than {{mvar|c}}.

In all these cases, however, there is no possibility that signals could be carried [[faster than light|faster than the speed of light in vacuum]], since the high value of {{mvar|v}}<sub>{{mvar|g}}</sub> does not help to speed up the true motion of the sharp wavefront that would occur at the start of any real signal. Essentially the seemingly superluminal transmission is an artifact of the narrow band approximation used above to define group velocity and happens because of resonance phenomena in the intervening medium. In a wide band analysis it is seen that the apparently paradoxical speed of propagation of the signal envelope is actually the result of local interference of a wider band of frequencies over many cycles, all of which propagate perfectly causally and at phase velocity. The result is akin to the fact that shadows can travel faster than light, even if the light causing them always propagates at light speed; since the phenomenon being measured is only loosely connected with causality, it does not necessarily respect the rules of causal propagation, even if it under normal circumstances does so and leads to a common intuition.<ref name=Boyd1170885/><ref name="DEWSL06">{{Citation |first1=Gunnar |last1=Dolling |first2=Christian |last2=Enkrich |first3=Martin |last3=Wegener |first4=Costas M. |last4=Soukoulis |first5=Stefan |last5=Linden |title=Simultaneous Negative Phase and Group Velocity of Light in a Metamaterial |journal=Science |volume=312 |pages=892–894 |year=2006 |doi=10.1126/science.1126021 |pmid=16690860 |issue=5775 |bibcode = 2006Sci...312..892D |s2cid=29012046 |url=https://publikationen.bibliothek.kit.edu/1000010972/901157 }}</ref><ref name="BLSB06">{{Citation |first1=Matthew S. |last1=Bigelow |first2=Nick N. |last2=Lepeshkin |first3=Heedeuk |last3=Shin |first4=Robert W. |last4=Boyd |title=Propagation of a smooth and discontinuous pulses through materials with very large or very small group velocities |journal=Journal of Physics: Condensed Matter |volume=18 |pages=3117–3126 |year=2006 |doi=10.1088/0953-8984/18/11/017 |issue=11 |bibcode = 2006JPCM...18.3117B |s2cid=38556364 }}</ref><ref name="GSBKB06">{{Citation |first1=George M. |last1=Gehring |first2=Aaron |last2=Schweinsberg |first3=Christopher |last3=Barsi |first4=Natalie |last4=Kostinski |first5=Robert W. |last5=Boyd |title=Observation of a Backward Pulse Propagation Through a Medium with a Negative Group Velocity |journal=Science |volume=312 |pages=895–897 |year=2006 |doi=10.1126/science.1124524 |pmid=16690861 |issue=5775 |bibcode = 2006Sci...312..895G |s2cid=28800603 }}</ref><ref name="SLBBJ05">{{Citation |first1=A. |last1=Schweinsberg |first2=N. N. |last2=Lepeshkin |first3=M.S. |last3=Bigelow |first4=R. W. |last4=Boyd |first5=S. |last5=Jarabo |title=Observation of superluminal and slow light propagation in erbium-doped optical fiber |journal=Europhysics Letters |volume=73 |issue=2 |pages=218–224 |year=2005 |doi=10.1209/epl/i2005-10371-0 |bibcode=2006EL.....73..218S |url=http://www.hep.princeton.edu/%7Emcdonald/examples/optics/schweinsberg_epl_73_218_06.pdf |citeseerx=10.1.1.205.5564 |s2cid=250852270 }}{{Dead link|date=June 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>