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Is it possible to have an index of refraction, $n < 1$, giving the "illusion" of a speed greater than $c$.

As far as I understand it, is only the phase-velocity (which does not carry any information) that exceeds the speed of light.

But what I would really like to know is, under what conditions it is possible to have $n<1$?

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    $\begingroup$ You'll need some unobtanium crystals. Other than n= -1 (mirror reflection) and n<-1 for certain specially created optical materials, n>=1 is required by definition, i.e. n=1 in a vacuum. $\endgroup$
    – Carl Witthoft
    Commented Jun 6, 2015 at 13:56
  • $\begingroup$ If I recall correctly, there are meta-materials that can mimic n<1, but I am not terribly familiar with the details & don't have much to give beyond that. $\endgroup$
    – Kyle Kanos
    Commented Jun 6, 2015 at 14:17
  • $\begingroup$ en.m.wikipedia.org/wiki/Negative_refraction...I wonder is this what you mean. $\endgroup$
    – user81619
    Commented Jun 6, 2015 at 14:18
  • $\begingroup$ I am talking about 0<n<1. $\endgroup$
    – Nillo
    Commented Jun 6, 2015 at 14:19
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    $\begingroup$ This can occur close to resonance frequencies, for absorbing media, in plasmas, and for X-rays wiki $\endgroup$
    – user46925
    Commented Jun 6, 2015 at 14:22

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I have been reaserching some more, and what I have found is something about waves in dispersive media. (The wave speed depends on the frequency of the wave). Source: (http://www.acs.psu.edu/drussell/Demos/Dispersion/dispersion.html) Apparently when the wave is traveling with a frequency close to the resonans frequency $n$ gets smaller than $1$. But only the group velocity exceeds $c$.

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