# Controllable faster-than-light phase velocity

This is not another question about faster-than-light travel or superluminal communication. I totally appreciate the speed limit capped by physical laws (or theories.)

Just curious, since there is no limit for phase velocity, is there any way to generate a wave with controllable phase velocity higher than speed of light?

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@skywaddler-- see my question-- What does Lijun Wang's experiment about supraluminal speed of light in a medium mean? –  Gordon Feb 18 '11 at 7:35

Yes. The phase velocity $v_\phi$ of light in a medium is equal to $c_0/n$, where $c_0$ is the speed of light in vacuum, and n is the material's refractive index. The index is usually greater than 1, so normally this doesn't happen; but occasionally it is smaller for certain frequencies of light (Wikipedia gives the examples of X-rays and frequencies near absorption resonances), giving a phase velocity greater than $c_0$.

It is possible to change the refractive index of a material: see for example the Pockels effect and the Kerr effect. I don't know if this means that it would actually be possible to build a material with a "phase velocity knob" though, as suggested in the comment below.

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OP wanted to know if you could control the phase velocity. I.E. build a "phase velocity dial" to turn it up and down at will, I think. –  Mark Eichenlaub Dec 22 '10 at 9:22
@Mark Eichenlaub, I understood the question to be whether you could design a material with any particular phase velocity that you wanted. But see the edit to my answer. –  ptomato Dec 22 '10 at 11:06
Interesting, thanks. –  Mark Eichenlaub Dec 22 '10 at 11:28
Doesn't the tunnel effect provide an in principle tunable mechanism? –  Raskolnikov Dec 22 '10 at 13:30

The phase velocity of light in a fully ionized plasma is strictly superluminal; see equation 1156 of Fitzpatrick. Like all media in which the speed of light is not $c$, plasmas are dispersive, but the phase velocity is still superluminal over a large bandwidth (from the plasma frequency on up).

The phase velocity can be tuned by tuning the density of the plasma. My old group used this denstiy-tuned index of refraction to make transient micro-optics out of plasma.

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