Can the phase velocity of light exceed c in a material whose index of refraction is less than 1? I’m sure no signal can be sent faster than c, but, nonetheless, even the phase velocity being greater than c is a surprise to me.
Absolutely. Reference Jackson (in my case, 3rd ed, Sect. 7.8), where n(k) is the index of refraction:
“The phase velocity is c/n(k) and is greater or smaller than c depending on whether n(k) is smaller or larger than unity. For most optical wavelengths n(k) is greater than unity in almost all substances.”
I admit I find this surprising.
Thanks g8rguy
I’m sure this is some kind of phase shift phenomenon but I either forgot about it or never learned it.
In fact I’m having problems visualizing just what’s going on.
P.S. Jackson is incomprehensible.
Well, I left my copy of Jackson at work, but if I understood him correctly, it was some sort of phase shifting phenomena in wave packets. Or some such.
But as you said, Jackson is incomprehensible, explaining my fear and loathing of E&M.
I don’t know if this staff report will help or not.
I’m not sure if this answers the question or not. I think a wave packet is a group effect not a phase effect. I’m aware of the apparent faster than light propagation of a wave packet in an anomalous material but I was referring to the phase velocity.
You get phase advance dielectrics when the behaviour of the medium is more complicated than the simple charge separation model from electrostatics. In what we think of as “normal” dielectrics, the polarization of, say, a molecule, is in-phase with the electric field. If the molecule has some resonant frequency, and your wave is near that, the behavior isn’t as simple.
It might be easier to think of an artificial dielectric made using thin wires oriented parallel to the electric field. If the wire length is short compared to a wavelength, the charge just follows the incident electric field. When the wires are around a half-wavelength long, they’re near-resonant, and the relative phase of the charge and current varies rapidly with length. For some frequencies near resonance, the dipole charge distribution can be opposite what you’d get from electrostatics.
It’s more complicated than I just described, because the effects of the current on the magnetic field can’t be neglected. The main point is you aren’t in a simple quasi-static regime anymore.
But I learned something, so “Thanks”[list][list][list]:o