neobaud said:
So what do you think? Will any part of the original light exit the medium at time d/c? Dale seems to think it won't (or at least a measurable amount) and everyone else seems uncommitted. Maybe it's too complicated to know for sure without a really good experiment?
The "wave front" propagates with the speed of light in standard dispersion theory (no matter whether you use a crude classical "Drude-like model" or quantum-mechanical or even full-fledged in-medium relativsitic QED). That's because the causality constraints are very robust, i.e., all you need are the analytical properties of the propagator, and for a hyperbolic differential equation as the (relativistic) wave equation that implies Einstein causality.
All this is well-known since 1907, when Sommerfeld answered the question by Willy Wien about waves in the frequency regime of "anomalous dispersion" of a medium, i.e., close to a resonance of the bound charged particles making up the dielectric. In such a region both the phase velocity and the group velocity are >c, which however does not mean a violation of relativistic causality, because both velocities/speeds do not describe a causal signal propagation velocity/speed. The phase velocity simply describes the dispersion relation between ##\omega## and ##\vec{k}## for a plane-wave solution, i.e., a solution, which describes and em. wave field that's "switched on" for a very long time and the medium is oscillating with the frequency of the em. wave, i.e., all transient states have damped out.
The group velocity as the velocity with which the "center" of a wave packet moves makes only sense when the stationary-phase approximation of the corresponding Fourier integral from ##\vec{k}## to position space is applicable, which it is not in the region of anomalous dispersion.
As has been shown by Sommerfeld in 1907 by using an elegant analytical argument (theorem of residues) one can show that for arbitrary waves with compact spatial support the boundary of the support moves with the speed of light in vacuum inside the medium. That's understandable, because the medium can only be disturbed by and react to the incoming wave when this wave reaches it. Only then the medium emits its own electromagnetic waves which superimposes with the incoming wave.
In 1914 these considerations have been worked out in 2 famous papers by Sommerfeld and Brillouin in great detail, where the onset of the propagation of the wave front in the medium has been described reaching the "stationary state" only after some time, and particularly without ever violating relativistic causality.
As already shown by Sommerfeld in 1907, this is due to pretty weak analytical properties related to the choice of the retarded Green's function. This in turn has been worked out in more detail, also in connection with more general wave equations and in connection with quantum (field) theory by Kramers and Kronig. These socalled Kramers-Kronig relations can be found in any textbook dealing with wave phenomena. The QFT analogue is the celebrated Källen-Lehmann representation of the (interacting) propagator of various relativistic wave fields and their generalizations for finite temperature and density in the many-body context.