thaiqi said:
It is said that there are cases where the phase velocity is larger than c. Why not consider it is the speed of the wave front in postulate 2 rather than phase velocity?
That's the point of the famous papers by Sommerfeld and Brillouin. In regions of anomalous dispersion the quantity you can formally calculate as ##v_{\text{g}}## can be larger than ##c##, it can be even pointing in the opposite direction from what you'd expect. The reason is that this quantity in the region of anomalous dispersion, i.e., around a resonance frequency of the matter, has no longer the physical meaning of some wave-propagation velocity. In regions of normal dispersion it describes how a wave packet moves in the sense of e.g., the maximum of the wave packet moves, while the packet's overall shape changes only very slowly. In regions of anomalous dispersion the wave packet is rather deforming quite quickly, and you cannot make sense of how to define a center or peak of the packet anymore. That's why the group velocity looses its physical meaning in this case, because the corresponding approximation doesn't apply anymore.
The only thing that always must be ##\leq c## is the front velocity, and this is guaranteed by the relativistic in-medium Maxwell equations as long as the model for the medium is causal, and then the function theory (theorem of residues) takes care of the causality of the wave propagation. In the usual simple Drude models (which can also be motivated by in-medium QED calculations!) the front velocity is precisely ##c##.
The reason is very intuitive: If the incoming wave first arrives at a point in the medium, the medium has not yet reacted to the corresponding em. field and also not emitted em. waves itself (the total em. field is the incoming field + the field emitted by the moving charges of the medium). That's why you can say, in the very first moment, the em. field is unaffected and moves as if would propagate in vacuo, i.e., with the vacuum velocity of light. But then you soon get quite fascinating transient states, the socalled Sommerfeld precursor followed by the Brilloui precursor.
The treatment of a semifinite wavetrain entering a dieelectric in Sommerfeld's way is among the most beautiful and elegant applications of dispersion theory, mathematically all based on complex-function theory applied to Fourier transformations. I highly recommend to read the treatment in
A. Sommerfeld, Lectures on Theoretical Physics vol. IV (optics)
It's boiled down to there to the most simple treatment possible. I'm not sure whether the two Annalen papers are translated to English, but I guess so, because they are real gems of the classical-field-theoretical literature.