[Tazerenix]

The actual answer is the assumptions which define a self-propagating wave do not apply once the wave leaves a vacuum. When it becomes incident onto some medium, due to the coupling of electrons within the medium to the electromagnetic field, the pure electromagnetic wave gets transformed into a phonon, which is a combination of electromagnetic and mechanical oscillation within the medium (and therefore has speed <c, depending on the particular properties of the medium). When the phonon subsequently leaves the system, those traveling oscillations induce a new self-propagating wave on the other side, sending the light on its way as usual.

[cbolton]

Is this more than a change of terminology? Is it wrong to say that the electromagnetic oscillation is still there in the medium but coupled to a mechanical oscillation, and the coupled system is called a phonon? (I mean there's still an electromagnetic field in the material, it still gets excited, it's not replaced with a new field that fuses the EM and matter fields). Then the question is by which process exactly is the electromagnetic oscillation slowed down, and is the answer much different from the explanations above? I.e. the moving charges due to the mechanical oscillation add perturbations to the EM field such that the net effect is a slower propagating wave.

[MichaelZuo]

What does it mean for something to oscillate electromagnetically and mechanically simultaneously?

Doesn't mechanical oscillation already occupy all three spatial dimensions plus a time dimension?

[zmgsabst]

The phonon oscillates both the electrons and the EM field.

A photon is EM only.

So you’re correct that it occupies all four dimensions, but we’re discussing an excitation in one field (photon) changing to an oscillation in multiple (phonon) and then back to only one field (photon).