When we have an electric field interacting with a dielectric medium, the equation governing the macroscopic polarization is given by $\vec{P} = \alpha\vec{E}$. This equation seems to also be used when the field is due to an EM wave, so the equation might look like $\vec{E}(z,t) = E_0\sin(kz-wt)$. If we look at the example of a rectangular slab, it seems like if we inspect the displacement of electrons at different z values over a wavelength of the wave, we will have dipole moments that average to 0. For example, at $z=\pi/(2k), t=0$ the electric field will have amplitude $E_0$ but at $z=\pi/k, t = 0$ the field will have amplitude $-E_0$, so the dipole moments at those two places will always cancel. With this in mind, how do we arrive at a net dipole moment that isn't negligible for most solids, assuming that the only net dipole moment will result from some portion of the dielectric not being in a full period of the EM wave?
This question first occurred to me because someone mentioned to me that for EM waves incident on a plasma or certain solids, the scattered waves will all be in the same direction as the incident wave (or favor a certain direction) because of the phase interference for the free electrons (assuming the ions are fixed). I am not sure why the same effect wouldn't occur in a dielectric, or if I am misunderstanding the effect for plasmas in general. I would appreciate any clarifications or references to materials I can read.
