Why don't dielectric materials radiate?

[nonequilibrium]

Say we have an electromagnetic wave propagating inside a dielectric material. Of course physically this material will radiate, due to the little electrons being excited by the wave (their wiggling is also the physical cause of the $$\epsilon \neq \epsilon_0$$), and oscillating dipoles radiate. And of course in usual situations this can and should be ignored, but my question is something else: how come in simple treatments of dielectric materials, there is no radiation, none at all? For example, in my book of Griffiths, in chapter 9 we deduce (the properties of) the reflection and refraction of light on a dielectric surface, but it turns out the energy going in (in the initial light beam), is the same as the energy in the reflected beam + the transmitted beam. In other words, the dielectric isn't radiating any energy. This would not seem weird if we had made that assumption beforehand, but it seems that we never made such an approximation. So even though usually negligible, shouldn't there be a certain amount of radiation due to the oscillating dipoles?

Apparently the equations of Maxwell for matter don't account for the radiation caused by the time-variation of $$\vec P \quad \textrm{ in } \quad \vec D = \epsilon_0 \vec E + \vec P,$$
is this correct? (if not correct, how do you explain the first paragraph?)

 

[dr. candy]

very good.

 

[nonequilibrium]

Another option is that the radiation of the dipoles is incorporated into the treatment, but somehow the dipole-radiation is contributing to the transmitted and/or reflected light beams, instead of floating away on its own right.

This would be, physically speaking, very unevident (no?), but I suppose it's perfectly possible.

 

[sophiecentaur]

It seems to me that you have described it exactly. This 're-radiated' energy will be appropriately phased from each part of the dielectric to constitute the (classically derived) transmitted and reflected 'rays'. This is what Huygen's construction does, btw.

 

[Antiphon]

Polarization currents radiate. It's just that for a dielectric and planewaves the radiation is coherent and all goes in the direction of the transmitted and reflected waves.

Edit: missed the above post. Concur fully with it.

 

[nonequilibrium]

fascinating!

 

[Antiphon]

Also this; look at a cloud. You're looking at the P vector.

 

[nonequilibrium]

Haha, touché.

But the question wasn't really "do dielectrics radiate or not?" (just chose that as a captive title), I knew they had to, but the question was mainly "how come I don't see the radiation in the treatment of monochromatic waves hitting a dielectric", the answer to which is now that it is there but it's coherent and a part of the transmitted and reflected waves.

I can't find a sensible physical reason for why it should be so; there probably isn't. Sometimes the math is enough :)

Thank you both

 

[sophiecentaur]

I can't find a sensible physical reason for why it should be so; there probably isn't. Sometimes the math is enough :)

Thank you both

Isn't the reason simply because the induced polarisation of the molecules in the dielectric is coherent across the interface and so the re-radiated waves will also be coherent. This is the same argument as why the reflection from a conductor follows 'ray' and diffraction theory so closely.