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The idea of the material Maxwell equation is almost clear. But I'm curious about the idea that except for material equation the pure Maxwell equation should work, but in harder sense: more currents and charges.

There are plenty of vacuum in solid body, so, I think, that there should be some precursors of electro-magnetic waves that propagates through the body: $v = c/n$ the speed of wave in body, but part of wave propagates in vacuum with the speed of $c$. And for any frequency some part of amplitude would be observed much earlier.

Is there some theory behind this and does this phenomena is observed?

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$n$ depends on the wave frequency. For high frequencies $n\rightarrow 1$. So for a general electromagnetic field each harmonic propagates with its own speed.

EDIT: In order to speak of a front propagation, you have to have a whole spectrum of harmonics that exist always and everywhere. Each harmonic does not have a front in space, it is their superposition who has. In other words, a front "spreads out" due to frequency dispersion of waves in material.

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Yes, but I mean that for any wave frequency some of it would be observed much earlier. –  m0nhawk Nov 23 '12 at 20:23
    
@m0nhawk: In order to speak of a front propagation, you have to have a whole spectrum of harmonics that exist always and everywhere. Each harmonic does not have a front in space, it is their superposition who has. In other words, a front "spreads out" due to frequency dispersion of waves in material. –  Vladimir Kalitvianski Nov 23 '12 at 20:31
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