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I'm studying laser-matter interactions and was wondering: Is there any physical meaning to a non-vanishing polarization field with non-trivial constitutive relation but vanishing divergence? (By non-trivial I mean the constitutive equation does not stipulate that the polarization and electric fields are directly proportional) Is this a model for anything? Could you think of a situation where one starts out (at a given time) with a non-zero, divergence-free polarization field (and lets it evolve according to the MW equations and the constitutive equation)?

From what I have seen so far in textbooks a divergence-free polarization field implies that the density of bound charges in the dielectric is zero. Can that still be considered a dielectric? Does such a thing ever arise, and if yes, in what context?

Thanks a lot for your help...Cliowa