Abstract

As a first step to deriving effective dynamics and ray op- tics, we prove that the perturbed periodic Maxwell operator in d = 3 can be seen as a pseudodifferential operator. This necessitates a better understanding of the periodic Maxwell operator M0. In particular, we characterize the behavior of M0 and the physical initial states at small crystal momenta k and small frequencies. Among other things, we prove that generically the band spectrum is symmetric with re- spect to inversions at k = 0 and that there are exactly 4 ground state bands with approximately linear dispersion near k = 0.