The Perturbed Maxwell Operator as Pseudodifferential Operator
Abstract
As a first step to deriving effective dynamics and ray optics, 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 M_0. In particular, we characterize the behavior of M_0 and the physical initial states at small crystal momenta $k$ and small frequencies \omega. Among other things, we prove that generically the band spectrum is symmetric with respect to inversions at k = 0 and that there are exactly 4 ground state bands with approximately linear dispersion near k = 0.
 Publication:

arXiv eprints
 Pub Date:
 February 2013
 DOI:
 10.48550/arXiv.1302.1956
 arXiv:
 arXiv:1302.1956
 Bibcode:
 2013arXiv1302.1956D
 Keywords:

 Mathematical Physics;
 35S05;
 35P99;
 35Q60;
 35Q61;
 78A48
 EPrint:
 41 pages, rewritten introduction, generalized results to include electric permittivity and magnetic permeability tensors