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 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 respect to inversions at k = 0 and that there are exactly 4 ground state bands with approximately linear dispersion near k = 0.
Original language | English |
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Pages (from-to) | 63-101 |
Number of pages | 39 |
Journal | Documenta Mathematica |
Volume | 19 |
Issue number | 1 |
Publication status | Published - 2014 |
Externally published | Yes |
Keywords
- Bloch-Floquet theory
- Maxwell equations
- Maxwell operator
- Pseudodifferential operators
ASJC Scopus subject areas
- Mathematics(all)