The perturbed maxwell operator as pseudodifferential operator

Giuseppe De Nittis, Max Lein

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)63-101
Number of pages39
JournalDocumenta Mathematica
Volume19
Issue number1
Publication statusPublished - 2014

Keywords

  • Bloch-Floquet theory
  • Maxwell equations
  • Maxwell operator
  • Pseudodifferential operators

ASJC Scopus subject areas

  • Mathematics(all)

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