On the role of symmetries in the theory of photonic crystals

Giuseppe De Nittis, Max Lein

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


We discuss the role of the symmetries in photonic crystals and classify them according to the Cartan-Altland-Zirnbauer scheme. Of particular importance are complex conjugation C and time-reversal T, but we identify also other significant symmetries. Borrowing the jargon of the classification theory of topological insulators, we show that C is a "particle-hole-type symmetry" rather than a "time-reversal symmetry" if one considers the Maxwell operator in the first-order formalism where the dynamical Maxwell equations can be rewritten as a Schrödinger equation; The symmetry which implements physical time-reversal is a "chiral-type symmetry". We justify by an analysis of the band structure why the first-order formalism seems to be more advantageous than the second-order formalism. Moreover, based on the Schrödinger formalism, we introduce a class of effective (tight-binding) models called Maxwell-Harper operators. Some considerations about the breaking of the "particle-hole-type symmetry" in the case of gyrotropic crystals are added at the end of this paper.

Original languageEnglish
Pages (from-to)568-587
Number of pages20
JournalAnnals of Physics
Publication statusPublished - 2014 Nov 1
Externally publishedYes


  • Cartan-Altland-Zirnbauer classification
  • Complex electromagnetic fields
  • Gyrotropic effect
  • Harper-Maxwell operator
  • Photonic crystal
  • Photonic topological insulators

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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