Abstract
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 language | English |
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Pages (from-to) | 568-587 |
Number of pages | 20 |
Journal | Annals of Physics |
Volume | 350 |
DOIs | |
Publication status | Published - 2014 Nov 1 |
Externally published | Yes |
Keywords
- 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)