On the role of symmetries in the theory of photonic crystals
de Nittis G, Lein M (2014)
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2014
Journal
Book Volume: 350
Pages Range: 568-587
DOI: 10.1016/j.aop.2014.07.032
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.
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APA:
de Nittis, G., & Lein, M. (2014). On the role of symmetries in the theory of photonic crystals. Annals of Physics, 350, 568-587. https://dx.doi.org/10.1016/j.aop.2014.07.032
MLA:
de Nittis, Giuseppe, and Max Lein. "On the role of symmetries in the theory of photonic crystals." Annals of Physics 350 (2014): 568-587.
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