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Title: On the role of symmetries in the theory of photonic crystals

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.
Authors:
 [1] ;  [2]
  1. Department Mathematik, Universität Erlangen-Nürnberg, Cauerstrasse 11, D-91058 Erlangen (Germany)
  2. University of Toronto and Fields Institute, Bahen Centre, Department of Mathematics, 40 St. George Street, Toronto, ON M5S 2E4 (Canada)
Publication Date:
OSTI Identifier:
22403452
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 350; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHIRALITY; CRYSTALS; ELECTROMAGNETIC FIELDS; MAXWELL EQUATIONS; PHOTONS; SCHROEDINGER EQUATION; SYMMETRY; T INVARIANCE; TOPOLOGY