Wannier functions of a one-dimensional photonic crystal with inversion symmetry

Abstract

The maximally localized magnetic and electric Wannier functions of a one-dimensional photonic crystal with inversion symmetry are investigated. The calculated Wannier functions are real and either symmetric or anti-symmetric about an inversion centre of the crystal. The magnetic and electric Wannier functions of each band are centred at the same point, but they have opposite inversion symmetries. Interestingly, for the first band, they show different kinds of asymptotic behaviour. In turn, for higher bands, both types of Wannier functions decay in the same way. When dealing with localized electromagnetic modes in a perturbed one-dimensional crystal, the knowledge of these properties should help to build an appropriate basis set of Wannier functions.