Maximally localized Wannier functions for photonic lattices

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Abstract
A method is described for the computation of the generalized Wannier functions corresponding to a composite group of electromagnetic bands in a photonic crystal. The Wannier functions are optimally localized, in that they have minimum real-space spread, defined as the average over the set of the second moment of the functions. The mathematical approach follows that developed by N. Marzari and D. Vanderbilt [Phys. Rev. B 56, 12 847 (1997)] to obtain similarly well-localized Wannier functions for electrons in crystalline solids. Results are presented for the lowest few TE and TM bands in two-dimensional photonic crystals consisting of square and triangular lattices of holes and rods.