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Wyckoff positions and the expression of polarization singularities in photonic crystals
Author(s) -
Jeffrey F. Wheeldon,
Henry Schriemer
Publication year - 2009
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.17.002111
Subject(s) - physics , polarization (electrochemistry) , gravitational singularity , homogeneous space , disclination , character table , rotational symmetry , symmetry group , photonic crystal , local symmetry , quantum mechanics , optics , geometry , liquid crystal , character (mathematics) , mathematics , chemistry , mechanics
We reveal the fundamental relation between linear photonic crystal symmetries and the local polarization states of its Bloch modes, in particular the location and nature of polarization singularities as established by rigorous group theoretic analysis, encompassing the full system symmetry. This is illustrated with the fundamental transverse electric mode of a two-dimensional hexagonal photonic crystal, in the vanishing contrast limit and at the K point. For general Wyckoff positions within the fundamental domain, the transformation of a local polarization state is determined by the nature of the symmetry operations that map to members of its crystallographic orbit. In particular, the site symmetries that correspond to specific Wyckoff positions constrain the local polarization state to singular character--circular, linear or disclination. Moreover, through the application of a local symmetry transformation relation, and the group's character table, the precise natures of the singularities may be determined from self-consistency arguments.

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