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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 4 — Feb. 16, 2009
  • pp: 2111–2121

Wyckoff positions and the expression of polarization singularities in photonic crystals

Jeffrey F. Wheeldon and Henry Schriemer  »View Author Affiliations


Optics Express, Vol. 17, Issue 4, pp. 2111-2121 (2009)
http://dx.doi.org/10.1364/OE.17.002111


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Abstract

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.

© 2009 Optical Society of America

OCIS Codes
(160.4760) Materials : Optical properties
(230.3990) Optical devices : Micro-optical devices
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Photonic Crystals

History
Original Manuscript: October 21, 2008
Revised Manuscript: January 12, 2009
Manuscript Accepted: January 13, 2009
Published: February 2, 2009

Citation
Jeffrey F. Wheeldon and Henry Schriemer, "Wyckoff positions and the expression of polarization singularities in photonic crystals," Opt. Express 17, 2111-2121 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-4-2111


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References

  1. J. V. Hajnal, "Singularities in the transverse fields of electromagnetic waves. I. Theory," Proc. R. Soc. Lond. A 414, 433-446 (1987). [CrossRef]
  2. M. V. Berry and M. R. Dennis, "Polarization singularities in isotropic random vector waves," Proc. R. Soc. Lond. A 457, 141-155 (2001). [CrossRef]
  3. I. Freund, "Polarization singularities in optical lattices," Opt. Let. 29, 875-877 (2004). [CrossRef]
  4. O. Toader, S. John, and K. Busch, "Optical trapping, Field enhancement and Laser cooling in photonic crystals," Opt. Express 8, 217-222 (2001). [CrossRef] [PubMed]
  5. M. Born and E. Wolf, Principles of optics: Electromagnetic theory of propagation, interference and diffraction of light, 7th edition (Cambridge, Cambridge University Press, 2003). [PubMed]
  6. J. F. Nye, Natural focusing and fine structure of light (Bath, IOP Publishing Ltd, 1999).
  7. J. F. Wheeldon, T. Hall and H. Schriemer, "Symmetry constraints and the existence of Bloch mode vortices in linear photonic crystals", Opt. Express 15, 3531-3542 (2007). [CrossRef] [PubMed]
  8. K. Sakoda, Optical Properties of Photonic Crystals (Springer, New York, 2005).
  9. M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964).
  10. J. D. Jackson, Classical Electrodynamics, 3rd ed. (USA, John Wiley and Sons, Inc., 1999).
  11. J. F. Wheeldon and H. Schriemer, "Symmetry and the local field response in photonic crystals," to appear in Proceedings of the NATO-ASI in Laser Control & Monitoring in New Materials, Biomedicine, Environment Security and Defense, Ottawa (Canada), November 24 - December 5 (2008),
  12. R. A. Evarestov and V. P. Smirnov, Site symmetry in crystals theory and applications, Springer series in solid-state sciences 108, (Springer-Verlag, New York, 1993).
  13. J. Wheeldon, Group Theoretic Expressions of Optical Singularities in Photonic Crystals (PhD Thesis, University of Ottawa, Ottawa, Canada, 2008).

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