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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 6 — Mar. 19, 2007
  • pp: 3531–3542

Symmetry constraints and the existence of Bloch mode vortices in linear photonic crystals

Jeffrey F. Wheeldon, Trevor Hall, and Henry Schriemer  »View Author Affiliations

Optics Express, Vol. 15, Issue 6, pp. 3531-3542 (2007)

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Modal phase singularities are identified in linear photonic crystals and the vortex state is explored in detail. Using group theory and phasor geometry, in the vanishing contrast limit, the modal symmetry requirements for the existence of phase singularities are determined. The vortex states are the partner functions of the symmetry groups, and hence one has a qualitative map of these modes in reciprocal space. We find that modes of even rotational symmetry are unable to form vortex states, while modes of odd rotational symmetry may form vortex states. The latter can be further classified into symmetry and accidental vortices. The insights gained using the vanishing contrast approximation are augmented by numerically solving the Maxwell’s equations for the high dielectric lattice forms using the Finite Element method; the general symmetry constraints are confirmed. In addition, symmetry vortices are found to demonstrate form and locational stability over large changes in dielectric contrast, whereas this is not so for the accidental vortices, which are more sensitive to such changes.

© 2007 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

Original Manuscript: January 30, 2007
Revised Manuscript: February 23, 2007
Manuscript Accepted: March 5, 2007
Published: March 19, 2007

Jeffrey F. Wheeldon, Trevor Hall, and Henry Schriemer, "Symmetry constraints and the existence of Bloch mode vortices in linear photonic crystals," Opt. Express 15, 3531-3542 (2007)

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  1. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. Lond. A 336, 165-190 (1974). [CrossRef]
  2. J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, "Angular momentum of optical vortex arrays," Opt. Express 14, 938-949 (2006). [CrossRef] [PubMed]
  3. D. G. Grier, "A revolution in optical manipulation," Nature 424, 21-27 (2006).
  4. K. Ladavac and D. G. Grier, "Micro optomechanical pumps assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004). [CrossRef] [PubMed]
  5. T. Sondergaard and K. H. Dridi, "Energy flow in photonic crystal waveguides," Phys Rev. B 61, 15688-15695 (2000). [CrossRef]
  6. K. H. Dridi, "Mode dispersion and photonic storage in planar defects within Bragg stacks of photonic crystal stabs," J. Opt. Soc. Am. B 21, 522-530 (2004). [CrossRef]
  7. A. Ferrando, M. Zacares, and M. Garcia-March, "Vorticity cutoff in Nonlinear Photonic Crystals," Phys. Rev. Lett. 95, 043901:1-4 (2005). [CrossRef]
  8. A. Ferrando, "Discrete-symmetry vortices as angular Bloch modes," Phys Rev. E 72, 036612: 1-6 (2005). [CrossRef]
  9. J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001). [CrossRef]
  10. K. O’Holleran, M. J. Padgett, and M. R. Dennis, "Topology of optical vortex lines formed by the interference of three, four, and five plane waves," Opt. Express 14, 3039-3044 (2006). [CrossRef] [PubMed]
  11. J. Yang and Z. H. Musslimnai, "Fundamental and vortex solitons in a two-dimensional optical lattice," Opt. Lett. 28, 2094-2096 (2003). [CrossRef] [PubMed]
  12. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992). [CrossRef] [PubMed]
  13. K. Sakoda, Optical Properties of Photonic Crystals (Springer, New York, 2005).
  14. M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill, New York, 1964).
  15. H. Schriemer, J. Wheeldon, and T. Hall, "Transport Properties of Nonlinear Photonic Crystals," in Photonic Applications in Devices and Communication Systems, Proc. SPIE 5971,10-18 (2005).
  16. M. V. Berry and M. R. Dennis "Quantum cores of optical phase singularities," J. Opt. A: Pure Appl. Opt. 6, S178-S180 (2004). [CrossRef]

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