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Optics Letters

Optics Letters


  • Editor: Alan E. Willner
  • Vol. 34, Iss. 18 — Sep. 15, 2009
  • pp: 2805–2807

Low-contrast bandgaps of a planar parabolic spiral lattice

Michael E. Pollard and Gregory J. Parker  »View Author Affiliations

Optics Letters, Vol. 34, Issue 18, pp. 2805-2807 (2009)

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We show that a planar aperiodic lattice, mimicking the appearance of a sunflower, supports photonic bandgaps for weak dielectric contrast. The pattern’s high orientational order and spatially uniform modal pitch yields an isotropic Fourier space. A 2D structure of cylinders ( ϵ = 2 ) in air possesses a wide 21% TM bandgap, versus 5.6% for a sixfold lattice or 14% for a 12-fold fractal tiling. The isotropic gap frequencies imply flat bands, and thus application in nonlinear optics and low threshold lasers, where a reduced group velocity in all directions may be desired.

© 2009 Optical Society of America

OCIS Codes
(220.2740) Optical design and fabrication : Geometric optical design
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(160.5293) Materials : Photonic bandgap materials

ToC Category:

Original Manuscript: May 28, 2009
Revised Manuscript: August 11, 2009
Manuscript Accepted: August 13, 2009
Published: September 10, 2009

Michael E. Pollard and Gregory J. Parker, "Low-contrast bandgaps of a planar parabolic spiral lattice," Opt. Lett. 34, 2805-2807 (2009)

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton U. Press, 2008).
  2. M. C. Rechtsman, H.-C. Jeong, P. M. Chaikin, S. Torquato, and P. J. Steinhardt, Phys. Rev. Lett. 101, 073902 (2008). [CrossRef] [PubMed]
  3. W. Steurer and D. Sutter-Widmer, J. Phys. D 40, R229 (2007). [CrossRef]
  4. M. Senechal, Not. Am. Math. Soc. 53, 886 (2006).
  5. C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Band, and B. Sun, Appl. Phys. Lett. 75, 1848 (1999). [CrossRef]
  6. C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang, Phys. Rev. B 61, 10762 (2000). [CrossRef]
  7. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, Nature 404, 740 (2000). [CrossRef] [PubMed]
  8. K. Wang, S. David, A. Chelnokov, and J. M. Lourtioz, J. Mod. Opt. 50, 2095 (2003).
  9. R. V. Moody, D. Postnikoff, and N. Strungaru, Ann. Henri Poincare 7, 711 (2006). [CrossRef]
  10. F. Zolla, D. Felbacq, and B. Guizal, Opt. Commun. 148, 6 (1998). [CrossRef]
  11. G. J. Parker, M. D. B. Charlton, M. E. Zoorob, J. J. Baumberg, M. C. Netti, and T. Lee, Philos. Trans. R. Soc. London Ser. A 364, 189 (2006). [CrossRef]
  12. A. Agrawal, N. Kejalakshmy, J. Chen, B. M. A. Rahman, and K. T. V. Grattan, Opt. Lett. 33, 2716 (2008). [CrossRef] [PubMed]
  13. H. Vogel, Math. Biosci. 44, 179 (1979). [CrossRef]
  14. J. Zarbakhsh, F. Hagmann, S. F. Mingaleev, K. Busch, and K. Kingerl, Appl. Phys. Lett. 84, 4687 (2004). [CrossRef]
  15. B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari, and K. S. Thomas, J. Mater. Sci. Mater. Electron. 14, 413 (2003). [CrossRef]
  16. M. Soljačić and J. D. Joannopoulos, Nature Mater. 3, 211 (2004). [CrossRef]

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