OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 19 — Sep. 14, 2009
  • pp: 16710–16715

Complex 2D photonic crystals with analogue local symmetry as 12-fold quasicrystals

Shih-Chieh Cheng, Xuelian Zhu, and Shu Yang  »View Author Affiliations


Optics Express, Vol. 17, Issue 19, pp. 16710-16715 (2009)
http://dx.doi.org/10.1364/OE.17.016710


View Full Text Article

Enhanced HTML    Acrobat PDF (1752 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We construct fourteen complex periodic two-dimensional (2D) photonic structures with different structural symmetries by arranging the small portions of a 12-fold quasicrystal on square or hexagonal lattices. The corresponding reciprocal lattices confirm that all of them demonstrate the 12-fold-like characteristics due to the analogue short-range arrangements. We then investigate their photonic bandgap properties at different dielectric contrast levels (dielectric rods in air background). Our results suggest that all structures possess analogue transverse magnetic (TM) gaps in both Si and glass photonic crystals due to the similarity of their local geometries. However, the arrangements of the basic elements, total symmetries, and the coupling between the local and the lattice symmetries have greater impact on the glass photonic crystals, which show much larger deviation of gap sizes from different structures. Furthermore, we find that the minimal dielectric contrast to achieve the TM gap in the complex lattices (dielectric-in-air) can be as low as ε = 1.44, whereas the inverse structures may open a 2D complete gap in silicon nitride (ε = 4.1).

© 2009 OSA

OCIS Codes
(160.5293) Materials : Photonic bandgap materials
(160.5298) Materials : Photonic crystals
(080.6755) Geometric optics : Systems with special symmetry

ToC Category:
Photonic Crystals

History
Original Manuscript: June 15, 2009
Revised Manuscript: August 21, 2009
Manuscript Accepted: August 31, 2009
Published: September 3, 2009

Citation
Shih-Chieh Cheng, Xuelian Zhu, and Shu Yang, "Complex 2D photonic crystals with analogue local symmetry as 12-fold quasicrystals," Opt. Express 17, 16710-16715 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16710


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. D. Joannopoulos, S. G. Johnson, R. D. Meade, and J. N. Winn, Photonic crystals (Princeton University Press, 2008).
  2. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998). [CrossRef]
  3. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000). [CrossRef] [PubMed]
  4. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003). [CrossRef]
  5. W. N. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005). [CrossRef] [PubMed]
  6. Y. Yang and G. P. Wang, “Two-dimensional photonic crystals constructed with a portion of photonic quasicrystals,” Opt. Express 15(10), 5991–5996 (2007). [CrossRef] [PubMed]
  7. Y. Yang, Q. Z. Li, and G. P. Wang, “Fabrication of periodic complex photonic crystals constructed with a portion of photonic quasicrystals by interference lithography,” Appl. Phys. Lett. 93(6), 061112 (2008). [CrossRef]
  8. M. Baake, R. Klitzing, and M. Schlottmann, “Fractally shaped acceptance domains of quasiperiodic square-triangular tilings with dodecaonal symmetry,” Physica A 191(1-4), 554–558 (1992). [CrossRef]
  9. A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006). [CrossRef] [PubMed]
  10. P. Stampfli, “A dodecagonal quasiperiodic lattice in two dimensions,” Helv. Phys. Acta 59, 1260–1263 (1986).
  11. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed]
  12. X. D. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63(8), 081105 (2001). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited