OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 24, Iss. 10 — Oct. 1, 2007
  • pp: A84–A88

Photonic bandgaps and resonators in the one-stage Sierpinski gasket basis

D. W. Cooley and David R. Andersen  »View Author Affiliations


JOSA B, Vol. 24, Issue 10, pp. A84-A88 (2007)
http://dx.doi.org/10.1364/JOSAB.24.000A84


View Full Text Article

Enhanced HTML    Acrobat PDF (316 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

This paper discusses theoretical calculations of photonic bandgaps found in the one-stage Sierpinski gasket basis in the hexagonal lattice. Dielectric triangles and cylinders as well as air triangles and cylinders are investigated. All of these structures exhibited complete bandgaps, with the largest complete gap having 6.1% fractional width. The largest TE and TM polarization gaps were 23% and 40% fractional width, respectively. Resonators constructed from these crystals with a Q ten to 2000 times greater than resonators constructed using one cylinder in the hex lattice are demonstrated.

© 2007 Optical Society of America

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators

History
Original Manuscript: January 26, 2007
Revised Manuscript: May 9, 2007
Manuscript Accepted: May 18, 2007
Published: August 14, 2007

Virtual Issues
Photonic Metamaterials (2007) JOSA A

Citation
D. W. Cooley and David R. Andersen, "Photonic bandgaps and resonators in the one-stage Sierpinski gasket basis," J. Opt. Soc. Am. B 24, A84-A88 (2007)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-10-A84


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: putting a new twist on light," Nature (London) 386, 143-149 (1997). [CrossRef]
  4. C. Lopez, "Three-dimensional photonic bandgap materials: semiconductors for light," J. Opt. A 8, R1-R14 (2006). [CrossRef]
  5. R. Wang, X. H. Wang, B. Y. Gu, and G. Z. Yang, "Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals," J. Appl. Phys. 90, 4307-4313 (2001). [CrossRef]
  6. W. Kuang, Z. Hou, Y. Liu, and H. Li, "The bandgap of a photonic crystal with triangular dielectric rods in a honeycomb lattice," J. Opt. A, Pure Appl. Opt. 7, 525-528 (2005). [CrossRef]
  7. N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002). [CrossRef]
  8. R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, "Nature of the photonic band gap: some insights from a field analysis," J. Opt. Soc. Am. B 10, 328-332 (1993). [CrossRef]
  9. L. Li, Y. C. Xie, Y. Q. Wang, X. Y. Hu, Z. F. Feng, and B. Y. Cheng, "Absolute gap of two-dimensional fractal photonic structure," Chin. Phys. Lett. 20, 1767-1769 (2003). [CrossRef]
  10. K. Sakoda, S. Kirihara, Y. Miyamoto, M. W. Takeda, and K. Honda, "Light scattering and transmission spectra of the Menger sponge fractal," Appl. Phys. B: Photophys. Laser Chem. 81, 321-324 (2005). [CrossRef]
  11. Z. Liu, J. J. Xu, and Z. F. Lin, "Photonic band gaps in two-dimensional crystals with fractal structure," Chin. Phys. Lett. 20, 516-518 (2003). [CrossRef]
  12. P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, "Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency," Phys. Rev. B 54, 7837-7842 (1996). [CrossRef]
  13. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998). [CrossRef]
  14. M. Qiu and B. Jaskorzynska, "Design of a channel drop filter in a two-dimensional triangular photonic crystal," Appl. Phys. Lett. 83, 1074-1076 (2003). [CrossRef]
  15. Z. Wang and S. Fan, "Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines," Phys. Rev. E 68, 066616(1)-(4) (2003). [CrossRef]
  16. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001). [CrossRef] [PubMed]
  17. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, 1995).
  18. J. N. Winn, R. D. Meade, and J. D. Joannopoulos, "Two-dimensional photonic band-gap materials," J. Mod. Opt. 41, 257-273 (1994). [CrossRef]
  19. R. Padjen, J. M. Gerard, and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," J. Mod. Opt. 41, 295-310 (1994). [CrossRef]
  20. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite Difference Time Domain Method, 3rd Ed. (Artech House, 2005).
  21. FDTD software is available at http://ab-initio.mit.edu/meep, for example.
  22. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994). [CrossRef]
  23. S. Gao and S. Albin, "Numerical techniques for excitation and analysis of defect modes in photonic crystals," Opt. Express 11, 1080 (2003). [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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited