OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 27, Iss. 2 — Feb. 1, 2010
  • pp: 246–258

Multipole method for modeling linear defects in photonic woodpiles

Dougal J. Kan, Ara A. Asatryan, Christopher G. Poulton, and Lindsay C. Botten  »View Author Affiliations


JOSA B, Vol. 27, Issue 2, pp. 246-258 (2010)
http://dx.doi.org/10.1364/JOSAB.27.000246


View Full Text Article

Enhanced HTML    Acrobat PDF (851 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We extend the multipole method to allow for rod-type defects in woodpiles composed of infinitely long cylinders. A coupled-resonator optical waveguide and a linear waveguide are considered, where each waveguide is embedded in a woodpile cladding. For both structures, low-loss waveguiding is observed ( Q 1 × 10 4 3 × 10 4 ) . Decreasing the radius of the defect rod shifts the transmission resonances to shorter wavelengths. The reflection and transmission coefficients of the woodpile are derived for the case of normal incidence in the long-wavelength limit, and it is shown that both the individual layers and the entire assemblage of layers homogenize to one-dimensional dielectric slabs. Expressions for the effective permittivities are given.

© 2010 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1960) Diffraction and gratings : Diffraction theory
(260.0260) Physical optics : Physical optics
(260.2110) Physical optics : Electromagnetic optics
(260.2065) Physical optics : Effective medium theory

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 28, 2009
Revised Manuscript: November 8, 2009
Manuscript Accepted: November 8, 2009
Published: January 12, 2010

Citation
Dougal J. Kan, Ara A. Asatryan, Christopher G. Poulton, and Lindsay C. Botten, "Multipole method for modeling linear defects in photonic woodpiles," J. Opt. Soc. Am. B 27, 246-258 (2010)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-2-246


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. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008).
  3. H. S. Sözüer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231-239 (1994). [CrossRef]
  4. G. A. Ozin, “The photonic opal: the jewel in the crown of optical information processing,” Chem. Commun. (Cambridge) 21, 2639-2643 (2003).
  5. K. Busch and S. John, “Photonic bandgap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896-3908 (1998). [CrossRef]
  6. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  7. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a plane-wave basis,” Opt. Express 8, 173-190 (2001). [CrossRef] [PubMed]
  8. A. Feigel, M. Veinger, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Three-dimensional simple cubic woodpile photonic crystals made from chalcogenide glasses,” Appl. Phys. Lett. 83, 4480-4482 (2003). [CrossRef]
  9. A. Feigel, Z. Kotler, B. Sfez, A. Arsh, M. Klebanov, and V. Lyubin, “Interference lithography for 3D photonic band gap crystal layer by layer fabrication,” in Materials Research Society Symposium Proceedings, 2001, E.D.Jones, O.Manasreh, K.D.Choquette, D.J.Friedman, and D.K.Johnstone, eds.,Vol. 692, K2.9.1. [CrossRef]
  10. M. Imada, L. H. Lee, M. Okano, S. Kawashima, and S. Noda, “Development of three-dimensional photonic-crystal waveguides at optical-communication wavelengths,” Appl. Phys. Lett. 88, 171107 (2006). [CrossRef]
  11. J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52-55 (2002). [CrossRef] [PubMed]
  12. S. Wu, J. Serbin, and M. Gu, “Two-photon polymerization for three-dimensional microfabrication,” J. Photochem. Photobiol., A 181, 1-11 (2006). [CrossRef]
  13. E. Nicoletti, G. Zhou, B. Jia, M. J. Ventura, D. Bulla, B. Luther-Davies, and M. Gu, “Observation of multiple higher-order stopgaps from three-dimensional chalcogenide glass photonic crystals,” Opt. Lett. 33, 2311-2313 (2008). [CrossRef] [PubMed]
  14. G. H. Smith, L. C. Botten, R. C. McPhedran, and N. A. Nicorovici, “Cylinder gratings in conical incidence with applications to woodpile structures,” Phys. Rev. E 67, 056620 (2003). [CrossRef]
  15. B. Gralak, M. de Dood, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic bandgaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003). [CrossRef]
  16. A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, “Effects of disorder on wave propagation in two-dimensional photonic crystals,” Phys. Rev. E 60, 6118-6127 (1999). [CrossRef]
  17. R. C. McPhedran, C. G. Poulton, N. A. Nicorovici, and A. B. Movchan, “Low frequency corrections to the static effective dielectric constant of a two-dimensional composite material,” Proc. R. Soc. London, Ser. A 452, 2231-2245 (1996). [CrossRef]
  18. J. Cheng, R. Hong, and J. Yang, “Analysis of planar defect structures in three-dimensional layer-by-layer photonic crystals,” J. Appl. Phys. 104, 063111 (2008). [CrossRef]
  19. M. Okano, S. Kako, and S. Noda, “Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal,” Phys. Rev. B 68, 235110 (2003). [CrossRef]
  20. G. von Freymann, S. Wong, G. A. Ozin, S. John, F. Pérez-Willard, M. Deubel, and M. Wegener, in Conference on Lasers and Electro-Optics, 2005, CTuU5, pp. 1002-1004.
  21. F. García-Santamaría, M. Xu, V. Lousse, S. Fan, P. V. Braun, and J. A. Lewis, “A germanium inverse woodpile structure with a large photonic bandgap,” Adv. Mater. 19, 1567-1570 (2007). [CrossRef]
  22. E. Centeno and D. Felbacq, “Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals,” J. Opt. Soc. Am. A 17, 320-327 (2000). [CrossRef]
  23. S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. de Sterke, “Modeling of defect modes in photonic crystals using the fictitious source superposition method,” Phys. Rev. E 71, 056606 (2005). [CrossRef]
  24. L. C. Botten, K. B. Dossou, S. Wilcox, R. C. McPhedran, C. M. de Sterke, N. A. Nicorovici, and A. A. Asatryan, “Highly accurate modelling of generalized defect modes in photonic crystals using the fictitious source superposition method,” Microwave Opt. Technol. Lett. 1, 133-145 (2006).
  25. G. H. Smith, L. C. Botten, R. C. McPhedran, and N. A. Nicorovici, “Cylinder gratings in conical incidence with applications to modes of air-cored photonic crystal fibers,” Phys. Rev. E 66, 056604 (2002). [CrossRef]
  26. L. C. Botten, N. A. Nicorovici, A. A. Asatryan, R. C. McPhedran, C. M. de Sterke, and P. A. Robinson, “Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method,” J. Opt. Soc. Am. A 17, 2165-2177 (2000). [CrossRef]
  27. A. Moroz, “Exponentially convergent lattice sums,” Opt. Lett. 26, 1119-1121 (2001). [CrossRef]
  28. B. Gralak, S. Enoch, and G. Tayeb, “From scattering or impedance matrices to Bloch modes of photonic crystals,” J. Opt. Soc. Am. A 19, 1547-1554 (2002). [CrossRef]
  29. A. Modinos, N. Stefanou, and V. Yannopapas, “Applications of the layer-KRR method to photonic crystals,” Opt. Express 8, 197-202 (2001). [CrossRef] [PubMed]
  30. J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904). [CrossRef]
  31. N. A. Nicorovici, R. C. McPhedran, and L. C. Botten, “Photonic bandgaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135-1145 (1995). [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.

Supplementary Material


» Media 1: AVI (394 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited