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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 36 — Dec. 20, 2011
  • pp: 6657–6666

Optical properties of three-dimensional woodpile photonic crystals composed of circular cylinders with planar defect structures

Shih-Hsuan Chung and Jaw-Yen Yang  »View Author Affiliations

Applied Optics, Vol. 50, Issue 36, pp. 6657-6666 (2011)

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The optical properties of three-dimensional woodpile photonic crystals (PhCs) composed of circular cylinder rods with a planar defect structure at the central layer are theoretically investigated using the parallel finite-difference time-domain method and plane-wave expansion method. Three types of planar defects are introduced into the PhC by alternating respectively the dielectric constant, cylinder diameter, and misalignment of the rods at the defect layer. The transmission spectrum and band diagram of each planar defect structure are systematically studied. The resonance and transmission properties of the defect structures can be characterized by two distinct resonant modes, the defect mode and the band-edge resonant mode, which have been identified by detailed spectrum analysis, calculated mode profiles and field patterns. It is shown that, by modifying the rod diameter or the dielectric constant of materials at the defect layer, the resonant modes can be varied and controlled. Also, by applying dislocation to a layer of dielectric rods, the photonic band edges can be shifted.

© 2011 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Diffraction and Gratings

Original Manuscript: June 22, 2011
Manuscript Accepted: August 23, 2011
Published: December 16, 2011

Shih-Hsuan Chung and Jaw-Yen Yang, "Optical properties of three-dimensional woodpile photonic crystals composed of circular cylinders with planar defect structures," Appl. Opt. 50, 6657-6666 (2011)

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  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. M. Okano, A. Chutinan, and S. Noda, “Analysis and design of single-defect cavities in a three-dimensional photonic crystals,” Phys. Rev. B 66, 165211 (2002). [CrossRef]
  4. A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys. 39, 2353–2356 (2000). [CrossRef]
  5. 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]
  6. Z.-Y. Li and K.-M. Ho, “Waveguides in three-dimensional layer-by-layer photonic crystals,” J. Opt. Soc. Am. B 20, 801–809 (2003). [CrossRef]
  7. M. E. B. Özbay, B. Temelkuran, M. M. Sigalas, C. M. Soukoulis, R. Biswas, and K. M. Ho, “Guiding, bending, and splitting of electromagnetic waves in highly confined photonic crystal waveguides,” Phys. Rev. B 63, 081107 (2001). [CrossRef]
  8. M. E. B. Özbay, “Dropping of electromagnetic waves through localized modes in three-dimensional photonic band gap structures,” Appl. Phys. Lett. 81, 4514–4516 (2002). [CrossRef]
  9. S. Noda, M. Imada, M. Okano, S. Ogawa, M. Mochizuki, and A. Chutinan, “Semiconductor three-dimensional and two-dimensional photonic crystals and devices,” IEEE J. Quantum Electron. 38, 726–735 (2002). [CrossRef]
  10. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70, 1438–1440 (1997). [CrossRef]
  11. S. Noda, N. Yamamoto, and A. Sasaki, “New realization method for three-dimensional photonic crystal in optical wavelength region,” Jpn. J. Appl. Phys. 35, L909–L912 (1996). [CrossRef]
  12. S. A. Rinne, F. Garcia-Santamaria, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photon. 2, 52–56 (2008). [CrossRef]
  13. K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nat. Mater. 2, 117–121 (2003). [CrossRef] [PubMed]
  14. K. Ishizaki, M. Okano, and S. Noda, “Numerical investigation of emission in finite-sized three-dimensional photonic crystals with structural fluctuations,” J. Opt. Soc. Am. B 26, 1157–1161 (2009). [CrossRef]
  15. M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004). [CrossRef] [PubMed]
  16. Y. Lin and P. R. Herman, “Effect of structural variation on the photonic band gap in woodpile photonic crystal with body-centered-cubic symmetry,” J. Appl. Phys. 98, 063104(2005). [CrossRef]
  17. P. V. Braun, S. A. Rinne, and F. Garcí-Santamaría, “Introducing defects in 3D photonic crystals: state of the art,” Adv. Mater. 18, 2665–2678 (2006). [CrossRef]
  18. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994). [CrossRef]
  19. E. Özbay, E. Michel, G. Tuttle, R. Biswas, M. Sigalas, and K. M. Ho, “Micromachined millimeter-wave photonic band-gap crystals,” Appl. Phys. Lett. 64, 2059–2061 (1994). [CrossRef]
  20. K. Ohlinger, F. Torres, Y. Lin, K. Lozano, D. Xu, and K. P. Chen, “Photonic crystals with defect structures fabricated through a combination of holographic lithography and two-photon lithography,” J. Appl. Phys. 108, 073113 (2010). [CrossRef]
  21. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000). [CrossRef] [PubMed]
  22. D. J. Kan, A. A. Asatryan, C. G. Poulton, and L. C. Botten, “Multipole method for modeling linear defects in photonic woodpiles,” J. Opt. Soc. Am. B 27, 246–258 (2010). [CrossRef]
  23. C. Sell, C. Christensen, J. Muehlmeier, G. Tuttle, Z. Y. Li, and K. M. Ho, “Waveguide networks in three-dimensional layer-by-layer photonic crystals,” Appl. Phys. Lett. 84, 4605–4607(2004). [CrossRef]
  24. 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]
  25. V. Ramanan, E. Nelson, A. Brzezinski, P. V. Braun, and P. Wiltzius, “Three dimensional silicon-air photonic crystals with controlled defects using interference lithography,” Appl. Phys. Lett. 92, 173304 (2008). [CrossRef]
  26. R. W. Tjerkstra, F. B. Segerink, J. J. Kelly, and W. L. Vos, “Fabrication of three-dimensional nanostructures by focused ion beam milling,” J. Vac. Sci. Technol. B 26, 973–977(2008). [CrossRef]
  27. S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nat. Mater. 8, 721–725 (2009). [CrossRef] [PubMed]
  28. D. Stieler, A. Barsic, G. Tuttle, M. Li, and K. M. Ho, “Effects of defect permittivity on resonant frequency and mode shape in the three-dimensional woodpile photonic crystal,” J. Appl. Phys. 105, 103109 (2009). [CrossRef]
  29. E. Özbay, G. Tuttle, M. Sigalas, C. M. Soukoulis, and K. M. Ho, “Defect structures in a layer-by-layer photonic band-gap crystal,” Phys. Rev. B 51, 13961–13965 (1995). [CrossRef]
  30. M. Okano and S. Noda, “Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,” Phys. Rev. B 70, 125105 (2004). [CrossRef]
  31. M. Iida, M. Tani, K. Sakai, M. Watanabe, H. Kitahara, T. Tohme, and M. W. Takeda, “Planar defect modes excited at the band edge of three-dimensional photonic crystals,” J. Phys. Soc. Jpn. 73, 2355–2357 (2004). [CrossRef]
  32. J. F. Chen, R. T. Hong, and J. Y. Yang, “Analysis of planar defect structures in three-dimensional layer-by-layer photonic crystals,” J. Appl. Phys. 104, 063111 (2008). [CrossRef]
  33. 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]
  34. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966). [CrossRef]
  35. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  36. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702(2010). [CrossRef]
  37. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).
  38. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200(1994). [CrossRef]
  39. E. Istrate and E. H. Sargent, “Photonic crystal heterostructures—resonant tunnelling, waveguides and filters,” J. Opt. A 4, S242 (2002). [CrossRef]
  40. P. Kopperschmidt, “Tetragonal photonic woodpile structures,” Appl. Phys. B 76, 729–734 (2003). [CrossRef]
  41. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383(1991). [CrossRef] [PubMed]

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