Abstract

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

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  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]
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  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).
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  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).
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    [CrossRef]
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    [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]

2010 (3)

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]

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]

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]

2009 (3)

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]

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]

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]

2008 (4)

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]

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]

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]

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]

2006 (2)

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]

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]

2005 (1)

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]

2004 (4)

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]

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]

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]

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]

2003 (4)

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]

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]

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]

P. Kopperschmidt, “Tetragonal photonic woodpile structures,” Appl. Phys. B 76, 729–734 (2003).
[CrossRef]

2002 (4)

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures—resonant tunnelling, waveguides and filters,” J. Opt. A 4, S242 (2002).
[CrossRef]

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]

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]

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]

2001 (2)

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]

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]

2000 (2)

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]

A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys. 39, 2353–2356 (2000).
[CrossRef]

1997 (1)

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]

1996 (1)

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]

1995 (1)

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]

1994 (3)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200(1994).
[CrossRef]

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]

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]

1991 (1)

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]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef] [PubMed]

1966 (1)

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]

Aoki, K.

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]

Aoyagi, Y.

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]

Asatryan, A. A.

Baba, T.

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]

Barsic, A.

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]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200(1994).
[CrossRef]

Bermel, P.

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]

Biswas, R.

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]

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]

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]

Botten, L. C.

Braun, P. V.

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]

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]

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]

Brommer, K. D.

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]

Brzezinski, A.

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]

Busch, A.

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]

Chan, C. T.

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]

Chen, J. F.

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]

Chen, K. P.

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]

Christensen, C.

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]

Chutinan, A.

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]

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]

A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys. 39, 2353–2356 (2000).
[CrossRef]

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]

Garcia-Santamaria, F.

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]

Garcí-Santamaría, F.

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]

Gmitter, T. J.

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]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Herman, P. R.

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]

Hirayama, H.

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]

Ho, K. M.

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]

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]

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).
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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]

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).
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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).
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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]

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]

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).
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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).
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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).
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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]

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).
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E. Istrate and E. H. Sargent, “Photonic crystal heterostructures—resonant tunnelling, waveguides and filters,” J. Opt. A 4, S242 (2002).
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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]

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).
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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]

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).
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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).
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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]

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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).
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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]

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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).
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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).
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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).
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[CrossRef]

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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]

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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]

Li, Z.-Y.

Lidorikis, E.

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]

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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).
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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).
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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]

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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).
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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]

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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]

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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]

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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]

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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]

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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).
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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]

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]

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]

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]

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).
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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]

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).
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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]

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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]

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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]

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]

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]

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]

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).
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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]

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).
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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).
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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).
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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]

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).
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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).
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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).
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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]

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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).
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Qi, M.

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]

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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]

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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]

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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).
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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).
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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).
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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]

Sakai, K.

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]

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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]

Sargent, E. H.

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures—resonant tunnelling, waveguides and filters,” J. Opt. A 4, S242 (2002).
[CrossRef]

Sasaki, A.

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]

Segerink, F. B.

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]

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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]

Shinya, N.

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]

Sigalas, M.

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]

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]

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]

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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]

Smith, H. I.

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]

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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]

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]

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]

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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]

Suzuki, K.

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).
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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).
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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]

Tani, M.

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]

Temelkuran, B.

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]

Tiedje, T.

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]

Tjerkstra, R. W.

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]

Tohme, T.

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]

Tomoda, K.

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]

Torres, F.

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]

Tuttle, G.

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]

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]

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]

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]

Vos, W. L.

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]

Watanabe, M.

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]

Wiltzius, P.

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]

Xu, D.

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]

Yablonovitch, E.

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]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

Yamamoto, N.

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]

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]

Yang, J. Y.

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]

Yee, K. S.

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]

Young, J. F.

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]

Adv. Mater. (1)

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]

Appl. Phys. B (1)

P. Kopperschmidt, “Tetragonal photonic woodpile structures,” Appl. Phys. B 76, 729–734 (2003).
[CrossRef]

Appl. Phys. Lett. (6)

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]

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]

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]

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]

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]

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]

Comput. Phys. Commun. (1)

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]

IEEE J. Quantum Electron. (1)

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]

IEEE Trans. Antennas Propag. (1)

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]

J. Appl. Phys. (4)

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]

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]

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]

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]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200(1994).
[CrossRef]

J. Opt. A (1)

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures—resonant tunnelling, waveguides and filters,” J. Opt. A 4, S242 (2002).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. Soc. Jpn. (1)

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]

J. Vac. Sci. Technol. B (1)

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]

Jpn. J. Appl. Phys. (2)

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]

A. Chutinan and S. Noda, “Design for waveguides in three-dimensional photonic crystals,” Jpn. J. Appl. Phys. 39, 2353–2356 (2000).
[CrossRef]

Nat. Mater. (2)

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]

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]

Nat. Photon. (1)

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]

Nature (1)

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]

Opt. Express (1)

Phys. Rev. B (5)

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]

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]

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]

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]

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]

Phys. Rev. Lett. (3)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062(1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489(1987).
[CrossRef] [PubMed]

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]

Science (1)

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]

Solid State Commun. (1)

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]

Other (2)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

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Figures (12)

Fig. 1
Fig. 1

Schematic of a three-dimensional woodpile PhC composed of circular cylindrical rods with an FCT symmetry. Here a is the lattice constant, d is the rod diameter, and h is the size of unit cell.

Fig. 2
Fig. 2

Photonic band structure for the FCT lattice of the woodpile structure with circular cylinder rods. The position of the high-symmetry points together with the Brillouin zone are shown in the inset.

Fig. 3
Fig. 3

Three categories of planar defects: (a)  ε d -type, (b)  r d -type, (c)  δ d -type.

Fig. 4
Fig. 4

A supercell with (a)  ( C ) 4 ( D ) 1 ( C ) 4 for FDTD and (b)  1 × 1 × 10 periods for PWE calculation. The woodpile structure has an ε d -type defect at the center.

Fig. 5
Fig. 5

Transmission spectrum versus band diagram. The dielectric constant of defect rods is (a)  ε d = 0.25 ε and (b)  ε d = 2.0 ε .

Fig. 6
Fig. 6

Transmission spectrum of the ( C ) 4 ( D ) 1 ( C ) 4 sandwich PhCs with ε d ε . The plane wave source incident along the z axis is with (a)  E x polarization (perpendicular to the defect rods) and (b)  E y polarization (parallel to the defect rods). The electric field pattern (c) is with ε d = 0.25 ε and E y polarization with frequency f m = 0.5093 ( c / a ) , according to the transmitted peak shown in Fig. 5a.

Fig. 7
Fig. 7

Transmission spectrum of the ( C ) 4 ( D ) 1 ( C ) 4 sandwich PhCs with ε d ε . The incident plane wave source is vertical with (a)  E x polarization and (b)  E y polarization. Electric field patterns of the ε d = 2.0 ε and the incident plane wave source with f m frequency is vertical with (c)  E x polarization, f m = 0.6170 ( c / a ) , (d)  E y polarization, f m = 0.6134 ( c / a ) , and (e)  E y polarization, f m = 0.6611 ( c / a ) . The frequencies of the plane wave source are selected according to the transmitted peaks shown in Fig. 5b.

Fig. 8
Fig. 8

Transmission spectrum versus band diagram. The thickness of defect rods is (a)  r d = 0.5 r and (b)  r d = 2.0 r .

Fig. 9
Fig. 9

Transmission spectrum of ( C ) 4 ( D ) 1 ( C ) 4 sandwich PhCs with r d r . The incident plane wave source is vertical with (a)  E x polarization and (b)  E y polarization. (c) Electric field pattern with r d = 0.50 r and E y polarization with frequency f m = 0.5133 ( c / a ) , which is according to the transmitted peaks shown in Fig. 8a.

Fig. 10
Fig. 10

Transmission spectrum of ( C ) 4 ( D ) 1 ( C ) 4 sandwich PhCs with r d r . The incident plane wave source is vertical with (a)  E x polarization and (b)  E y polarization. Electric field patterns of the r d = 2.0 r and the incident plane wave source is vertical with (c)–(e)  E x polarization and (f), (g)  E y polarization. The frequencies are selected as (c)  f m = 0.5001 ( c / a ) , (d)  f m = 0.5302 ( c / a ) , (e)  f m = 0.6111 ( c / a ) , (f)  f m = 0.4769 ( c / a ) , and (g)  f m = 0.6411 ( c / a ) , which are according to the transmitted peak shown in Fig. 8b.

Fig. 11
Fig. 11

Transmission spectrum versus band diagram. The shifted distance of the dielectric rods in defect layer is δ d = a / 2 .

Fig. 12
Fig. 12

Transmission spectrum of the ( C ) 4 ( D ) 1 ( C ) 4 sandwich PhCs with δ d -type planar defect. The incident plane wave source is vertical with (a)  E y polarization and (b)  E x polarization. (c) Electric field pattern with δ d = a / 2 and E y polarization with frequency f m = 0.4489 ( c / a ) .

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