Abstract

We present a numerical study of optical properties of an octagonal quasi-periodic lattice of dielectric rods. We report on a complete photonic bandgap in TM polarization up to extremely low dielectric constants of rods. The first photonic bandgap remains open down to dielectric constant as small as ε=1.6 (n=1.26). The properties of an optical microcavity and waveguides are examined for the system of rods with dielectric constant ε=5.0 (n=2.24) in order to design an add-drop filter. Proposed add-drop filter is numerically characterized and further optimized for efficient operation. The two-dimensional finite difference time domain method was exploited for numerical calculations. We provide a numerical evidence of effective add-drop filter based on low index material, thus opening further opportunities for application of low refractive index materials in photonic bandgap optics.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]

2004 (2)

2003 (6)

S. Guo and S. Albin, “Numerical techniques for excitation and analysis of defect modes in photonic crystals,” Opt. Express 11, 1080–1089 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-1080.
[CrossRef] [PubMed]

D. J. W. Klunder, et al., “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21, 1099–1110 (2003).
[CrossRef]

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

T. Asano, B.S. Song, Y. Tanaka, and S. Noda, “Investigation of a channel-add/drop filtering device using acceptor-type point defects in a two-dimensional photonic crystal slab,” Appl. Phys Lett. 83, 407 (2003).
[CrossRef]

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]

K. Wang, S. David, A. Chelnokov, and J.-M. Lourtioz, “Photonic band gaps in quasicrystal-related approximant structures,” J. Mod. Optics 50, 2095–2105 (2003)

2002 (3)

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

M. Bayindir and E. Ozbay, “Dropping of electromagnetic waves through localized modes in three-dimensional photonic bandgap structures,” Appl. Phys Lett. 81, 4514–4516 (2002).
[CrossRef]

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[CrossRef]

2001 (3)

M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–490 (2001).
[CrossRef]

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

2000 (4)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[CrossRef] [PubMed]

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

1999 (2)

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4098 (1999).
[CrossRef]

1998 (4)

Y. S. Chan, C. T. Chang, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

B. E. Little, et al., “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
[CrossRef] [PubMed]

1997 (2)

D. Rafizadeh, et al., “Waveguide coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range,” Opt. Lett. 22, 1244–1246 (1997).
[CrossRef] [PubMed]

S. C. Hagness, et al., “FDTD microcavity simulations: design and experimental realization of waveguide coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

Abram, R. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Albin, S.

Asano, T.

T. Asano, B.S. Song, Y. Tanaka, and S. Noda, “Investigation of a channel-add/drop filtering device using acceptor-type point defects in a two-dimensional photonic crystal slab,” Appl. Phys Lett. 83, 407 (2003).
[CrossRef]

Baba, T.

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84, 4875–4877 (2004).
[CrossRef]

Baumerg, J. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[CrossRef] [PubMed]

Bayindir, M.

M. Bayindir and E. Ozbay, “Dropping of electromagnetic waves through localized modes in three-dimensional photonic bandgap structures,” Appl. Phys Lett. 81, 4514–4516 (2002).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Borel, P. I.

Botten, L. C.

Brand, S.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Chan, C. T.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4098 (1999).
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chang, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

Chang, C. T.

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[CrossRef]

Y. S. Chan, C. T. Chang, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

Charlton, M. D. B.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[CrossRef] [PubMed]

Chelnokov, A.

K. Wang, S. David, A. Chelnokov, and J.-M. Lourtioz, “Photonic band gaps in quasicrystal-related approximant structures,” J. Mod. Optics 50, 2095–2105 (2003)

Cheng, B.

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

Cheng, S. S. M.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4098 (1999).
[CrossRef]

Chong, H. M. H.

David, S.

K. Wang, S. David, A. Chelnokov, and J.-M. Lourtioz, “Photonic band gaps in quasicrystal-related approximant structures,” J. Mod. Optics 50, 2095–2105 (2003)

de Dood, M. J. A.

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[CrossRef]

De La Rue, R.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

De La Rue, R. M.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

de Sterke, C. M.

Edagawa, K.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92, pp.123906.
[PubMed]

Egashira, M.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Fan, S.

Frandsen, L. H.

Guo, S.

Hagness, S. C.

S. C. Hagness, et al., “FDTD microcavity simulations: design and experimental realization of waveguide coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

Harpøth, A.

Hase, M.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Haus, H. A.

Hu, X.

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

Jaskorzynska, B.

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]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 1995).

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Kee, C.-S.

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

Kim, J.-E.

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

Kim, T. I.

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

Klunder, D. J. W.

Kojima, K. M.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Krauss, T. F.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Kristensen, M.

Lavrinenko, A.

Lee, R. K.

Li, L. M.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4098 (1999).
[CrossRef]

Lim, H.

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

Little, B. E.

B. E. Little, et al., “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

Liu, Z. Y.

Y. S. Chan, C. T. Chang, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

Lourtioz, J.-M.

K. Wang, S. David, A. Chelnokov, and J.-M. Lourtioz, “Photonic band gaps in quasicrystal-related approximant structures,” J. Mod. Optics 50, 2095–2105 (2003)

McPhedran, R. C.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 1995).

Millar, P.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Miyazaki, H.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Moroz, A.

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[CrossRef]

Netti, M. C.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[CrossRef] [PubMed]

Niemi, T.

Noda, S.

T. Asano, B.S. Song, Y. Tanaka, and S. Noda, “Investigation of a channel-add/drop filtering device using acceptor-type point defects in a two-dimensional photonic crystal slab,” Appl. Phys Lett. 83, 407 (2003).
[CrossRef]

Notomi, M.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92, pp.123906.
[PubMed]

Nozaki, K.

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84, 4875–4877 (2004).
[CrossRef]

Oh, S. S.

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

Ozbay, E.

M. Bayindir and E. Ozbay, “Dropping of electromagnetic waves through localized modes in three-dimensional photonic bandgap structures,” Appl. Phys Lett. 81, 4514–4516 (2002).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Park, H. Y.

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

Park, I.

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

Parker, G. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[CrossRef] [PubMed]

Polman, A.

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[CrossRef]

Qiu, M.

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]

Rafizadeh, D.

Scherer, A.

Shinya, N.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Snoeks, E.

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[CrossRef]

Song, B.S.

T. Asano, B.S. Song, Y. Tanaka, and S. Noda, “Investigation of a channel-add/drop filtering device using acceptor-type point defects in a two-dimensional photonic crystal slab,” Appl. Phys Lett. 83, 407 (2003).
[CrossRef]

Steel, M. J.

Suzuki, H.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92, pp.123906.
[PubMed]

Tamamura, T.

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92, pp.123906.
[PubMed]

Tanaka, Y.

T. Asano, B.S. Song, Y. Tanaka, and S. Noda, “Investigation of a channel-add/drop filtering device using acceptor-type point defects in a two-dimensional photonic crystal slab,” Appl. Phys Lett. 83, 407 (2003).
[CrossRef]

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Thorhauge, M.

Uchida, S.

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Villeneuve, P. R.

Wang, K.

K. Wang, S. David, A. Chelnokov, and J.-M. Lourtioz, “Photonic band gaps in quasicrystal-related approximant structures,” J. Mod. Optics 50, 2095–2105 (2003)

Wang, Y.W.

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

White, T. P.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 1995).

Xu, X.

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

Xu, Y.

Yariv, A.

Zhang, D.

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

Zhang, X.

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[CrossRef]

Zhang, Z. Q.

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[CrossRef]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4098 (1999).
[CrossRef]

Zoorob, M. E.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[CrossRef] [PubMed]

Appl. Phys Lett. (2)

M. Bayindir and E. Ozbay, “Dropping of electromagnetic waves through localized modes in three-dimensional photonic bandgap structures,” Appl. Phys Lett. 81, 4514–4516 (2002).
[CrossRef]

T. Asano, B.S. Song, Y. Tanaka, and S. Noda, “Investigation of a channel-add/drop filtering device using acceptor-type point defects in a two-dimensional photonic crystal slab,” Appl. Phys Lett. 83, 407 (2003).
[CrossRef]

Appl. Phys. Lett. (3)

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]

S. S. Oh, C.-S. Kee, J.-E. Kim, H. Y. Park, T. I. Kim, I. Park, and H. Lim, “Duplexer using microwave photonic band gap structure,” Appl. Phys. Lett. 76, 2301–2303 (2000).
[CrossRef]

K. Nozaki and T. Baba, “Quasiperiodic photonic crystal microcavity lasers,” Appl. Phys. Lett. 84, 4875–4877 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. E. Little, et al., “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998).
[CrossRef]

J. Lightwave Technol. (2)

D. J. W. Klunder, et al., “Experimental and numerical study of SiON microresonators with air and polymer cladding,” J. Lightwave Technol. 21, 1099–1110 (2003).
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S. C. Hagness, et al., “FDTD microcavity simulations: design and experimental realization of waveguide coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15, 2154–2165 (1997).
[CrossRef]

J. Mod. Opt. (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

J. Mod. Optics (1)

K. Wang, S. David, A. Chelnokov, and J.-M. Lourtioz, “Photonic band gaps in quasicrystal-related approximant structures,” J. Mod. Optics 50, 2095–2105 (2003)

J. Phys. Cond. Matt. (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, “Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals,” J. Phys. Cond. Matt. 13, 10459–10470 (2001).
[CrossRef]

Nature (1)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (3)

Opt. Quantum Electr. (1)

M. J. A. de Dood, E. Snoeks, A. Moroz, and A. Polman, “Design and optimization of 2D photonic crystal waveguides based on silicon,” Opt. Quantum Electr. 34, 145–159 (2002).
[CrossRef]

Phys. Rev. B (3)

Y.W. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68, 165106 (2003).
[CrossRef]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, “Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems,” Phys. Rev. B 59, 4091–4098 (1999).
[CrossRef]

M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S. Uchida, “Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals”, Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Phys. Rev. B. (1)

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[CrossRef]

Phys. Rev. Lett. (4)

M. Notomi, H. Suzuki, T. Tamamura, and K. Edagawa, “Lasing Action due to the Two-Dimensional Quasiperiodicity of Photonic Quasicrystals with a Penrose Lattice,” Phys. Rev. Lett. 92, pp.123906.
[PubMed]

Y. S. Chan, C. T. Chang, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).
[CrossRef] [PubMed]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton Univ. Press, 1995).

J.-B. Suck, M. Schreiber, and P. Häussler, eds., Quasicrystals (Springer, Berlin, 2002).

Supplementary Material (4)

» Media 1: GIF (924 KB)     
» Media 2: GIF (786 KB)     
» Media 3: GIF (776 KB)     
» Media 4: GIF (682 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

(Left panel) Sketch of the analyzed 8-fold quasi-periodic structure. Building tiles are depicted in red. (Right panel) The gap map of the first PBG in TM polarization for the PQC versus dielectric constant. The minimum (black line) and maximum (red line) normalized frequencies of the gap as a function of the dielectric constant are shown. The inset shows the gap width to midgap ratio as a function of the dielectric constant (points) together with an interpolation fit (green line).

Fig. 2.
Fig. 2.

(Left panel) Sketch of the microcavity made by removing rods around the central one. (Right panel) Energy density inside the PQC (black dashed line) and inside the cavity (solid blue line). The spectral range of a complete PBG is shown. Three cavity modes are designated by Ω 1, Ω 2 and Ω 3.

Fig. 3.
Fig. 3.

Field patterns of the cavity modes of PQC corresponding to the spectral range of the first PBG. Mode Ω 1 is a quadropole, mode Ω 2 is a hexapole and mode Ω 3 is a dipole. Two degenerated hexapole modes are shown in central panels. Hexapole-0 (Hexapole-90) mode is even with respect to the vertical (horizontal) plane. Colors represent electric field amplitude. Arrows show magnetic field lines. Circles show positions of rods in the structure.

Fig. 4.
Fig. 4.

(Top panel) Sketch of different PQC waveguide configurations. W1, W2 and W3 waveguides are shown. (Bottom panel) Transmission efficiency spectra for W1 (green), W2 (red) and W3 (black) waveguides. Spectral positions of the cavity modes are shown as a vertical blue lines.

Fig. 5.
Fig. 5.

Energy density stored in the cavity by hexapole modes. (Left panel) Two hexapole modes are completely degenerate in square patch of PQC. (Center panel) Degeneracy is lifted, when the symmetry of the system is broken by waveguides. Hexapole-0 and Hexapole-90 modes have different resonant frequencies. (Right panel) The modes overlap is partially restored in the system based on a rectangular patch of PQC. Sketches of considered structures are shown in the top panel above the corresponding energy density spectra.

Fig. 6.
Fig. 6.

Field patterns are shown for the Hexapole-0 (left panel) and Hexapole-90 (center panel) modes and for their superposition (right panel) decaying into the waveguides channels. Colors represent electric field amplitude. Circles show positions of rods in the structure. In the top panel, the sign of the electric field amplitude in waveguide channels in the direct vicinity of the cavity is shown for the appropriate modes.

Fig. 7.
Fig. 7.

(Left panel) Transmission efficiency of the add-drop filter based on a square patch of octagonal PQC. Transmission in the main channel (black line), reflection back at the entrance of the filter (blue line), backward (red line) and forward (green line) transmission in the upper waveguide is shown. Energy density stored in the Hexapole-0 and Hexapole-90 modes are shown for comparison by dashed black and dashed red lines, respectively. Energy density spectra are normalized to their maximum value. Electric field patterns are shown for the resonance (center panel) and out of the resonant (right panel) frequencies. Light is coupled to the add-drop filter at the Input channel and propagates in backward (forward) direction in the Output-2 (Output-1) channel for the resonance (out of the resonant) frequency. Colors represent electric field amplitude. Circles show positions of rods in the structure. (Movies 946 KB, 805 KB)

Fig. 8.
Fig. 8.

(Left panel) Transmission efficiency of the optimized add-drop filter based on a rectangular patch of octagonal PQC. Transmission in the main channel (black line), reflection back at the entrance of the filter (blue line), backward (red line) and forward (green line) transmission in the upper waveguide is shown. Energy density stored in the Hexapole-0 and Hexapole-90 modes are shown for comparison by dashed black and dashed red, respectively. Energy density spectra are normalized to their maximum value. Electric field patterns are shown for the resonance (center panel) and out of the resonant (right panel) frequencies. Light is coupled to the add-drop filter at the Input channel and propagates in backward (forward) direction in the Output-2 (Output-1) channel for the resonant (out of the resonance) frequency. Colors represent electric field amplitude. Circles show positions of rods in the structure. (Movies 794 KB, 699 KB)

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