Abstract

We theoretically investigate the spectral and localization properties of two-dimensional (2D) deterministic aperiodic (DA) arrays of photonic nanopillars characterized by singular continuous (Thue-Morse sequence) and absolutely continuous (Rudin-Shapiro sequence) Fourier spectra. A rigorous and efficient numerical technique based on the 2D Generalized Multiparticle Mie Theory is used to study the formation of optical gaps and the confinement properties of eigenmodes supported by DA photonic lattices. In particular, we demonstrate the coexistence of optical modes with various degrees of localization (localized, extended and critical) and show that in-plane and out-of-plane optical energy confinement of extended critical modes can be optimally balanced. These results make aperiodic photonic structures very attractive for the engineering of novel passive and active photonic devices, such as low-threshold microlasers, sensitive detectors and bio-chemical sensors.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  2. K. Mnaymneh and R. C. Gauthier, "Mode localization and band-gap formation in defect-free photonic quasicrystals," Opt. Express,  15, 5089-5099 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-5089.
    [CrossRef]
  3. A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
    [CrossRef] [PubMed]
  4. Y. 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]
  5. Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
    [CrossRef]
  6. E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
    [CrossRef]
  7. X. Xu, H. Chen, and D. Zhang, "Enhancement of stimulated emission in 12-fold symmetric quasi-crystals," Appl. Phys. B 89, 29-34 (2007).
    [CrossRef]
  8. 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, 123906 (2004).
    [CrossRef] [PubMed]
  9. E. Macia, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006).
    [CrossRef]
  10. L. Dal Negro, N.-N. Feng, and A. Gopinath, "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays," J. Opt. A: Pure Appl. Opt. 10064013 (2008).
    [CrossRef]
  11. M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
    [CrossRef]
  12. W. Gellermann, M. Kohmoto, B. Southerland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1993).
    [CrossRef]
  13. L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
    [CrossRef] [PubMed]
  14. L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
    [CrossRef]
  15. L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
    [CrossRef]
  16. S. Chakraborty, M. C. Parker, and R. J. Mears, "A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices," Photon. Nanostruct. Fundam. Appl. 3, 139-147 (2005).
    [CrossRef]
  17. A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  19. S. V. Boriskina, A. Gopinath, and L. Dal Negro, "Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures," Physica E (in the press), doi:10.1016/j.physe.2008.08.039.
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    [CrossRef]
  22. M. Tokushima, H. Yamada, and Y. Arakawa, "1.5-?m-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
    [CrossRef]
  23. D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, "Coupled nanopillar waveguides optical properties and applications," Phys. Status Solidi A 204, 3647-3661 (2007).
    [CrossRef]
  24. S. Xiao and N. A. Mortensen, "Highly dispersive photonic band-gap-edge optofluidic biosensors," J. Eur. Opt. Soc. 1, 06026 (2006).
    [CrossRef]
  25. P. S. Nunes, N. A. Mortensen, J. P. Kutter, and K. B. Mogensen, "Photonic crystal resonator integrated in a microfluidic system," Opt. Lett. 33, 1623-1625 (2008).
    [CrossRef] [PubMed]
  26. S. V. Boriskina and L. Dal Negro, "Sensitive label-free biosensing using critical modes in aperiodic photonic structures," Opt. Express 16, 12511-12522 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12511.
    [CrossRef] [PubMed]
  27. C. S. Ryu, G. Y. Oh, and M. H. Lee, "Extended and critical wave functions in a Thue-Morse chain," Phys. Rev. B 46, 5162-5168 (1992).
    [CrossRef]
  28. L. Kroon, E. Lennholm, and R. Riklund, "Localization-delocalization in aperiodic systems," Phys. Rev. B 66, 094204 (2002).
    [CrossRef]
  29. L. Kroon and R. Riklund, "Absence of localization in a model with correlation measure as a random lattice," Phys. Rev. B 69, 094204 (2004).
    [CrossRef]
  30. M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
    [CrossRef]
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    [CrossRef]
  33. S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," J. Lightwave Technol. 25, 2487-2494 (2007).
    [CrossRef]
  34. Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals," Phys. Rev. B 76, 165132 (2007).
    [CrossRef]
  35. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Photonic bound states in periodic dielectric materials," Phys. Rev. B 44, 13772-13774 (1991).
    [CrossRef]
  36. 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]
  37. A. Yamilov and H. Cao, "Highest-quality modes in disordered photonic crystals," Phys. Rev. A 69, 031803 (2004).
    [CrossRef]
  38. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
    [CrossRef] [PubMed]
  39. K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
    [CrossRef]
  40. E. Macia, "Physical nature of critical modes in Fibonacci quasicrystals," Phys. Rev. B 60, 10032-10036 (1999).
    [CrossRef]

2008

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

L. Dal Negro, N.-N. Feng, and A. Gopinath, "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays," J. Opt. A: Pure Appl. Opt. 10064013 (2008).
[CrossRef]

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
[CrossRef] [PubMed]

P. S. Nunes, N. A. Mortensen, J. P. Kutter, and K. B. Mogensen, "Photonic crystal resonator integrated in a microfluidic system," Opt. Lett. 33, 1623-1625 (2008).
[CrossRef] [PubMed]

S. V. Boriskina and L. Dal Negro, "Sensitive label-free biosensing using critical modes in aperiodic photonic structures," Opt. Express 16, 12511-12522 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12511.
[CrossRef] [PubMed]

2007

D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, "Coupled nanopillar waveguides optical properties and applications," Phys. Status Solidi A 204, 3647-3661 (2007).
[CrossRef]

S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," J. Lightwave Technol. 25, 2487-2494 (2007).
[CrossRef]

Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals," Phys. Rev. B 76, 165132 (2007).
[CrossRef]

L. Moretti and V. Mocella, "Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence," Opt. Express,  15, 15314-15323 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-23-15314.
[CrossRef]

X. Xu, H. Chen, and D. Zhang, "Enhancement of stimulated emission in 12-fold symmetric quasi-crystals," Appl. Phys. B 89, 29-34 (2007).
[CrossRef]

K. Mnaymneh and R. C. Gauthier, "Mode localization and band-gap formation in defect-free photonic quasicrystals," Opt. Express,  15, 5089-5099 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-5089.
[CrossRef]

2006

C. Rockstuhl, U. Peschel, and F. Lederer, "Correlation between single-cylinder properties and bandgap formation in photonic structures," Opt. Lett. 31, 1741-1743 (2006).
[CrossRef] [PubMed]

E. Macia, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006).
[CrossRef]

S. Xiao and N. A. Mortensen, "Highly dispersive photonic band-gap-edge optofluidic biosensors," J. Eur. Opt. Soc. 1, 06026 (2006).
[CrossRef]

2005

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

S. Chakraborty, M. C. Parker, and R. J. Mears, "A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices," Photon. Nanostruct. Fundam. Appl. 3, 139-147 (2005).
[CrossRef]

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

2004

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, 123906 (2004).
[CrossRef] [PubMed]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5-?m-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

L. Kroon and R. Riklund, "Absence of localization in a model with correlation measure as a random lattice," Phys. Rev. B 69, 094204 (2004).
[CrossRef]

A. Yamilov and H. Cao, "Highest-quality modes in disordered photonic crystals," Phys. Rev. A 69, 031803 (2004).
[CrossRef]

2003

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Y. 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]

2002

L. Kroon, E. Lennholm, and R. Riklund, "Localization-delocalization in aperiodic systems," Phys. Rev. B 66, 094204 (2002).
[CrossRef]

2001

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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
[CrossRef] [PubMed]

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
[CrossRef]

1999

E. Macia, "Physical nature of critical modes in Fibonacci quasicrystals," Phys. Rev. B 60, 10032-10036 (1999).
[CrossRef]

1998

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

1994

1993

W. Gellermann, M. Kohmoto, B. Southerland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1993).
[CrossRef]

1992

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

C. S. Ryu, G. Y. Oh, and M. H. Lee, "Extended and critical wave functions in a Thue-Morse chain," Phys. Rev. B 46, 5162-5168 (1992).
[CrossRef]

1991

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Photonic bound states in periodic dielectric materials," Phys. Rev. B 44, 13772-13774 (1991).
[CrossRef]

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]

Andreone, A.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

Arakawa, Y.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5-?m-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Asatryan, A. A.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
[CrossRef]

Assefa, S.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Benson, T. M.

Bienstman, P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Boriskina, S. V.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
[CrossRef] [PubMed]

S. V. Boriskina and L. Dal Negro, "Sensitive label-free biosensing using critical modes in aperiodic photonic structures," Opt. Express 16, 12511-12522 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12511.
[CrossRef] [PubMed]

S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, "Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends," J. Lightwave Technol. 25, 2487-2494 (2007).
[CrossRef]

S. V. Boriskina, A. Gopinath, and L. Dal Negro, "Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures," Physica E (in the press), doi:10.1016/j.physe.2008.08.039.

Botten, L. C.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
[CrossRef]

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Photonic bound states in periodic dielectric materials," Phys. Rev. B 44, 13772-13774 (1991).
[CrossRef]

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]

Busch, K.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
[CrossRef]

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

Cao, H.

A. Yamilov and H. Cao, "Highest-quality modes in disordered photonic crystals," Phys. Rev. A 69, 031803 (2004).
[CrossRef]

Capolino, F.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Castaldi, G.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

Chakraborty, S.

S. Chakraborty, M. C. Parker, and R. J. Mears, "A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices," Photon. Nanostruct. Fundam. Appl. 3, 139-147 (2005).
[CrossRef]

Chan, C.-H.

Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals," Phys. Rev. B 76, 165132 (2007).
[CrossRef]

Chen, H.

X. Xu, H. Chen, and D. Zhang, "Enhancement of stimulated emission in 12-fold symmetric quasi-crystals," Appl. Phys. B 89, 29-34 (2007).
[CrossRef]

Cheng, B.

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

Y. 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]

Chigrin, D. N.

D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, "Coupled nanopillar waveguides optical properties and applications," Phys. Status Solidi A 204, 3647-3661 (2007).
[CrossRef]

Colocci, M.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Dal Negro, L.

L. Dal Negro, N.-N. Feng, and A. Gopinath, "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays," J. Opt. A: Pure Appl. Opt. 10064013 (2008).
[CrossRef]

S. V. Boriskina and L. Dal Negro, "Sensitive label-free biosensing using critical modes in aperiodic photonic structures," Opt. Express 16, 12511-12522 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-17-12511.
[CrossRef] [PubMed]

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
[CrossRef] [PubMed]

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

S. V. Boriskina, A. Gopinath, and L. Dal Negro, "Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures," Physica E (in the press), doi:10.1016/j.physe.2008.08.039.

Della Villa, A.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Di Gennaro, E.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

Duan, X.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

Dulea, M.

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

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, 123906 (2004).
[CrossRef] [PubMed]

Enoch, S.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Felbacq, D.

Feng, N.-N.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
[CrossRef] [PubMed]

L. Dal Negro, N.-N. Feng, and A. Gopinath, "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays," J. Opt. A: Pure Appl. Opt. 10064013 (2008).
[CrossRef]

Feng, Z.

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

Gaburro, Z.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Galdi, V.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Gauthier, R. C.

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Southerland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1993).
[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]

Gopinath, A.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
[CrossRef] [PubMed]

L. Dal Negro, N.-N. Feng, and A. Gopinath, "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays," J. Opt. A: Pure Appl. Opt. 10064013 (2008).
[CrossRef]

S. V. Boriskina, A. Gopinath, and L. Dal Negro, "Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures," Physica E (in the press), doi:10.1016/j.physe.2008.08.039.

Haavisto, J.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

Hu, X.

Y. 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]

Ippen, E. P.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Joannopoulos, J. D.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Photonic bound states in periodic dielectric materials," Phys. Rev. B 44, 13772-13774 (1991).
[CrossRef]

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]

Johansson, M.

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

John, S.

K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

Johnson, P.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Johnson, S. G.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
[CrossRef] [PubMed]

Kimerling, L. C.

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Southerland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1993).
[CrossRef]

Kolodziejski, L. A.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Kroha, J.

D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, "Coupled nanopillar waveguides optical properties and applications," Phys. Status Solidi A 204, 3647-3661 (2007).
[CrossRef]

Kroon, L.

L. Kroon and R. Riklund, "Absence of localization in a model with correlation measure as a random lattice," Phys. Rev. B 69, 094204 (2004).
[CrossRef]

L. Kroon, E. Lennholm, and R. Riklund, "Localization-delocalization in aperiodic systems," Phys. Rev. B 66, 094204 (2002).
[CrossRef]

Kutter, J. P.

Lagendijk, A.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Lai, Y.

Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals," Phys. Rev. B 76, 165132 (2007).
[CrossRef]

Lavrinenko, A. V.

D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, "Coupled nanopillar waveguides optical properties and applications," Phys. Status Solidi A 204, 3647-3661 (2007).
[CrossRef]

LeBlanc, J.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

Lederer, F.

Lee, M. H.

C. S. Ryu, G. Y. Oh, and M. H. Lee, "Extended and critical wave functions in a Thue-Morse chain," Phys. Rev. B 46, 5162-5168 (1992).
[CrossRef]

Lennholm, E.

L. Kroon, E. Lennholm, and R. Riklund, "Localization-delocalization in aperiodic systems," Phys. Rev. B 66, 094204 (2002).
[CrossRef]

Li, Z.-Y.

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

Macia, E.

E. Macia, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006).
[CrossRef]

E. Macia, "Physical nature of critical modes in Fibonacci quasicrystals," Phys. Rev. B 60, 10032-10036 (1999).
[CrossRef]

Martijn de Sterke, C.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
[CrossRef]

Maystre, D.

McPhedran, R. C.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
[CrossRef]

Meade, R. 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]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Photonic bound states in periodic dielectric materials," Phys. Rev. B 44, 13772-13774 (1991).
[CrossRef]

Mears, R. J.

S. Chakraborty, M. C. Parker, and R. J. Mears, "A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices," Photon. Nanostruct. Fundam. Appl. 3, 139-147 (2005).
[CrossRef]

Michel, J.

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

Miletto, C.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

Mnaymneh, K.

Mocella, V.

Mogensen, K. B.

Morello, D.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

Moretti, L.

Mortensen, N. A.

P. S. Nunes, N. A. Mortensen, J. P. Kutter, and K. B. Mogensen, "Photonic crystal resonator integrated in a microfluidic system," Opt. Lett. 33, 1623-1625 (2008).
[CrossRef] [PubMed]

S. Xiao and N. A. Mortensen, "Highly dispersive photonic band-gap-edge optofluidic biosensors," J. Eur. Opt. Soc. 1, 06026 (2006).
[CrossRef]

Nguyen, V.

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

Nicorovici, N. A.

A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
[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, 123906 (2004).
[CrossRef] [PubMed]

Nunes, P. S.

Oh, G. Y.

C. S. Ryu, G. Y. Oh, and M. H. Lee, "Extended and critical wave functions in a Thue-Morse chain," Phys. Rev. B 46, 5162-5168 (1992).
[CrossRef]

Oton, C. J.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Parker, M. C.

S. Chakraborty, M. C. Parker, and R. J. Mears, "A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices," Photon. Nanostruct. Fundam. Appl. 3, 139-147 (2005).
[CrossRef]

Pavesi, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Peschel, U.

Petrich, G. S.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Pierro, V.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Pishko, S. V.

Rakich, P. T.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Rappe, A. M.

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]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Photonic bound states in periodic dielectric materials," Phys. Rev. B 44, 13772-13774 (1991).
[CrossRef]

Reinhard, B. M.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
[CrossRef] [PubMed]

Righini, R.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Riklund, R.

L. Kroon and R. Riklund, "Absence of localization in a model with correlation measure as a random lattice," Phys. Rev. B 69, 094204 (2004).
[CrossRef]

L. Kroon, E. Lennholm, and R. Riklund, "Localization-delocalization in aperiodic systems," Phys. Rev. B 66, 094204 (2002).
[CrossRef]

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

Rockstuhl, C.

Ryu, C. S.

C. S. Ryu, G. Y. Oh, and M. H. Lee, "Extended and critical wave functions in a Thue-Morse chain," Phys. Rev. B 46, 5162-5168 (1992).
[CrossRef]

Savo, S.

E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

Sewell, P.

Smith, H. I.

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

Southerland, B.

W. Gellermann, M. Kohmoto, B. Southerland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1993).
[CrossRef]

Stolfi, M.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

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, 123906 (2004).
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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, 123906 (2004).
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Tayeb, G.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
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W. Gellermann, M. Kohmoto, B. Southerland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1993).
[CrossRef]

Tokushima, M.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5-?m-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Tsang, L.

Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals," Phys. Rev. B 76, 165132 (2007).
[CrossRef]

Wang, Y.

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

Y. 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]

Wiersma, D. S.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
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Xiao, S.

S. Xiao and N. A. Mortensen, "Highly dispersive photonic band-gap-edge optofluidic biosensors," J. Eur. Opt. Soc. 1, 06026 (2006).
[CrossRef]

Xu, X.

X. Xu, H. Chen, and D. Zhang, "Enhancement of stimulated emission in 12-fold symmetric quasi-crystals," Appl. Phys. B 89, 29-34 (2007).
[CrossRef]

Y. 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]

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]

Yamada, H.

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5-?m-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

Yamilov, A.

A. Yamilov and H. Cao, "Highest-quality modes in disordered photonic crystals," Phys. Rev. A 69, 031803 (2004).
[CrossRef]

Yi, J. H.

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

Yi, Y.

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

Zhang, D.

X. Xu, H. Chen, and D. Zhang, "Enhancement of stimulated emission in 12-fold symmetric quasi-crystals," Appl. Phys. B 89, 29-34 (2007).
[CrossRef]

Y. 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, D.-Z.

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

Zhang, X.

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

Zhang, Z.-Q.

Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals," Phys. Rev. B 76, 165132 (2007).
[CrossRef]

Zhukovsky, S. V.

D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, "Coupled nanopillar waveguides optical properties and applications," Phys. Status Solidi A 204, 3647-3661 (2007).
[CrossRef]

Appl. Phys. B

X. Xu, H. Chen, and D. Zhang, "Enhancement of stimulated emission in 12-fold symmetric quasi-crystals," Appl. Phys. B 89, 29-34 (2007).
[CrossRef]

Appl. Phys. Lett.

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

L. Dal Negro, J. H. Yi, Y. Yi, V. Nguyen, J. Michel, and L. C. Kimerling, "Spectrally enhanced light emission from aperiodic photonic structures," Appl. Phys. Lett.,  86, 261905, 2005
[CrossRef]

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 ?m light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
[CrossRef]

M. Tokushima, H. Yamada, and Y. Arakawa, "1.5-?m-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).
[CrossRef]

J. Eur. Opt. Soc.

S. Xiao and N. A. Mortensen, "Highly dispersive photonic band-gap-edge optofluidic biosensors," J. Eur. Opt. Soc. 1, 06026 (2006).
[CrossRef]

J. Lightwave Technol.

J. Opt. A: Pure Appl. Opt.

L. Dal Negro, N.-N. Feng, and A. Gopinath, "Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays," J. Opt. A: Pure Appl. Opt. 10064013 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Nano Lett.

A. Gopinath, S. V. Boriskina, N.-N. Feng, B. M. Reinhard, and L. Dal Negro, "Photonic-plasmonic scattering resonances in determinsitic aperiodic structures," Nano Lett. 8, 2423-2431 (2008).
[CrossRef] [PubMed]

Opt. Express

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Photon. Nanostruct. Fundam. Appl.

S. Chakraborty, M. C. Parker, and R. J. Mears, "A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices," Photon. Nanostruct. Fundam. Appl. 3, 139-147 (2005).
[CrossRef]

Phys. Rev. A

A. Yamilov and H. Cao, "Highest-quality modes in disordered photonic crystals," Phys. Rev. A 69, 031803 (2004).
[CrossRef]

Phys. Rev. B

E. Macia, "Physical nature of critical modes in Fibonacci quasicrystals," Phys. Rev. B 60, 10032-10036 (1999).
[CrossRef]

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L. Kroon and R. Riklund, "Absence of localization in a model with correlation measure as a random lattice," Phys. Rev. B 69, 094204 (2004).
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Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, "Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals," Phys. Rev. B 76, 165132 (2007).
[CrossRef]

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E. Di Gennaro, C. Miletto, S. Savo, A. Andreone, D. Morello, V. Galdi, G. Castaldi, and V. Pierro, "Evidence of local effects in anomalous refraction and focusing properties of dodecagonal photonic quasicrystals," Phys. Rev. B 77, 193104 (2008).
[CrossRef]

Y. 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]

M. Dulea, M. Johansson, and R. Riklund, "Localization of electrons and electromagnetic waves in a deterministic aperiodic system," Phys. Rev. B 45, 105-114 (1992).
[CrossRef]

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A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, "Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length," Phys. Rev. E 63, 046612 (2001).
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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).
[CrossRef] [PubMed]

W. Gellermann, M. Kohmoto, B. Southerland, and P. C. Taylor, "Localization of light waves in Fibonacci dielectric multilayers," Phys. Rev. Lett. 72, 633 (1993).
[CrossRef]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, "Light transport through the band-edge states of Fibonacci quasicrystals," Phys. Rev. Lett. 90, 055501 (2003).
[CrossRef] [PubMed]

Z. Feng, X. Zhang, Y. Wang, Z.-Y. Li, B. Cheng, and D.-Z. Zhang, "Negative refraction and imaging using 12-fold-symmetry quasicrystals," Phys. Rev. Lett. 94, 247402 (2005).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

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, 123906 (2004).
[CrossRef] [PubMed]

Phys. Status Solidi A

D. N. Chigrin, S. V. Zhukovsky, A. V. Lavrinenko, and J. Kroha, "Coupled nanopillar waveguides optical properties and applications," Phys. Status Solidi A 204, 3647-3661 (2007).
[CrossRef]

Physica E

S. V. Boriskina, A. Gopinath, and L. Dal Negro, "Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures," Physica E (in the press), doi:10.1016/j.physe.2008.08.039.

Rep. Prog. Phys.

E. Macia, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006).
[CrossRef]

Other

J. D. Joannopolous, S. Johnson, R. D. Meade, and J. N. Winn, Photonic crystals: Molding the flow of light (Princeton University, Princeton, 2008).

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Figures (11)

Fig. 1.
Fig. 1.

Real-space lattices of Thue-Morse (a) and Rudin-Shapiro (c) 2D photonic structures and their corresponding reciprocal space representations (lattice Fourier spectra) (b,d).

Fig. 2.
Fig. 2.

The radiation power spectra of a TM-polarized line source located in the center of (a,b) a periodic square lattice, (c,d) Thue-Morse lattice and (e,f) Rudin-Shapiro lattice of dielectric cylinders with N P=100, N TM=128, N RS=120, ε=10.5, r/a=0.2 (black lines), r/a=0.25 (red lines), r/a=0.3 (blue lines), and r/a=0.35 (green lines) in air. Spectral positions of the first bandgaps of infinite square-lattice periodic PhCs with matching parameters are indicated with vertical lines and horizontal bars in (a,b).

Fig. 3.
Fig. 3.

The evolution of optical component mode frequencies associated with the transformation of the periodic PhC into aperiodic structures by reducing the radii of the rods at the positions determined by the aperiodic sequences. Defect rods radii of r/a=0.2 correspond to a square-lattice periodic PhC with N P=64, and r/a=0 correspond to the Thue-Morse (a) and Rudin-Shapiro (b) aperiodic photonic structures with N TM=N RS=32. The frequency ranges of the first TM bandgaps of the periodic and aperiodic lattices are shown as red and blue sidebars, respectively.

Fig. 4.
Fig. 4.

Electric field patterns (|E z |) of the band-edge and acceptor modes in the first TM bandgap of the Thue-Morse structure with N TM=32: (a) a/λ=0.264; (b) a/λ=0.276; (c) a/λ=0.341; (d) a/λ=0.384; (e) a/λ=0.417; (f) a/λ=0.468.

Fig. 5.
Fig. 5.

Electric field patterns (|E z |) of the band-edge and acceptor modes in the first TM bandgap of the Rudin-Shapiro structure with N RS=32: (a) a/λ=0.255; (b) a/λ=0.278; (c) a/λ=0.307; (d) a/λ=0.308; (e) a/λ=0.370; (f) a/λ=0.405; (g) a/λ=0.445; (h) a/λ=0.461.

Fig. 6.
Fig. 6.

The radiation power spectra of a TM-polarized line source located in the center of (a) Thue-Morse and (b) Rudin-Shapiro lattice of dielectric cylinders (ε=10.5, r/a=0.2) in air. Three cluster sizes are considered for each aperiodic structure: 7a×7a, N TM=N RS=32 (black); 15a×15a, N TM=128, N RS=120 (blue); and 31a×31a, N TM=N RS=512 (red).

Fig. 7.
Fig. 7.

Electric field patterns (|E z |) of selected critical modes in and around the first TM bandgap of the Thue-Morse structure with N TM=512: (a) a/λ=0.452, Q=8.91×102; (b) a/λ=0.417, Q=1.694×104; (c) a/λ=0.339, Q=3.363×103; (d) a/λ=0.262, Q=8.6×102.

Fig. 8.
Fig. 8.

Electric field patterns (|E z |) of select critical modes in and around the first TM bandgap of the Rudin-Shapiro structure with N RS=512: (a) a/λ=0.397, Q=4.107×104; (b) a/λ=0.361, Q=3.002×103; (c) a/λ=0.4, Q=3.153×104; (d) a/λ=0.279, Q=1.212×103.

Fig. 9.
Fig. 9.

The electric field profiles (|E z |) of (a) a monopole mode localized in a point defect created in a periodic PhC by reducing the permittivity of a single rod (a/λ=0.2, ε rod=12, ε def=6, a/λ=0.304, Q=2.618×103); (c) the same mode, which is delocalized in the plane by reducing the permittivity of the central rod and four neighboring rods (a/λ=0.2, ε rod=12, ε def=6, a/λ=0.345, Q=2.283×103); (e) a monopole mode localized in the defect formed by removing the central rod (a/λ=0.2, ε rod=10.5, ε def=1, a/λ=0.384, Q=5.104×104); and (g) an extended band-edge mode in a defect-free periodic PhC (a/λ=0.2, ε rod=10.5, a/λ=0.434, Q=4.51×102). The corresponding 2D Fourier transform spectra of the modes electric field distributions (b,d,f,h). The areas inside the white circles correspond to the leaky regions.

Fig. 10.
Fig. 10.

2D Fourier transform spectra of the electric field distributions of the critical modes supported by the Thue-Morse structure shown in Fig. 7 (a-d), respectively.

Fig. 11.
Fig. 11.

2D Fourier transform spectra of the electric field distributions of the critical and localized modes supported by the Rudin-Shapiro structure shown in Fig. 8 (a–d), respectively.

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