Abstract

Quasicrystals, realized in metal alloys, are a class of lattices exhibiting symmetries that fall outside the usual classification for periodic crystals. They do not have translational symmetry and yet the lattice points are well ordered. Furthermore, they exhibit higher rotational symmetry than periodic crystals. Because of the higher symmetry (more spherical), they are more optimal than periodic crystals in achieving complete photonic bandgaps in a new class of materials called photonic crystals in which the propagation of light in certain frequency ranges is forbidden. The potential of quasicrystals has been demonstrated in two dimensions for the infrared range and, recently, in three-dimensional icosahedral quasicrystals fabricated using a stereo lithography method for the microwave range and direct laser writing for the IR range. Here, we report the fabrication and optical characterization of icosahedral quasicrystals using a holographic lithography method for the visible range. The icosahedral pattern, generated using a novel 7-beam optical interference holography, is recorded on photoresists and holographic plates. Electron micrographs of the photoresist samples show clearly the symmetry of the icosahedral quasicrystals in the submicron range, while the holographic plate samples exhibit bandgaps in the angular-dependent transmission spectra in the visible range. Calculations of the bandgaps due to reflection planes inside the icosahedral quasicrystal show good agreement with the experimental results.

© 2007 Optical Society of America

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  1. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientataional order and no translational symmetry,” Phys. Rev. Lett. 53,1951–1953 (1984).
    [CrossRef]
  2. D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
    [CrossRef] [PubMed]
  3. P. J. Steinhardt and S. Ostlund, The Physics of Quasicrystals (Singapore, World Scientific, 1987).
  4. Z. M. Stadnik, Physical Properties of Quasicrystals (Berlin, Springer, 1999).
    [CrossRef]
  5. Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80,956–959 (1998).
    [CrossRef]
  6. X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63,081105/1-4 (2001).
    [CrossRef]
  7. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404,740–743 (2000).
    [CrossRef] [PubMed]
  8. 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.: Condens. Matter. 13,10459–10470 (2001).
    [CrossRef]
  9. C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
    [CrossRef]
  10. B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
    [CrossRef] [PubMed]
  11. C. M. Soukoulis, Photonic Bandgap Materials (Dordrecht, Kluwer, 1996).
  12. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton, New Jersey, Princeton Univ. Press, 1995).
  13. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58,2059–2062 (1987).
    [CrossRef] [PubMed]
  14. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58,2486–2489 (1987).
    [CrossRef] [PubMed]
  15. J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281,802–804 (1998).
    [CrossRef]
  16. E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
    [CrossRef]
  17. N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36,1907–1911 (1997).
    [CrossRef]
  18. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
    [CrossRef]
  19. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
    [CrossRef] [PubMed]
  20. S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
    [CrossRef]
  21. Yu. V. Miklyaev, D. C. Meisel, A. Blanco, and G. von Freymann, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography fabrication optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82,1284–1286 (2003).
    [CrossRef]
  22. X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
    [CrossRef]
  23. Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14,9013–9019 (2006).
    [CrossRef]
  24. M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
    [CrossRef]
  25. W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436,993–996 (2005).
    [CrossRef] [PubMed]
  26. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
    [CrossRef]
  27. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
    [CrossRef]
  28. X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
    [CrossRef]
  29. W. Y. Tam “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89,251111 and http://arxiv.org/ftp/physics/papers/0609/0609032.pdf (2006).
    [CrossRef]
  30. D. S. Rokhsar, D. C. Wright, and N. D. Mermin, “Scale equivalence of quasicrystallographic space groups,” Phys. Rev. B 37,8145–8149 (1988).
    [CrossRef]
  31. R. Ma, J. Xu, and W. Y. Tam, “Wide bandgap photonic structures in dichromate gelatin emulsions,” Appl. Phys. Lett. 89,081116 (2006).
    [CrossRef]

2006 (6)

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14,9013–9019 (2006).
[CrossRef]

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

W. Y. Tam “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89,251111 and http://arxiv.org/ftp/physics/papers/0609/0609032.pdf (2006).
[CrossRef]

R. Ma, J. Xu, and W. Y. Tam, “Wide bandgap photonic structures in dichromate gelatin emulsions,” Appl. Phys. Lett. 89,081116 (2006).
[CrossRef]

2005 (1)

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436,993–996 (2005).
[CrossRef] [PubMed]

2004 (1)

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

2003 (3)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
[CrossRef]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, and G. von Freymann, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography fabrication optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82,1284–1286 (2003).
[CrossRef]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

2002 (2)

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
[CrossRef]

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

2001 (2)

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.: Condens. Matter. 13,10459–10470 (2001).
[CrossRef]

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63,081105/1-4 (2001).
[CrossRef]

2000 (3)

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

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
[CrossRef] [PubMed]

1998 (3)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

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

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281,802–804 (1998).
[CrossRef]

1997 (1)

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36,1907–1911 (1997).
[CrossRef]

1988 (1)

D. S. Rokhsar, D. C. Wright, and N. D. Mermin, “Scale equivalence of quasicrystallographic space groups,” Phys. Rev. B 37,8145–8149 (1988).
[CrossRef]

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]

1985 (1)

D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
[CrossRef] [PubMed]

1984 (1)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientataional order and no translational symmetry,” Phys. Rev. Lett. 53,1951–1953 (1984).
[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.: Condens. Matter. 13,10459–10470 (2001).
[CrossRef]

Aizenberg, J.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

Bartal, G.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

Baumberg, J. J.

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

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Blanco, A.

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, and G. von Freymann, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography fabrication optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82,1284–1286 (2003).
[CrossRef]

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
[CrossRef]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientataional order and no translational symmetry,” Phys. Rev. Lett. 53,1951–1953 (1984).
[CrossRef]

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.: Condens. Matter. 13,10459–10470 (2001).
[CrossRef]

Bur, J.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Busch, K.

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

Cademartiri, L.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientataional order and no translational symmetry,” Phys. Rev. Lett. 53,1951–1953 (1984).
[CrossRef]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
[CrossRef] [PubMed]

Chaikin, P. M.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436,993–996 (2005).
[CrossRef] [PubMed]

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

Chan, C. T.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
[CrossRef]

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63,081105/1-4 (2001).
[CrossRef]

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

Chan, Y. S.

Y. S. Chan, C. T. Chan, 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. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404,740–743 (2000).
[CrossRef] [PubMed]

Chen, Y. L.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Cheng, B. Y.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
[CrossRef]

Christodoulides, D. N.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
[CrossRef] [PubMed]

Deuble, M.

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

Fleischer, J. W.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

Fleming, J. G.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Freedman, B.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

Freymann, G. V.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

Freymann, G. von

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, and G. von Freymann, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography fabrication optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82,1284–1286 (2003).
[CrossRef]

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientataional order and no translational symmetry,” Phys. Rev. Lett. 53,1951–1953 (1984).
[CrossRef]

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
[CrossRef] [PubMed]

Hermatschweiler, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

Hetherington, D. L.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Ho, C. T.

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14,9013–9019 (2006).
[CrossRef]

Ho, K. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Ibisate, M.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
[CrossRef]

Jin, C. J.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton, New Jersey, Princeton Univ. Press, 1995).

John, S.

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

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.: Condens. Matter. 13,10459–10470 (2001).
[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.: Condens. Matter. 13,10459–10470 (2001).
[CrossRef]

Kurtz, S. R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Ledermann, A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

Lee, J. C. W.

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14,9013–9019 (2006).
[CrossRef]

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

Levine, D.

D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
[CrossRef] [PubMed]

Li, Z. L.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
[CrossRef]

Lifshitz, R.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

Lin, S. Y.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Liu, Z. Y.

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

López, C.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
[CrossRef]

Lubensky, T. C.

D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
[CrossRef] [PubMed]

Ma, R.

R. Ma, J. Xu, and W. Y. Tam, “Wide bandgap photonic structures in dichromate gelatin emulsions,” Appl. Phys. Lett. 89,081116 (2006).
[CrossRef]

Man, B. Y.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
[CrossRef]

Man, W.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436,993–996 (2005).
[CrossRef] [PubMed]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton, New Jersey, Princeton Univ. Press, 1995).

Megens, M.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436,993–996 (2005).
[CrossRef] [PubMed]

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

Meisel, D. C.

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, and G. von Freymann, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography fabrication optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82,1284–1286 (2003).
[CrossRef]

Mermin, N. D.

D. S. Rokhsar, D. C. Wright, and N. D. Mermin, “Scale equivalence of quasicrystallographic space groups,” Phys. Rev. B 37,8145–8149 (1988).
[CrossRef]

Meseguer, F.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
[CrossRef]

Miklyaev, Yu. V.

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, and G. von Freymann, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography fabrication optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82,1284–1286 (2003).
[CrossRef]

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.: Condens. Matter. 13,10459–10470 (2001).
[CrossRef]

Netti, M. C.

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

Ng, C. Y.

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
[CrossRef]

Noda, S.

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36,1907–1911 (1997).
[CrossRef]

Ostlund, S.

D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
[CrossRef] [PubMed]

P. J. Steinhardt and S. Ostlund, The Physics of Quasicrystals (Singapore, World Scientific, 1987).

Ozin, G. A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

Palacios-Lidón, E.

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
[CrossRef]

Pang, Y. K.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14,9013–9019 (2006).
[CrossRef]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Parker, G. J.

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

Pereira, S.

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

Ramaswamy, S.

D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
[CrossRef] [PubMed]

Rokhsar, D. S.

D. S. Rokhsar, D. C. Wright, and N. D. Mermin, “Scale equivalence of quasicrystallographic space groups,” Phys. Rev. B 37,8145–8149 (1988).
[CrossRef]

Rue, R. M. De La

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.: Condens. Matter. 13,10459–10470 (2001).
[CrossRef]

Russel, W. B.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

Sasaki, A.

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36,1907–1911 (1997).
[CrossRef]

Segev, M.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
[CrossRef] [PubMed]

Shechtman, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientataional order and no translational symmetry,” Phys. Rev. Lett. 53,1951–1953 (1984).
[CrossRef]

Sheng, P.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
[CrossRef]

Sigalas, M. M.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Smith, B. K.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Soukoulis, C. M.

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

C. M. Soukoulis, Photonic Bandgap Materials (Dordrecht, Kluwer, 1996).

Stadnik, Z. M.

Z. M. Stadnik, Physical Properties of Quasicrystals (Berlin, Springer, 1999).
[CrossRef]

Steinhardt, P. J.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436,993–996 (2005).
[CrossRef] [PubMed]

D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
[CrossRef] [PubMed]

P. J. Steinhardt and S. Ostlund, The Physics of Quasicrystals (Singapore, World Scientific, 1987).

Su, H. M.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Tam, W. Y.

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14,9013–9019 (2006).
[CrossRef]

W. Y. Tam “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89,251111 and http://arxiv.org/ftp/physics/papers/0609/0609032.pdf (2006).
[CrossRef]

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

R. Ma, J. Xu, and W. Y. Tam, “Wide bandgap photonic structures in dichromate gelatin emulsions,” Appl. Phys. Lett. 89,081116 (2006).
[CrossRef]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
[CrossRef]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Toninelli, C.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
[CrossRef] [PubMed]

Vos, W. L.

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281,802–804 (1998).
[CrossRef]

Wang, H. Z.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Wang, X.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
[CrossRef]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Wegener, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

Wiersma, D. S.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

Wijnhoven, J. E. G. J.

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281,802–804 (1998).
[CrossRef]

Wiltzius, P.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton, New Jersey, Princeton Univ. Press, 1995).

Wright, D. C.

D. S. Rokhsar, D. C. Wright, and N. D. Mermin, “Scale equivalence of quasicrystallographic space groups,” Phys. Rev. B 37,8145–8149 (1988).
[CrossRef]

Xu, J.

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

R. Ma, J. Xu, and W. Y. Tam, “Wide bandgap photonic structures in dichromate gelatin emulsions,” Appl. Phys. Lett. 89,081116 (2006).
[CrossRef]

Xu, J. F.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Yablonovitch, E.

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

Yamamoto, N.

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36,1907–1911 (1997).
[CrossRef]

Yang, S.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

Zeng, Z. H.

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

Zhang, D. Z.

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
[CrossRef]

Zhang, X.

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63,081105/1-4 (2001).
[CrossRef]

Zhang, Z. Q.

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63,081105/1-4 (2001).
[CrossRef]

Zoorob, M. E.

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

Zubrzycki, W.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

Adv. Mat. (1)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mat. 15,1526–1528 (2003).
[CrossRef]

Appl. Phys. Lett. (6)

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, “Realization of optical periodic quasicrystals using holographic lithography,” Appl. Phys. Lett. 88,051901 (2006).
[CrossRef]

W. Y. Tam “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89,251111 and http://arxiv.org/ftp/physics/papers/0609/0609032.pdf (2006).
[CrossRef]

Yu. V. Miklyaev, D. C. Meisel, A. Blanco, and G. von Freymann, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography fabrication optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82,1284–1286 (2003).
[CrossRef]

X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, H. Z. Wang, Y. K. Pang, and W. Y. Tam, “Three-dimensional photonic crystals fabricated by visible light holographic lithography,” Appl. Phys. Lett. 82,2212–2214 (2003).
[CrossRef]

R. Ma, J. Xu, and W. Y. Tam, “Wide bandgap photonic structures in dichromate gelatin emulsions,” Appl. Phys. Lett. 89,081116 (2006).
[CrossRef]

E. Palacios-Lidón, A. Blanco, M. Ibisate, F. Meseguer, and C. López, “Optical study of the full photonic band gap in silicon inverse opals,” Appl. Phys. Lett. 81,4925–4927 (2002).
[CrossRef]

Chem. Mat. (1)

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mat. 14,2831–2833 (2002).
[CrossRef]

J. Phys.: Condens. Matter. (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.: Condens. Matter. 13,10459–10470 (2001).
[CrossRef]

Jpn. J. Appl. Phys. (1)

N. Yamamoto, S. Noda, and A. Sasaki, “New realization method for three-dimensional photonic crystal in the optical wavelength region: experimental consideration,” Jpn. J. Appl. Phys. 36,1907–1911 (1997).
[CrossRef]

Nature (5)

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “Three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394,251–253 (1998).
[CrossRef]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404,53–56 (2000).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440,1166–1169 (2006).
[CrossRef] [PubMed]

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

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436,993–996 (2005).
[CrossRef] [PubMed]

Nature Mater. (2)

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. V. Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nature Mater. 5,942–945 (2006).
[CrossRef]

M. Deuble, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3,444–447 (2004).
[CrossRef]

Opt. Express (1)

Y. K. Pang, J. C. W. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14,9013–9019 (2006).
[CrossRef]

Phys. Rev. B (3)

D. S. Rokhsar, D. C. Wright, and N. D. Mermin, “Scale equivalence of quasicrystallographic space groups,” Phys. Rev. B 37,8145–8149 (1988).
[CrossRef]

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, and D. Z. Zhang, “Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region,” Phys. Rev. B 61,10762–10767 (2000).
[CrossRef]

X. Zhang, Z. Q. Zhang, and C. T. Chan, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B 63,081105/1-4 (2001).
[CrossRef]

Phys. Rev. Lett. (5)

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

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long range orientataional order and no translational symmetry,” Phys. Rev. Lett. 53,1951–1953 (1984).
[CrossRef]

D. Levine, T. C. Lubensky, S. Ostlund, S. Ramaswamy, and P. J. Steinhardt, “Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals,” Phys. Rev. Lett. 54,1520–1523 (1985).
[CrossRef] [PubMed]

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]

Science (1)

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281,802–804 (1998).
[CrossRef]

Other (4)

C. M. Soukoulis, Photonic Bandgap Materials (Dordrecht, Kluwer, 1996).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton, New Jersey, Princeton Univ. Press, 1995).

P. J. Steinhardt and S. Ostlund, The Physics of Quasicrystals (Singapore, World Scientific, 1987).

Z. M. Stadnik, Physical Properties of Quasicrystals (Berlin, Springer, 1999).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Beam configuration for icosahedral quasicrystals. (a) 7-beam configuration for the icosahedral quasicrystal. (b) Icosahedral quasicrystal lattice (red) with φ= 63.4° and the simulated 5-fold (F), 3-fold (U), and 2-fold (P) symmetry projections using 70% intensity cutoff. (c) Actual 7-beam arrangement (for 5-fold symmetry) using a truncated pentagonal prism. (d) Setup for obtaining 2-fold and 3-fold symmetry projections on the surface of photoresist using a pair of prisms.

Fig. 2.
Fig. 2.

Electron micrographs of fabricated icosahedral quasicrystals using incidence angle φ = 63.4° in SU8. (a) Icosahedral quasicrystal lattice using φ = 63.4°. (b) SEM image of the 5-fold symmetry obtained using configuration in Fig. 1(b). (c) SEM image of the 3-fold symmetry obtained using configuration in Fig. 1(c) with prism angle 37.4°. (d) SEM image of the 2-fold symmetry obtained using configuration in Fig. 1(c) with prism angle 31.7°. The upper-left insets in (b-d) are simulated projections of the corresponding symmetries using a 40% intensity cutoff. The circle in (b) shows the 5-fold symmetry. The lower-right inset in (b) is the cross-sectional SEM image of the sample. The lower-left inset, size 60 μm x 80 μm, in (b) is a 5-fold normal reflection image. The scale bars are all 1 μm.

Fig. 3.
Fig. 3.

Electron micrographs of fabricated icosahedral quasicrystals using incidence angle φ = 53.2° in SU8. (a). Icosahedral quasicrystal lattice using φ = 53.2°. (b). SEM image of the 5-fold symmetry obtained using configuration in Fig. 1(b). (c). SEM image of the 3-fold symmetry obtained using configuration in Fig. 1(c) with prism angle 30°. (d). SEM image of the 2-fold symmetry obtained using configuration in Fig. 1(c) with prism angle 30°. The upper-left insets in (b-d) are simulated projections of the corresponding symmetries using a 40% intensity cutoff. The circle in (b) shows the 5-fold symmetry. The lower-right inset in (b) is the cross-sectional SEM image of the sample. The scale bars are all 1 μm.

Fig. 4.
Fig. 4.

Optical measurements of fabricated icosahedral quasicrystals using incidence angle cp = 55.7° in DCG gelatin. (a) Normal reflectance (green) and transmittance (red) of the DCG icosahedral quasicrystal sample using the setup in the top inset. Right inset is a diffraction pattern of icosahedral quasicrystal. Lower-left insets are photos of the normal reflection (top green) and transmission (bottom light purple) from diffuse white light. (b) and (c), Angular transmission spectra for rotation along and perpendicular to the 5-fold axis, respectively. The scale bar on the right is the transmittance. The color lines are bandgaps of reflection planes inside the icosahedral quasicrystal obtained by the reciprocal vectors ∆k0–6 (magenta), ∆k i–6(green), ∆k0–j (red), and ∆k jj (yellow), for i,j= 1–5.

Tables (1)

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Table 1. Structural parameters for the icosahedral quasicrystal. τ = (1 + √5)/2 is the Golden Mean.

Equations (5)

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[ a 0 = ( 0,1 , τ ) = OF ¯ a 1 = ( τ , 0,1 ) = OA ¯ a 2 = ( 1 , τ , 0 ) = OB ¯ a 3 = ( 1 , τ , 0 ) = OC ¯ a 4 = ( τ , 0,1 ) = OD ¯ a 5 = ( 0, 1 , τ ) = OE ¯ ]
[ q 0 = 2 a 0 = ( 0,2,2 τ ) q 1 = a 0 + a 1 = ( τ , 1,1 + τ ) q 2 = a 0 + a 2 = ( 1,1 + τ , τ ) q 3 = a 0 + a 3 = ( 1,1 + τ , τ ) q 4 = a 0 + a 4 = ( τ , 1,1 + τ ) q 5 = a 0 + a 5 = ( 0,0,2 τ ) ]
[ k 0 = ( 0,1 , τ ) k 1 = ( τ , 0, 1 ) k 2 = ( 1 , τ , 0 ) k 3 = ( 1 , τ , 0 ) k 4 = ( τ , 0 , 1 , ) k 5 = ( 0,1 , τ ) k 6 = ( 0, 1 , τ ) = k 0 ]
[ q 0 = k 0 k 6 q n = k 0 k n , n = 1 5 ]
I ( r ) = l , m = 0 6 E l e i k l r i δ l E m * e i k m r + i δ m ,

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