Abstract

From group theory, we have deduced the minimum number of laser beams to create corresponding two-dimensional photonic quasilattices with high-order symmetries. One case is that a quasi-periodicity with eightfold, tenfold, or twelvefold symmetry can be formed by only five linearly polarized beams, which can reduce fabrication complexity and considerably improve feasibility. Accordingly, we have fabricated large-area eightfold and twelvefold photonic quasi crystals by use of a minimum beam single-exposure holographic lithography technique. The high-order symmetries of the fabricated microstructures are confirmed by scanning electron microscopy images and diffraction patterns.

© 2006 Optical Society of America

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  1. D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1954 (1984).
    [CrossRef]
  2. D. Levine and P. J. Steinhardt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
    [CrossRef]
  3. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  4. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  5. Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-969 (1998).
    [CrossRef]
  6. S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4099 (1999).
    [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. 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]
  9. 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]
  10. 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]
  11. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
    [CrossRef] [PubMed]
  12. 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]
  13. W. D. Mao, J. W. Dong, Y. C. Zhong, G. Q. Liang, and H. Z. Wang, "Formation principles of two-dimensional compound photonic lattices by one-step holographic lithography," Opt. Express 13, 2994-2999 (2005).
    [CrossRef] [PubMed]
  14. Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]
  15. Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
    [CrossRef]
  16. W. D. Mao, G. Q. Liang, H. Zou, and H. Z. Wang, "Controllable fabrication of two-dimensional compound photonic crystals by single-exposure holographic lithography," Opt. Lett. 31, 1708-1710 (2006).
    [CrossRef] [PubMed]
  17. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, "Large-area two-dimensional mesoscale quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
    [CrossRef]
  18. R. C. Gauthier and A. Ivanov, "Production of quasi-crystal template patterns using a dual beam multiple exposure technique," Opt. Express 12, 990-1003 (2004).
    [CrossRef] [PubMed]
  19. S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005).
    [CrossRef]
  20. 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]
  21. D. A. Rabson, N. D. Mermin, D. S. Rokhsar, and D. C. Wright, "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733 (1991).
    [CrossRef]

2006 (2)

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. D. Mao, G. Q. Liang, H. Zou, and H. Z. Wang, "Controllable fabrication of two-dimensional compound photonic crystals by single-exposure holographic lithography," Opt. Lett. 31, 1708-1710 (2006).
[CrossRef] [PubMed]

2005 (5)

W. D. Mao, J. W. Dong, Y. C. Zhong, G. Q. Liang, and H. Z. Wang, "Formation principles of two-dimensional compound photonic lattices by one-step holographic lithography," Opt. Express 13, 2994-2999 (2005).
[CrossRef] [PubMed]

S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005).
[CrossRef]

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (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]

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 (2)

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]

R. C. Gauthier and A. Ivanov, "Production of quasi-crystal template patterns using a dual beam multiple exposure technique," Opt. Express 12, 990-1003 (2004).
[CrossRef] [PubMed]

2003 (2)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, "Large-area two-dimensional mesoscale quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
[CrossRef]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

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]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

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]

1999 (1)

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4099 (1999).
[CrossRef]

1998 (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-969 (1998).
[CrossRef]

1991 (1)

D. A. Rabson, N. D. Mermin, D. S. Rokhsar, and D. C. Wright, "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733 (1991).
[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]

1984 (2)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1954 (1984).
[CrossRef]

D. Levine and P. J. Steinhardt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

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]

Blanco, A.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1954 (1984).
[CrossRef]

Busch, K.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1954 (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]

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]

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]

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 quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
[CrossRef]

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4099 (1999).
[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-969 (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, 956-969 (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, J. M.

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
[CrossRef]

Chen, Y. L.

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
[CrossRef]

Cheng, S. S. M.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4099 (1999).
[CrossRef]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Crawford, G. P.

S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005).
[CrossRef]

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]

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]

Deubel, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

Dong, J. W.

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]

Enkrich, C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

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]

Galdi, V.

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.

Gorkhali, S. P.

S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005).
[CrossRef]

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, "Metallic phase with long-range orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1954 (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]

Ivanov, A.

John, S.

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

Koch, W.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

Lee, J. C. W.

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 and P. J. Steinhardt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

Li, L. M.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4099 (1999).
[CrossRef]

Liang, G. Q.

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, 956-969 (1998).
[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]

Mao, W. D.

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]

Meisel, D. C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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. A. Rabson, N. D. Mermin, D. S. Rokhsar, and D. C. Wright, "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733 (1991).
[CrossRef]

Miklyaev, Y. V.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

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 quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
[CrossRef]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

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]

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]

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]

Pierro, V.

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]

Qi, J.

S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005).
[CrossRef]

Rabson, D. A.

D. A. Rabson, N. D. Mermin, D. S. Rokhsar, and D. C. Wright, "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733 (1991).
[CrossRef]

Rokhsar, D. S.

D. A. Rabson, N. D. Mermin, D. S. Rokhsar, and D. C. Wright, "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733 (1991).
[CrossRef]

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 orientational order and no translational symmetry," Phys. Rev. Lett. 53, 1951-1954 (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 quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
[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 and P. J. Steinhardt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
[CrossRef]

Su, H. M.

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
[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).
[CrossRef] [PubMed]

Tam, W. Y.

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 quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
[CrossRef]

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).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

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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]

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Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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).
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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).
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X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, "Large-area two-dimensional mesoscale quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
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Wegener, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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).
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D. A. Rabson, N. D. Mermin, D. S. Rokhsar, and D. C. Wright, "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733 (1991).
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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).
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S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

Zeng, Z. H.

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
[CrossRef]

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S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4099 (1999).
[CrossRef]

Zhong, Y. C.

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
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Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
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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).
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Adv. Mater. (Weinheim, Ger.) (1)

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, "Large-area two-dimensional mesoscale quasicrystals," Adv. Mater. (Weinheim, Ger.) 15, 1526-1528 (2003).
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[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]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. VonFreymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, "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]

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
[CrossRef]

Nature (3)

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]

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).
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[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091-4099 (1999).
[CrossRef]

Phys. Rev. Lett. (7)

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]

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D. Levine and P. J. Steinhardt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
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[CrossRef]

Rev. Mod. Phys. (1)

D. A. Rabson, N. D. Mermin, D. S. Rokhsar, and D. C. Wright, "The space groups of axial crystals and quasicrystals," Rev. Mod. Phys. 63, 699-733 (1991).
[CrossRef]

Science (1)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, "Full three-dimensional photonic bandgap crystals at near-infrared wavelengths," Science 289, 604-606 (2000).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Beam geometry for generating photonic quasi crystals. Five linearly polarized laser beams are incident from the same quarter space.

Fig. 2
Fig. 2

In the semicircle, three kinds of wave-vector configurations projected on the x y plane can be used to construct photonic quasi lattices for (a) eightfold, (b) tenfold, and (c) twelvefold symmetries, respectively.

Fig. 3
Fig. 3

(a) Scanning electron microscopy image of a polymeric photonic quasi crystal with eightfold symmetry. (b) Diffraction pattern of the sample by He–Ne laser confirms the eightfold symmetry. (c) Low magnification view of (a), exhibiting the large-area uniform quasiperiodicity of the sample.

Fig. 4
Fig. 4

Scanning electron microscopy images of twelvefold symmetric 2D Penrose photonic quasi crystals. (a) A twelvefold symmetric photonic quasiperiodic microstructure. (b) Another twelvefold symmetric quasi lattice obtained by different polarization configuration, revealing greater complexity of the microstructure. The left-side view reveals well-defined features of micropores through the depth of the sample. (c) Low magnification view of (a). The inset is the diffraction pattern of the sample.

Equations (3)

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ν = ϕ ( N ) = N ( p 1 1 ) p 1 ( p 2 1 ) p 2 ,
I ( r ) = i , j E i E j * e i ( k i k j ) r ,
k n = ( cos 2 n π N , sin 2 n π N ) , n = 0 4 ,

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