Abstract

We demonstrate theoretically and experimentally a useful technique for fabrication of two- and three-dimensional (2D or 3D) quasi-periodic structures by a double-exposure of a periodic interference pattern. With three-beam and three-beam-plus-one interference techniques, one can fabricate a periodic 2D and 3D structure having six-fold symmetry, respectively. When this structure is duplicated in another orientation, its combination results in a quasi-periodic twelve-fold symmetry structure. Experimental results obtained by using two-exposure of three-beam and/or three-beam-plus-one interference pattern at 442 nm into a positive photoresist (AZ-4620) proved the theoretical predictions. This study is potentially useful for photonic researches and applications.

© 2006 Optical Society of America

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  1. P. J. Steinhardt and S. Ostlund, The Physics of Quasicrystals (World Scientific, Singapore 1987).
  2. Z. M. Stadnik, Physical Properties of Quasicrystals (Springer, Berlin 1999).
    [CrossRef]
  3. 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, 1951-1953 (1984).
    [CrossRef]
  4. 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]
  5. C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
    [CrossRef]
  6. 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]
  7. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
    [CrossRef]
  8. X. Zhang, Z. Q. Zhang, and C. T. Chan, "Absolute photonic bandgaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105R (2001).
    [CrossRef]
  9. M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
    [CrossRef]
  10. 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]
  11. S. Wong, V. Kitaev, and G. A. Ozin, "Colloidal crystal films: Advances in universality and perfection," J. Am. Chem. Soc. 125, 15589-15598 (2003).
    [CrossRef] [PubMed]
  12. V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
    [CrossRef]
  13. 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]
  14. T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
    [CrossRef]
  15. H. B. Sun, S. Matsuo, and H. Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett. 74, 786-788 (1999).
    [CrossRef]
  16. M. Straub and M. Gu, "Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization," Opt. Lett. 27, 1824-1826 (2002).
    [CrossRef]
  17. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, "Large-area two-dimensional mesoscale quasi-crystals," Adv. Mater. 15, 1526-1528 (2003).
    [CrossRef]
  18. J. H. Klein-Wiele and P. Simon, "Fabrication of periodic nanostructures by phase-controlled multiple-beam interference," Appl. Phys. Lett. 83, 4707-4709 (2003).
    [CrossRef]
  19. S. P. Gorkhali, J. Qi, and P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005).
    [CrossRef]
  20. R. C. Gauthier and A. I.vanov, "Production of quasi-crystal template patterns using the dual beam multiple exposure technique," Opt. Express 12, 990-1003 (2004).
    [CrossRef] [PubMed]
  21. 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]
  22. L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
    [CrossRef]
  23. N. D. Lai, W. P. Liang, J. H. Lin, C. C. Hsu, and C. H. Lin, "Fabrication of two- and three-dimensional periodic structures by multi-exposure of two-beam interference technique," Opt. Express 13, 9605-9610 (2005).
    [CrossRef] [PubMed]

2006

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]

2005

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

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

N. D. Lai, W. P. Liang, J. H. Lin, C. C. Hsu, and C. H. Lin, "Fabrication of two- and three-dimensional periodic structures by multi-exposure of two-beam interference technique," Opt. Express 13, 9605-9610 (2005).
[CrossRef] [PubMed]

2003

S. Wong, V. Kitaev, and G. A. Ozin, "Colloidal crystal films: Advances in universality and perfection," J. Am. Chem. Soc. 125, 15589-15598 (2003).
[CrossRef] [PubMed]

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

J. H. Klein-Wiele and P. Simon, "Fabrication of periodic nanostructures by phase-controlled multiple-beam interference," Appl. Phys. Lett. 83, 4707-4709 (2003).
[CrossRef]

2002

M. Straub and M. Gu, "Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization," Opt. Lett. 27, 1824-1826 (2002).
[CrossRef]

M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
[CrossRef]

2001

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

X. Zhang, Z. Q. Zhang, and C. T. Chan, "Absolute photonic bandgaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105R (2001).
[CrossRef]

2000

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]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (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]

1999

H. B. Sun, S. Matsuo, and H. Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett. 74, 786-788 (1999).
[CrossRef]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

1998

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]

1997

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

1984

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, 1951-1953 (1984).
[CrossRef]

Abram, R. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Ban, S.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[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]

Berger, V.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[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, 1951-1953 (1984).
[CrossRef]

Brand, S.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[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, 1951-1953 (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]

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]

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

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

X. Zhang, Z. Q. Zhang, and C. T. Chan, "Absolute photonic bandgaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105R (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]

Cheng, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Costard, E.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Crawford, P.

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

De La Rue, R.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

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]

Gauthier-Lafaye, O.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Gorkhali, S. P.

S. P. Gorkhali, J. Qi, and 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, 1951-1953 (1984).
[CrossRef]

Gu, M.

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]

Hase, M.

M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Hsu, C. C.

Jin, C.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Juodkazis, S.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Kitaev, V.

S. Wong, V. Kitaev, and G. A. Ozin, "Colloidal crystal films: Advances in universality and perfection," J. Am. Chem. Soc. 125, 15589-15598 (2003).
[CrossRef] [PubMed]

Klein-Wiele, J. H.

J. H. Klein-Wiele and P. Simon, "Fabrication of periodic nanostructures by phase-controlled multiple-beam interference," Appl. Phys. Lett. 83, 4707-4709 (2003).
[CrossRef]

Kojima, K. M.

M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Kondo, T.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

Krauss, T. F.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Lai, N. D.

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]

Li, Z.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Liang, W. P.

Lin, C. H.

Lin, J. H.

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]

Man, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[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]

Matsuo, S.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

H. B. Sun, S. Matsuo, and H. Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett. 74, 786-788 (1999).
[CrossRef]

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]

Millar, P.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Misawa, H.

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

H. B. Sun, S. Matsuo, and H. Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett. 74, 786-788 (1999).
[CrossRef]

Miyazaki, H.

M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
[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. Mater. 15, 1526-1528 (2003).
[CrossRef]

Ozin, G. A.

S. Wong, V. Kitaev, and G. A. Ozin, "Colloidal crystal films: Advances in universality and perfection," J. Am. Chem. Soc. 125, 15589-15598 (2003).
[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]

Qi, J.

S. P. Gorkhali, J. Qi, and P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005).
[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, 1951-1953 (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. Mater. 15, 1526-1528 (2003).
[CrossRef]

Shinya, N.

M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Simon, P.

J. H. Klein-Wiele and P. Simon, "Fabrication of periodic nanostructures by phase-controlled multiple-beam interference," Appl. Phys. Lett. 83, 4707-4709 (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]

Straub, M.

Sun, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Sun, H. B.

H. B. Sun, S. Matsuo, and H. Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett. 74, 786-788 (1999).
[CrossRef]

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 quasi-crystals," Adv. Mater. 15, 1526-1528 (2003).
[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]

Uchida, S. I.

M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Wang, G. P.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
[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. Mater. 15, 1526-1528 (2003).
[CrossRef]

Wong, K. S.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

Wong, S.

S. Wong, V. Kitaev, and G. A. Ozin, "Colloidal crystal films: Advances in universality and perfection," J. Am. Chem. Soc. 125, 15589-15598 (2003).
[CrossRef] [PubMed]

Wu, L.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
[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]

Zhang, D.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[CrossRef]

Zhang, X.

X. Zhang, Z. Q. Zhang, and C. T. Chan, "Absolute photonic bandgaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105R (2001).
[CrossRef]

Zhang, Z. Q.

X. Zhang, Z. Q. Zhang, and C. T. Chan, "Absolute photonic bandgaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105R (2001).
[CrossRef]

Zhong, Y.

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
[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]

Adv. Mater.

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

Appl. Phys. Lett.

J. H. Klein-Wiele and P. Simon, "Fabrication of periodic nanostructures by phase-controlled multiple-beam interference," Appl. Phys. Lett. 83, 4707-4709 (2003).
[CrossRef]

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

T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001).
[CrossRef]

H. B. Sun, S. Matsuo, and H. Misawa, "Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin," Appl. Phys. Lett. 74, 786-788 (1999).
[CrossRef]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, "Band gap and wave guiding effect in a quasiperiodic photonic crystal," Appl. Phys. Lett. 75, 1848-1850 (1999).
[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]

L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, "Fabrication of large area two-and three-dimensional polymer photonic crystals using single refracting prism holographic lithography," Appl. Phys. Lett. 86, 241102 (2005).
[CrossRef]

J. Am. Chem. Soc.

S. Wong, V. Kitaev, and G. A. Ozin, "Colloidal crystal films: Advances in universality and perfection," J. Am. Chem. Soc. 125, 15589-15598 (2003).
[CrossRef] [PubMed]

J. Appl. Phys.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Nanotechnology

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Nature

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]

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]

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]

Opt. Express

Opt. Lett.

Phys. Rev. B

X. Zhang, Z. Q. Zhang, and C. T. Chan, "Absolute photonic bandgaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105R (2001).
[CrossRef]

M. Hase, H. Miyazaki, N. Shinya, K. M. Kojima, and S. I. Uchida, "Isotropic photonic bandgap and anisotropic structures in transmission spectra of two-dimensional five fold and eight fold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002).
[CrossRef]

Phys. Rev. Lett.

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, 1951-1953 (1984).
[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]

Other

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

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

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Projection of a multi-surface prism along the z axis. O, A1, A2, and A3 denote the surfaces corresponding to the center beam and three ambient beams, respectively. (b) Three ambient beams after passing through the prism changed their directions, and overlapped with the center beam at one point in the z axis in which a photoresist sample was placed for the fabrication. The sample can be rotated by angle α for multi-exposure.

Fig. 2.
Fig. 2.

Calculated light intensity distribution of the multi-beam interference with two exposures at α = 0° and 90°. (a) 3D view of the 2D quasi-periodic structure. (b) and (c) top views of 2D quasi-periodic structures obtained with two different rotation center positions. (d) 3D view of the 3D quasi-periodic structure. (e) and (f) cross-section views in the xy plan of the 3D quasi-periodic structure obtained at different z positions.

Fig. 3.
Fig. 3.

SEM images of 2D quasi-periodic structures: (a) top view showing the capability of fabricating large area photonic quasi-crystal by interference technique; (b) zoom on a particular area to demonstrate a twelve-fold symmetry level of structures. (c) a 2D quasi-periodic structure obtained with another arbitrary rotation center; (d) the diffraction pattern of these structures. (e) A simulation result of transmission spectra of 2D quasi-periodic structures obtained with different incident angles; a is the lattice constant of corresponding 2D periodic structure (obtained by one exposure) and λ is the wavelength; for the sake of clarity the results at different incident angles have been shifted in the vertical axis by a value of 0.5.

Fig. 4.
Fig. 4.

SEM images of 3D quasi-periodic structures. (a) Top view. The white circle indicates the twelve-fold symmetry in the xy plan of structure. (b) A 3D view showing different layers in the z direction of 3D quasi-periodic structures. Inset of (b) shows the diffraction pattern of the 3D quasi-periodic structures

Equations (1)

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I multi exposure = n I α n ,

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