Abstract

Large-area three-dimensional Penrose-type photonic quasicrystals are fabricated through a holographic lithography method using a lab-made diffractive optical element and a single laser exposure. The diffractive optical element consists of five polymer gratings symmetrically orientated around a central opening. The fabricated Penrose-type photonic quasicrystal shows ten-fold rotational symmetry. The Laue diffraction pattern from the photonic quasi-crystal is observed to be similar to that of the traditional alloy quasi-crystal. A golden ratio of 1.618 is also observed for the radii of diffraction rings, which has not been observed before in artificial photonic quasicrystals.

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
    [CrossRef] [PubMed]
  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(6779), 740–743 (2000).
    [CrossRef] [PubMed]
  4. W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
    [CrossRef] [PubMed]
  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(6690), 251–253 (1998).
    [CrossRef]
  6. J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281(5378), 802–804 (1998).
    [CrossRef]
  7. M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
    [CrossRef] [PubMed]
  8. 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(6773), 53–56 (2000).
    [CrossRef] [PubMed]
  9. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
    [CrossRef] [PubMed]
  10. S. P. Gorkhali, J. Qi, and G. P. Grawford, “Electrically switchable mesoscale Penrose quasicrystal structure,” Appl. Phys. Lett. 86(1), 011110 (2005).
    [CrossRef]
  11. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
    [CrossRef]
  12. 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(5), 051901 (2006).
    [CrossRef]
  13. W. Y. Tam, “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89(25), 251111 (2006).
    [CrossRef]
  14. J. Xu, R. Ma, X. Wang, and W. Y. Tam, “Icosahedral quasicrystals for visible wavelengths by optical interference holography,” Opt. Express 15(7), 4287–4295 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-7-4287 .
    [CrossRef] [PubMed]
  15. Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett . 86, 071117/1–3 (2005).
    [CrossRef]
  16. Y. Lin, A. Harb, D. Rodriguez, K. Lozano, D. Xu, and K. P. Chen, “Fabrication of two-layer integrated phase mask for single-beam and single-exposure fabrication of three-dimensional photonic crystal,” Opt. Express 16(12), 9165–9172 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-9165 .
    [CrossRef] [PubMed]
  17. N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
    [CrossRef]
  18. 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(20), 1951–1953 (1984).
    [CrossRef]
  19. D. Levine and P. J. Steinhardt, “Quasicrystal: a new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
    [CrossRef]

2008

2007

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(5), 051901 (2006).
[CrossRef]

W. Y. Tam, “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89(25), 251111 (2006).
[CrossRef]

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
[CrossRef]

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

2005

S. P. Gorkhali, J. Qi, and G. P. Grawford, “Electrically switchable mesoscale Penrose quasicrystal structure,” Appl. Phys. Lett. 86(1), 011110 (2005).
[CrossRef]

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[CrossRef] [PubMed]

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett . 86, 071117/1–3 (2005).
[CrossRef]

2004

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[CrossRef] [PubMed]

2003

X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, “Large-area two-dimensional mesoscale quasi-crystals,” Adv. Mater. 15(18), 1526–1528 (2003).
[CrossRef]

2000

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(6773), 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(6779), 740–743 (2000).
[CrossRef] [PubMed]

1998

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(6690), 251–253 (1998).
[CrossRef]

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281(5378), 802–804 (1998).
[CrossRef]

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

1984

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(20), 1951–1953 (1984).
[CrossRef]

D. Levine and P. J. Steinhardt, “Quasicrystal: a new class of ordered structures,” Phys. Rev. Lett. 53(26), 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(6779), 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(6690), 251–253 (1998).
[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(20), 1951–1953 (1984).
[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(6690), 251–253 (1998).
[CrossRef]

Busch, K.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[CrossRef] [PubMed]

Cademartiri, L.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

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(20), 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(6773), 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(7053), 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(5), 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(18), 1526–1528 (2003).
[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(6779), 740–743 (2000).
[CrossRef] [PubMed]

Chen, K. P.

Darmawikarta, K.

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett . 86, 071117/1–3 (2005).
[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(6773), 53–56 (2000).
[CrossRef] [PubMed]

Deubel, M.

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
[CrossRef]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[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(6690), 251–253 (1998).
[CrossRef]

Gorkhali, S. P.

S. P. Gorkhali, J. Qi, and G. P. Grawford, “Electrically switchable mesoscale Penrose quasicrystal structure,” Appl. Phys. Lett. 86(1), 011110 (2005).
[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(20), 1951–1953 (1984).
[CrossRef]

Grawford, G. P.

S. P. Gorkhali, J. Qi, and G. P. Grawford, “Electrically switchable mesoscale Penrose quasicrystal structure,” Appl. Phys. Lett. 86(1), 011110 (2005).
[CrossRef]

Harb, A.

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(6773), 53–56 (2000).
[CrossRef] [PubMed]

Herman, P. R.

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett . 86, 071117/1–3 (2005).
[CrossRef]

Hermatschweiler, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (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(6690), 251–253 (1998).
[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(6690), 251–253 (1998).
[CrossRef]

John, S.

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

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(6690), 251–253 (1998).
[CrossRef]

Ledermann, A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

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(5), 051901 (2006).
[CrossRef]

Levine, D.

D. Levine and P. J. Steinhardt, “Quasicrystal: a new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[CrossRef]

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(6690), 251–253 (1998).
[CrossRef]

Lin, Y.

Y. Lin, A. Harb, D. Rodriguez, K. Lozano, D. Xu, and K. P. Chen, “Fabrication of two-layer integrated phase mask for single-beam and single-exposure fabrication of three-dimensional photonic crystal,” Opt. Express 16(12), 9165–9172 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-9165 .
[CrossRef] [PubMed]

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett . 86, 071117/1–3 (2005).
[CrossRef]

Lozano, K.

Ma, R.

Man, W.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[CrossRef] [PubMed]

Megens, M.

W. Man, M. Megens, P. J. Steinhardt, and P. M. Chaikin, “Experimental measurement of the photonic properties of icosahedral quasicrystals,” Nature 436(7053), 993–996 (2005).
[CrossRef] [PubMed]

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(6779), 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(18), 1526–1528 (2003).
[CrossRef]

Ozin, G. A.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
[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(5), 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(6779), 740–743 (2000).
[CrossRef] [PubMed]

Pereira, S.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[CrossRef] [PubMed]

Perez-Willard, F.

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
[CrossRef]

Qi, J.

S. P. Gorkhali, J. Qi, and G. P. Grawford, “Electrically switchable mesoscale Penrose quasicrystal structure,” Appl. Phys. Lett. 86(1), 011110 (2005).
[CrossRef]

Rodriguez, D.

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(6773), 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(20), 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(5), 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(18), 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(6690), 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(6690), 251–253 (1998).
[CrossRef]

Soukoulis, C. M.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[CrossRef] [PubMed]

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(7053), 993–996 (2005).
[CrossRef] [PubMed]

D. Levine and P. J. Steinhardt, “Quasicrystal: a new class of ordered structures,” Phys. Rev. Lett. 53(26), 2477–2480 (1984).
[CrossRef]

Tam, W. Y.

J. Xu, R. Ma, X. Wang, and W. Y. Tam, “Icosahedral quasicrystals for visible wavelengths by optical interference holography,” Opt. Express 15(7), 4287–4295 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-7-4287 .
[CrossRef] [PubMed]

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(5), 051901 (2006).
[CrossRef]

W. Y. Tam, “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89(25), 251111 (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(18), 1526–1528 (2003).
[CrossRef]

Tereault, N.

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
[CrossRef]

Toninelli, C.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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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(6773), 53–56 (2000).
[CrossRef] [PubMed]

von Freymann, G.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
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N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
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M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
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J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281(5378), 802–804 (1998).
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J. Xu, R. Ma, X. Wang, and W. Y. Tam, “Icosahedral quasicrystals for visible wavelengths by optical interference holography,” Opt. Express 15(7), 4287–4295 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-7-4287 .
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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(5), 051901 (2006).
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Wegener, M.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
[CrossRef]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[CrossRef] [PubMed]

Wiersma, D. S.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

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J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281(5378), 802–804 (1998).
[CrossRef]

Xu, D.

Xu, J.

J. Xu, R. Ma, X. Wang, and W. Y. Tam, “Icosahedral quasicrystals for visible wavelengths by optical interference holography,” Opt. Express 15(7), 4287–4295 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-7-4287 .
[CrossRef] [PubMed]

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(5), 051901 (2006).
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E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
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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(6779), 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(6690), 251–253 (1998).
[CrossRef]

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(18), 1526–1528 (2003).
[CrossRef]

N. Tereault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mater. 18(4), 457–460 (2006).
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Appl. Phys. Lett

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett . 86, 071117/1–3 (2005).
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Appl. Phys. Lett.

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(5), 051901 (2006).
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W. Y. Tam, “Icosahedral quasicrystals by optical interference holography,” Appl. Phys. Lett. 89(25), 251111 (2006).
[CrossRef]

S. P. Gorkhali, J. Qi, and G. P. Grawford, “Electrically switchable mesoscale Penrose quasicrystal structure,” Appl. Phys. Lett. 86(1), 011110 (2005).
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Nat. Mater.

A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. 5(12), 942–945 (2006).
[CrossRef] [PubMed]

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004).
[CrossRef] [PubMed]

Nature

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(6773), 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(6779), 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(7053), 993–996 (2005).
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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(6690), 251–253 (1998).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Science

J. E. G. J. Wijnhoven and W. L. Vos, “Preparation of photonic crystals made of air spheres in titania,” Science 281(5378), 802–804 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) The scheme for the lab fabricated diffractive optical element. Each of the five oriented gratings has the structure as imaged by AFM in (b) with a periodicity of 0.781 μm as measured by the section analysis (c).

Fig. 2
Fig. 2

(a) Laser experimental setup for the holographic lithography; (b) Enlarged view of the lab-made DOE and beam propagation for generating the six-beam interference for the holographic fabrication of photonic quasi-crystals.

Fig. 3
Fig. 3

(a, b) SEM image of the holographically formed photonic quasicrystal at both large (a) and small (b) scales. (a) Inserts are simulation on the right side and eye-guidance pentagons in the middle. (b) Overlay geometries provide eye-guidance in establishing the symmetry and tiling. (c) SEM image of cross-section of the holographically formed photonic quasicrystal and (d) the simulation of formed 3D structures.

Fig. 4
Fig. 4

(a) Laue diffraction pattern from the photonic quasicrystal using 532 nm laser. The diffraction spots are connected using pentagon and form ghost-face like pattern. (b) Projections of the wave vectors (in black) on the plane perpendicular to the ko direction. The first and second order reciprocal vectors are represented by pink lines and blue lines, respectively.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I = i = 1 6 E i 2 + i < j 6 E i E j cos     [ ( k i k j ) r + Δ δ i j ]                                      
k 0 = K ( 0 ,     0 , 1 )                                                   
k n = K ( sin α cos ( 4 n + 1 ) π 10 , sin α sin ( 4 n + 1 ) π 10 , cos α ) ,     for n = 1-5
Δ k n = k n 1 k n 2 = 2 K sin α     cos ( 3 π 10 ) ( cos 2 n π 5 , sin 2 n π 5 , 0 )

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