Abstract

We present a dual beam multiple exposure technique that can generate complex 2-D quasi-crystal template structures. The optical system is based on the interference of two laser beams producing a family of high intensity planes. Controlled reorientation of a photosensitive sample between exposures results in an exposure dose, when developed, returns a quasi-crystal pattern. Results are shown in which quasi-crystal patterns with 8, 10, and 12-fold rotation symmetry are produced in photoresist. The results of several test runs are shown in which the quasi-crystal patterns developed in photoresist are subsequently etched into silicon. Based on an extended application of the dual beam multiple exposure optical system, a potential technique for producing 3-D quasi-crystal patterns is presented.

© 2004 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  2. S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
    [Crossref] [PubMed]
  3. See for instance; K. Sakoda, Optical properties of photonic crystals, (Springer-Verlag Berlin2001)
  4. See for instance; M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of photonic crystal optical waveguides,” J. Opt. Laser Technol. 18, 1402–1411 (2000).
  5. Y. S. Chan, C. T. Chang, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).
    [Crossref]
  6. Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
    [Crossref]
  7. X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
    [Crossref]
  8. M. Koshiba and K. Saitoh, “Finite-element analysis of birefringence and dispersion in actual an idealized holey fiber structures,” Appl. Opt. 42, 6267–6275 (2003).
    [Crossref] [PubMed]
  9. 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]
  10. 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, 4091–4098 (1999).
    [Crossref]
  11. L. Z. Cai, X. L. Yang, and Y. R. Wang, “Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A 19, 2238–2244 (2002).
    [Crossref]
  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. 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]
  14. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).
  15. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).
  16. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
    [Crossref] [PubMed]
  17. J. D. Joannopoulus, R. D. Meade, and J. N. Winn, Photonic crystals; Modeling the flow of light, (Princeton University Press, 1995).
  18. S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mater. 14, 2831–2833 (2002).
    [Crossref]
  19. Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

2003 (3)

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]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

M. Koshiba and K. Saitoh, “Finite-element analysis of birefringence and dispersion in actual an idealized holey fiber structures,” Appl. Opt. 42, 6267–6275 (2003).
[Crossref] [PubMed]

2002 (3)

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

L. Z. Cai, X. L. Yang, and Y. R. Wang, “Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A 19, 2238–2244 (2002).
[Crossref]

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[Crossref]

2001 (2)

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[Crossref]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

2000 (4)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

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

See for instance; M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of photonic crystal optical waveguides,” J. Opt. Laser Technol. 18, 1402–1411 (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, 53–56 (2000).
[Crossref] [PubMed]

1999 (2)

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]

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, 4091–4098 (1999).
[Crossref]

1998 (1)

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

1994 (1)

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[Crossref] [PubMed]

1987 (1)

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

Abram, R. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Aizenberg, J.

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

Baumerg, J. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, 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. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Brand, S.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Busch, K.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Cai, L. Z.

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.

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

Chan, C. T.

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]

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, 4091–4098 (1999).
[Crossref]

Chan, Y. S.

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

Chang, C. T.

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[Crossref]

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

Cheng, B.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[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]

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, 4091–4098 (1999).
[Crossref]

De La Rue, R.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

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. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Doll, T.

See for instance; M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of photonic crystal optical waveguides,” J. Opt. Laser Technol. 18, 1402–1411 (2000).

Enrich, C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

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]

Jin, C.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[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]

Joannopoulus, J. D.

J. D. Joannopoulus, R. D. Meade, and J. N. Winn, Photonic crystals; Modeling the flow of light, (Princeton University Press, 1995).

John, S.

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[Crossref] [PubMed]

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Kock, W.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Koshiba, M.

Krauss, T. F.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Li, J.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[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, 4091–4098 (1999).
[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]

Liu, Z. Y.

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

Loncar, M.

See for instance; M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of photonic crystal optical waveguides,” J. Opt. Laser Technol. 18, 1402–1411 (2000).

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]

Meade, R. D.

J. D. Joannopoulus, R. D. Meade, and J. N. Winn, Photonic crystals; Modeling the flow of light, (Princeton University Press, 1995).

Megens, M.

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

Meisel, D. C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Meng, X.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[Crossref]

Miklyaev, Y. V.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Millar, P.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

Netti, M. C.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumerg, 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]

Ouyang, Z.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[Crossref]

Parker, G. J.

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

Quang, T.

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[Crossref] [PubMed]

Russel, W. B.

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

Saitoh, K.

Sakoda, K.

See for instance; K. Sakoda, Optical properties of photonic crystals, (Springer-Verlag Berlin2001)

Scherer, A.

See for instance; M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of photonic crystal optical waveguides,” J. Opt. Laser Technol. 18, 1402–1411 (2000).

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]

Sheng, P.

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]

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]

Tam, W. 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]

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]

von Freymann, G.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Vuckovic, J.

See for instance; M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of photonic crystal optical waveguides,” J. Opt. Laser Technol. 18, 1402–1411 (2000).

Wang, X.

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]

Wang, Y. R.

Wegener, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Wiltzius, P.

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

Winn, J. N.

J. D. Joannopoulus, R. D. Meade, and J. N. Winn, Photonic crystals; Modeling the flow of light, (Princeton University Press, 1995).

Yablonovitch, E.

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

Yang, G.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[Crossref]

Yang, S.

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

Yang, X. L.

Zhang, D.

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[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]

Zhang, X.

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[Crossref]

Zhang, Z. Q.

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[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, 4091–4098 (1999).
[Crossref]

Zoorob, M. E.

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

Adv. Mater. (1)

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. Opt. (1)

Appl. Phys. Lett. (2)

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]

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Kock, C. Enrich, 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]

Chem. Mater. (1)

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

J. Mod. Opt. (2)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “The design of two-dimensional photonic quasicrystals by means of a Fourier transform method,” J. Mod. Opt. 48, 9–14 (2001).

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. De La Rue, and P. Millar, “Two-dimensional Penrose-tiled photonic quasicrystals; diffraction of light and fractal density of modes,” J. Mod. Opt. 47, 1771–1778 (2000).

J. Opt. A: Pure Appl. Opt. (1)

Z. Ouyang, C. Jin, D. Zhang, B. Cheng, X. Meng, G. Yang, and J. Li, “Photonic bandgaps in two-dimensional short-range periodic structures,” J. Opt. A: Pure Appl. Opt. 4, 23–28 (2002).
[Crossref]

J. Opt. Laser Technol. (1)

See for instance; M. Loncar, T. Doll, J. Vuckovic, and A. Scherer, “Design and fabrication of photonic crystal optical waveguides,” J. Opt. Laser Technol. 18, 1402–1411 (2000).

J. Opt. Soc. Am. A (1)

Nature (2)

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. Baumerg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404, 740–743 (2000).
[Crossref] [PubMed]

Phys. Rev. A (1)

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[Crossref] [PubMed]

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, 4091–4098 (1999).
[Crossref]

Phys. Rev. B. (1)

X. Zhang, Z. Q. Zhang, and C. T. Chang, “Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals,” Phys. Rev. B. 63, 081105-1 to 081105-5 (2001).
[Crossref]

Phys. Rev. Lett. (2)

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

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

Other (2)

J. D. Joannopoulus, R. D. Meade, and J. N. Winn, Photonic crystals; Modeling the flow of light, (Princeton University Press, 1995).

See for instance; K. Sakoda, Optical properties of photonic crystals, (Springer-Verlag Berlin2001)

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Figures (11)

Fig. 1.
Fig. 1.

Experimental dual beam multiple exposure optical system. The blue line of the Argon Ion laser is linearly polarized and divided into two equal intensity beams. These beams are recombined producing an interference pattern in a photosensitive material. The three rotation and translation stages allow the accurate orientation and positioning of the interference pattern relative to previous exposure steps.

Fig. 2.
Fig. 2.

Interface planes used in the production of an 8-fold quasi-crystal pattern. (A) Extend view of the intersecting planes indicating zones where the 4 planes overlap. (B) Enlarged view of the central region of (A) and (C) is a 3-D view of the interference planes extending through the thickness of the exposed material.

Fig. 3.
Fig. 3.

Simulation of the exposed pattern in the photosensitive material when a threshold level of 8 out of a maximum of 16 selected. All exposure levels below 8 are in black and levels above 8 are in white. The 8-fold symmetry about the central point and other plane coincidence locations is clearly visible in the figure.

Fig. 4.
Fig. 4.

Image of the 8-fold symmetry pattern produced using 4 exposures of the dual beam multiple exposure experimental system. The intersected projection of the two arrows indicates the center of the pattern. About the center 8-fold rotational symmetry is observed. Dimension bar shown inclined to correspond to orientation of the quasi-crystal pattern.

Fig. 5.
Fig. 5.

Image of the 10-fold rotational symmetry pattern produced through 5 equal time exposures. (A) Extended view of the 10-fold pattern, experimental. (B) Orientation of the family of exposure planes taken about the center. (C) Computed exposure pattern about the center (exposure threshold of 10 out of a maximum of 20).

Fig. 6.
Fig. 6.

12-fold rotational symmetry pattern produced using 6 equal time exposures. (A) Extended view of the 12-fold pattern, experimental. (B) Orientation of the family of exposure planes taken about the center. (C) Computed exposure pattern about the center (exposure threshold of 12 out of a maximum of 24). (D) Expanded view of the central region of the experimentally obtained 12-fold pattern of (A).

Fig. 7.
Fig. 7.

Eight-fold (left) and 12-fold (right) quasi-crystal patterns produced and etched into a silicon wafer. Etch is 1 µm deep.

Fig. 8.
Fig. 8.

Quasi-crystal patterns produced using a lower threshold of 6 out of 16 for the 8-fold symmetry (A) theory, (B) experimental. A highly interconnected pattern results. Quasi-crystal patterns produced using a lower threshold of 10 out of 16 for the 8-fold symmetry (C) theory, (D) experimental. A disconnected pattern results.

Fig. 9.
Fig. 9.

Experimentally obtained diffraction patterns for the (A) 8-fold, (B) 10-fold and (C) 12-fold quasi-crystal patterns experimentally produced and displayed in Fig. 4, 5, and 6 respectively. The diffraction patterns display the rotational symmetry associated with the corresponding quasi-crystal pattern.

Fig. 10.
Fig. 10.

View of the interference planes required producing the three axes 8-fold symmetric 3-D quasi-crystal pattern. There are 4 sets of intersection planes oriented at angles of 0, 45, 90 and 135 degrees about each of the three mutually perpendicular axes.

Fig. 11.
Fig. 11.

3-D view and (x, y) plane slices of the 8-fold 3 axis quasi-crystal pattern produced using the interference planes of Fig. 10. Slices are in 0.1-micron increments along the z-axis starting at A1 (z=0 microns) to C3 (z=1.0 microns). Increment sequence is A1, A2, A3, A4, B1, B2, B3, B4, C1, C2 and C3. The center of the pattern in A1 corresponds to the coordinate origin.

Equations (5)

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I j = E j 1 2 + E j 2 2 + 2 F j 1 E j 2 cos ( θ j 12 ) cos ( [ k j 1 k j 2 ] r + φ o j 1 + φ o j 2 )
A j x + B j y + C j z + D j = 0
D j = ( φ o j 1 φ o j 2 ) + w j λ ( 1 2 ) 2 + ( m 1 m 2 ) 2 + ( n 1 n 2 ) 2
N = R 2 , θ = 360 R , t = 2 * t total R
( Step ) ( Euler angels ) ( 1 2 3 4 5 6 7 8 9 ) = ( 0 0 0 45 0 0 90 0 0 135 0 0 90 45 0 90 90 0 90 135 0 90 45 90 90 135 90 )

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