Abstract

Recently important efforts have been dedicated to the realization of a new kind of photonic crystals, known as photonic quasicrystals, in which the lack of the translational symmetry is compensated by rotational symmetries not achievable by the conventional periodic crystals. Here we show a novel approach to their fabrication based on the use of a programmable Spatial Light Modulator encoding Computer-Generated Holograms. Using this single beam technique we fabricated Penrose-tiled structures possessing rotational symmetry up to 23-fold, and a two-dimensional Thue-Morse structure, which is an aperiodic structure not achievable by multiple beam holography.

© 2008 Optical Society of America

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References

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  1. D. Levine and P. J. Steinhartdt, "Quasicrystals: a new class of ordered structures," Phys. Rev. Lett. 53, 2477-2480 (1984).
    [CrossRef]
  2. P. J. Steinhartdt and S. Ostlund, (eds.) The Physics of Quasicrystals (Word Scientific, River Edge, NJ, 1987).
  3. Z. M. Stadnik, (eds.) Physical Properties of Quasicrystals (Springer, New York, 1999).
    [CrossRef]
  4. 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]
  5. Y. S. Chan, C. T. Chan, and Z. Y. Liu, "Photonic band gaps in two-dimensional photonic quasicrystals," Phys. Rev. Lett. 80, 956-959 (1998).
    [CrossRef]
  6. X. Zhang, Z. Q. Zhang, and C. T. Chan, "Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105/1-4 (2001).
    [CrossRef]
  7. S. S. M. Cheng, L. Li, C. T. Chan, and Z. Q. Zhang, "Defect and transmission properties of two-dimensional quasiperiodic photonic band-gap systems," Phys. Rev. B 59, 4091- 4099 (1999).
    [CrossRef]
  8. 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]
  9. 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]
  10. V. Berger, O. Gauthier-Lafaye, and E. Costard, "Fabrication of a 2D photonic band gap by a holographic method," Electron. Lett. 33, 425-426 (1997).
    [CrossRef]
  11. X. Wang, C. Y. Ng, W. Y. Tam, C. T. Chan, and P. Sheng, "Large-area two-dimensional mesoscale quasicrystals," Adv. Mater. 15, 1526-1528 (2003).
    [CrossRef]
  12. R. C. Gauthier and A. Ivanov, "Production of quasicrystal template patterns using a dual beam multiple exposure technique," Opt. Express 12, 990-1003 (2004).
    [CrossRef] [PubMed]
  13. 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, 051901/1-3 (2006).
    [CrossRef]
  14. S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110/1-3 (2005).
    [CrossRef]
  15. Y. Yang, S. Zhang, and G. P. Wang, "Fabrication of two-dimensional metallodielectric quasicrystals by single-beam holography," Appl. Phyis. Lett. 88, 251104/1-3 (2006).
    [CrossRef]
  16. S. P. Gorkhali, J. Qi, and G. P. Crawford, "Switchable quasicrystal structures with five-, seven-, and ninefold symmetries," J. Opt. Soc. Am. B 23, 149-158 (2006).
    [CrossRef]
  17. E. Macià, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006).
    [CrossRef]
  18. F. Axel and H. Terauchi, "High-resolution X-ray-diffraction spectra of Thue-Morse GaAs-AlAs heterostructures: towards a novel description of disorder," Phys. Rev. Lett. 66, 2223-2226 (1991).
    [CrossRef] [PubMed]
  19. F. Axel and H. Terauchi, "Axel and Terauchi reply," Phys. Rev. Lett. 73,1308-1308 (1994).
    [CrossRef] [PubMed]
  20. M. Kolar, "High-resolution X-ray-diffraction spectra of Thue-Morse GaAs-AlAs heterostructures," Phys. Rev. Lett. 73, 1307-1307 (1994).
    [CrossRef] [PubMed]
  21. L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
    [CrossRef]
  22. H. Y. Lee and G. Y. Nam, "Realization of ultrawide omnidirectional photonic band gap in multiple one-dimensional photonic crystals," J. Appl. Phys. 100, 083501/1-5 (2006).
    [CrossRef]
  23. H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, "Photonic band gap structures in the Thue-Morse lattice," Phys. Rev B 75, 205109/1-10 (2007).
    [CrossRef]
  24. L. Moretti and V. Mocella, "Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence," Opt. Express 15, 15314-15323 (2007).
    [CrossRef] [PubMed]
  25. V. A. Soifer, (eds.) Methods for Computer Design of Diffractive Optical Elements (John Wiley & Sons, Inc., New York, 2002).
  26. G. Lee, S. H. Song, C. -H. Oh, and P. -S. Kim, "Arbitrary structuring of two-dimensional photonic crystals by use of phase-only Fourier gratings," Opt. Lett. 29, 2539-2541 (2004).
    [CrossRef] [PubMed]
  27. W. Mao, G. Liang, H. Zou, R. Zhang, H. Wang, and Z. Zeng, "Design and fabrication of two-dimensional holographic photonic quasi crystals with high-order symmetries," J. Opt. Soc. Am. B 23, 2046-2050 (2006).
    [CrossRef]
  28. G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, "Computer-generated holographic gratings in soft matter," Mol. Cryst. Liq. Cryst. 465, 371-378 (2007).
    [CrossRef]
  29. J. W. Goodman, (eds.) Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  30. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, "Encoding amplitude information onto phase-only filters," Appl. Opt. 38, 5004-5013 (1999).
    [CrossRef]
  31. R. L. Sutherland, L.V. Natarajan, V. P. Tondiglia, and T. J. Bunning, "Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes," Chem. Mater. 5, 1533-1538 (1993).
    [CrossRef]
  32. F. Vita, A. Marino, V. Tkachenko, G. Abbate, D. E. Lucchetta, L. Criante, and F. Simoni, "Visible and near-infrared characterization and modeling of nanosized holographic-polymer-dispersed liquid crystal gratings," Phys. Rev. E 72, 011702/1-8 (2005).
    [CrossRef]
  33. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, "Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals," J. Phys.: Condens. Matter 13, 10459-10470 (2001).
    [CrossRef]
  34. B. Apter, Y. David, I. Baal-Zedaka, and U. Efron, "Experimental study and computer simulation of ultra-small-pixel liquid crystal device," presented at the Eleventh Meeting on Optical Engineering and Science, Tel Aviv, Israel, 26-27 March 2007.

2007

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, "Photonic band gap structures in the Thue-Morse lattice," Phys. Rev B 75, 205109/1-10 (2007).
[CrossRef]

L. Moretti and V. Mocella, "Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence," Opt. Express 15, 15314-15323 (2007).
[CrossRef] [PubMed]

G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, "Computer-generated holographic gratings in soft matter," Mol. Cryst. Liq. Cryst. 465, 371-378 (2007).
[CrossRef]

2006

H. Y. Lee and G. Y. Nam, "Realization of ultrawide omnidirectional photonic band gap in multiple one-dimensional photonic crystals," J. Appl. Phys. 100, 083501/1-5 (2006).
[CrossRef]

W. Mao, G. Liang, H. Zou, R. Zhang, H. Wang, and Z. Zeng, "Design and fabrication of two-dimensional holographic photonic quasi crystals with high-order symmetries," J. Opt. Soc. Am. B 23, 2046-2050 (2006).
[CrossRef]

Y. Yang, S. Zhang, and G. P. Wang, "Fabrication of two-dimensional metallodielectric quasicrystals by single-beam holography," Appl. Phyis. Lett. 88, 251104/1-3 (2006).
[CrossRef]

S. P. Gorkhali, J. Qi, and G. P. Crawford, "Switchable quasicrystal structures with five-, seven-, and ninefold symmetries," J. Opt. Soc. Am. B 23, 149-158 (2006).
[CrossRef]

E. Macià, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006).
[CrossRef]

X. Wang, J. Xu, J. C. W. Lee, Y. K. Pang, W. Y. Tam, C. T. Chan, and P. Sheng, "Realization of optical periodic quasicrystals using holographic lithography," Appl. Phys. Lett. 88, 051901/1-3 (2006).
[CrossRef]

2005

S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110/1-3 (2005).
[CrossRef]

F. Vita, A. Marino, V. Tkachenko, G. Abbate, D. E. Lucchetta, L. Criante, and F. Simoni, "Visible and near-infrared characterization and modeling of nanosized holographic-polymer-dispersed liquid crystal gratings," Phys. Rev. E 72, 011702/1-8 (2005).
[CrossRef]

2004

2003

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

2001

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

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, "Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals," J. Phys.: Condens. Matter 13, 10459-10470 (2001).
[CrossRef]

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. 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

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

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]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, "Encoding amplitude information onto phase-only filters," Appl. Opt. 38, 5004-5013 (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, "Fabrication of a 2D photonic band gap by a holographic method," Electron. Lett. 33, 425-426 (1997).
[CrossRef]

1994

F. Axel and H. Terauchi, "Axel and Terauchi reply," Phys. Rev. Lett. 73,1308-1308 (1994).
[CrossRef] [PubMed]

M. Kolar, "High-resolution X-ray-diffraction spectra of Thue-Morse GaAs-AlAs heterostructures," Phys. Rev. Lett. 73, 1307-1307 (1994).
[CrossRef] [PubMed]

1993

R. L. Sutherland, L.V. Natarajan, V. P. Tondiglia, and T. J. Bunning, "Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes," Chem. Mater. 5, 1533-1538 (1993).
[CrossRef]

1991

F. Axel and H. Terauchi, "High-resolution X-ray-diffraction spectra of Thue-Morse GaAs-AlAs heterostructures: towards a novel description of disorder," Phys. Rev. Lett. 66, 2223-2226 (1991).
[CrossRef] [PubMed]

1984

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

Adv. Mater.

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

Appl. Opt.

Appl. Phyis. Lett.

Y. Yang, S. Zhang, and G. P. Wang, "Fabrication of two-dimensional metallodielectric quasicrystals by single-beam holography," Appl. Phyis. Lett. 88, 251104/1-3 (2006).
[CrossRef]

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, 051901/1-3 (2006).
[CrossRef]

S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110/1-3 (2005).
[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]

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, "Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasicrystals," Appl. Phys. Lett. 84, 5186-5188 (2004).
[CrossRef]

Chem. Mater.

R. L. Sutherland, L.V. Natarajan, V. P. Tondiglia, and T. J. Bunning, "Bragg gratings in an acrylate polymer consisting of periodic polymer-dispersed liquid-crystal planes," Chem. Mater. 5, 1533-1538 (1993).
[CrossRef]

Electron. Lett.

V. Berger, O. Gauthier-Lafaye, and E. Costard, "Fabrication of a 2D photonic band gap by a holographic method," Electron. Lett. 33, 425-426 (1997).
[CrossRef]

J. Appl. Phys.

H. Y. Lee and G. Y. Nam, "Realization of ultrawide omnidirectional photonic band gap in multiple one-dimensional photonic crystals," J. Appl. Phys. 100, 083501/1-5 (2006).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys.: Condens. Matter

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, P. Millar, and R. M. De La Rue, "Diffraction and transmission of light in low-refractive index Penrose-tiled photonic quasicrystals," J. Phys.: Condens. Matter 13, 10459-10470 (2001).
[CrossRef]

Mol. Cryst. Liq. Cryst.

G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, "Computer-generated holographic gratings in soft matter," Mol. Cryst. Liq. Cryst. 465, 371-378 (2007).
[CrossRef]

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, 53-56 (2000).
[CrossRef] [PubMed]

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

Opt. Express

Opt. Lett.

Phys. Rev B

H. Lei, J. Chen, G. Nouet, S. Feng, Q. Gong, and X. Jiang, "Photonic band gap structures in the Thue-Morse lattice," Phys. Rev B 75, 205109/1-10 (2007).
[CrossRef]

Phys. Rev. B

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

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

Phys. Rev. E

F. Vita, A. Marino, V. Tkachenko, G. Abbate, D. E. Lucchetta, L. Criante, and F. Simoni, "Visible and near-infrared characterization and modeling of nanosized holographic-polymer-dispersed liquid crystal gratings," Phys. Rev. E 72, 011702/1-8 (2005).
[CrossRef]

Phys. Rev. Lett.

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

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

F. Axel and H. Terauchi, "High-resolution X-ray-diffraction spectra of Thue-Morse GaAs-AlAs heterostructures: towards a novel description of disorder," Phys. Rev. Lett. 66, 2223-2226 (1991).
[CrossRef] [PubMed]

F. Axel and H. Terauchi, "Axel and Terauchi reply," Phys. Rev. Lett. 73,1308-1308 (1994).
[CrossRef] [PubMed]

M. Kolar, "High-resolution X-ray-diffraction spectra of Thue-Morse GaAs-AlAs heterostructures," Phys. Rev. Lett. 73, 1307-1307 (1994).
[CrossRef] [PubMed]

Rep. Prog. Phys.

E. Macià, "The role of aperiodic order in science and technology," Rep. Prog. Phys. 69, 397-441 (2006).
[CrossRef]

Other

P. J. Steinhartdt and S. Ostlund, (eds.) The Physics of Quasicrystals (Word Scientific, River Edge, NJ, 1987).

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

B. Apter, Y. David, I. Baal-Zedaka, and U. Efron, "Experimental study and computer simulation of ultra-small-pixel liquid crystal device," presented at the Eleventh Meeting on Optical Engineering and Science, Tel Aviv, Israel, 26-27 March 2007.

V. A. Soifer, (eds.) Methods for Computer Design of Diffractive Optical Elements (John Wiley & Sons, Inc., New York, 2002).

J. W. Goodman, (eds.) Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Penrose-tiled quasicrystal structure with 8-fold rotational symmetry and phase set 1 (φi =0, for i={1,…,8}); (b) Penrose-tiled structure with 8-fold symmetry and phase set 2 (φ2= φ4 =φ6 =φ8 =π/2+φ, where φ represents the phase of the remaining beams). (a)–(b) Top left inset: calculated irradiance profile (IP), top right inset: 2D Fourier transform (FT) of the irradiance profile, bottom inset: observed diffraction pattern (DP); d estimates the self-similarity cell size of the structures.

Fig. 2.
Fig. 2.

(a) Penrose-tiled quasicrystal structure with 9-fold rotational symmetry, (b) 10-fold symmetry, (c) 12-fold symmetry, (d) 17-fold symmetry, (e) 23-fold symmetry. (f) Two-dimensional Thue-Morse quasicrystal structure. (a)–(f) Top left inset: calculated irradiance profile (IP), top right inset: 2D Fourier transform (FT) of the irradiance profile, bottom inset: observed diffraction pattern (DP); d estimates the self-similarity cell size of the structures.

Equations (3)

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

I ( r ) = m = 1 N n = 1 N A m A n * exp [ i ( k m k n ) · r + i ( φ m φ n ) ] ,
k m = 2 π n λ ( sin ( 2 π m N ) sin θ , cos ( 2 π m N ) sin θ , cos θ ) ,
M n + 1 = ( I n , n M n , n M n , n M n , n I n , n M n , n ) , I n , n = ( 1 11 1 1 n 1 n 1 1 nn ) ,

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