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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 22 — Oct. 30, 2006
  • pp: 10746–10752

Fabrication of two- and three-dimensional quasi-periodic structures with 12-fold symmetry by interference technique

Ngoc Diep Lai, Jian Hung Lin, Yi Ya Huang, and Chia Chen Hsu  »View Author Affiliations

Optics Express, Vol. 14, Issue 22, pp. 10746-10752 (2006)

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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

OCIS Codes
(090.0090) Holography : Holography
(110.5220) Imaging systems : Photolithography
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.4000) Optical design and fabrication : Microstructure fabrication
(260.3160) Physical optics : Interference

ToC Category:
Optical Design and Fabrication

Original Manuscript: August 9, 2006
Revised Manuscript: October 11, 2006
Manuscript Accepted: October 11, 2006
Published: October 30, 2006

Ngoc D. Lai, Jian H. Lin, Yi Y. Huang, and Chia C. Hsu, "Fabrication of two- and three-dimensional quasi-periodic structures with 12-fold symmetry by interference technique," Opt. Express 14, 10746-10752 (2006)

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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]

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