OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 23 — Aug. 10, 2007
  • pp: 5645–5648

Fabrication of highly rotational symmetric quasi-periodic structures by multiexposure of a three-beam interference technique

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

Applied Optics, Vol. 46, Issue 23, pp. 5645-5648 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (860 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A simple and efficient interference method for fabricating highly symmetric two-dimensional (2-D) quasi-periodic structures (QPSs) is theoretically and experimentally demonstrated. With a three-beam interference technique, one can fabricate a periodic 2-D structure having sixfold symmetry. When this structure is multiduplicated into other specific orientations its combination results in a QPS with multifold symmetry. By use of n exposures with a rotation angle of 60 ° / n , one can create a 2-D QPS with six n-fold symmetry. The QPS with a super high symmetry level, as high as 60-fold, is demonstrated for the first time to the best of our knowledge. The diffraction pattern of a QPS is consistent with the Fourier transform calculation. The fabricated structures should be useful for many applications, such as isotropic bandgap materials and extraction enhancement of light-emitting diodes.

© 2007 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: March 8, 2007
Revised Manuscript: May 2, 2007
Manuscript Accepted: May 30, 2007
Published: August 8, 2007

Ngoc Diep Lai, Jian Hung Lin, and Chia Chen Hsu, "Fabrication of highly rotational symmetric quasi-periodic structures by multiexposure of a three-beam interference technique," Appl. Opt. 46, 5645-5648 (2007)

Sort:  Year  |  Journal  |  Reset  


  1. 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]
  2. 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]
  3. P. L. Hagelstein and D. R. Denison, "Nearly isotropic photonic bandgap structures in two dimensions," Opt. Lett. 24, 708-710 (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. C. Jin, B. Cheng, B. Man, Z. Li, and D. Zhang, "Two-dimensional dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region," Phys. Rev. B 61, 10762-10767 (2000). [CrossRef]
  6. S. David, A. Chelnokov, and J.-M. Lourtioz, "Wide angularly isotropic photonic bandgaps obtained from two-dimensional photonic crystals with Archimedean-like tilings," Opt. Lett. 25, 1001-1003 (2000). [CrossRef]
  7. X. Zhang, Z.-Q. Zhang, and C. T. Chan, "Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals," Phys. Rev. B 63, 081105 (2001). [CrossRef]
  8. M. Hase, H. Miyazaki, M. Egashira, N. Shinya, K. M. Kojima, and S.-I. Uchida, "Isotropic photonic band gap and anisotropic structures in transmission spectra of two-dimensional fivefold and eightfold symmetric quasiperiodic photonic crystals," Phys. Rev. B 66, 214205 (2002). [CrossRef]
  9. 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]
  10. V. Berger, O. Gauthier-Lafaye, and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997). [CrossRef]
  11. 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]
  12. 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]
  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. S. P. Gorkhali, J. Qi, and G. P. Crawford, "Electrically switchable mesoscale Penrose quasicrystal structure," Appl. Phys. Lett. 86, 011110 (2005). [CrossRef]
  15. 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]
  16. N. D. Lai, J. H. Lin, Y. Y. Huang, and C. C. Hsu, "Fabrication of two- and three-dimensional quasi-periodic structures with 12-fold symmetry by interference technique," Opt. Express 14, 10746-10752 (2006). [CrossRef] [PubMed]
  17. 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, 9605-9611 (2005). [CrossRef] [PubMed]
  18. C. S. Vikram, W. K. Witherow, and J. D. Trolinger, "Fringe contrast and phase effects in multi-colour holography," J. Mod. Opt. 41, 1531-1536 (1994). [CrossRef]
  19. A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, "Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice," Phys. Rev. Lett. 94, 183903 (2005). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited