Abstract

Photonic quasicrystals (PQs) can produce interesting photonic properties. However, the exact prediction on photonic band structures (PBSs) of the PQs is currently a fundamental challenge due to the lack of periodicity of the structures. Here, we propose a kind of complex periodic two-dimensional photonic crystal (PC) structures constructed with a small portion of different PQs for the purposes of overcoming the difficulty of numerical calculations on the PBSs but maintaining the photonic properties of the original PQs owned. Theoretically calculated results on PBSs of the complex PCs with a local feature consistent with 12-fold rotational symmetry show that, in the cases of dielectric cylinders in air, air-holes in a dielectric, and metal cylinders in air, respectively, the complex PCs can indeed produce similar photonic properties of the original 12-fold PQs such as the uniform or isotropic PBGs under much lower dielectric contrast etc. Because the complex PCs can be constructed with the local parts of any high symmetric PQs, we believe that the PCs presented in this article may provide a way for creating novel photonic functional materials.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  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 (2001).
    [CrossRef]
  7. M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
    [CrossRef]
  8. K. Wang, "Light wave states in two-dimensional quasiperiodic media," Phys. Rev. B 73, 235122 (2006).
    [CrossRef]
  9. D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
    [CrossRef]
  10. X. Wang, C. Y. Ng, W. T. Tam, C. T. Chan and P. Sheng, "Large-area two-dimensional mesoscale quasi-crystals," Adv. Mater. 15, 1526-1528 (2003).
    [CrossRef]
  11. Y. Yang, S. Zhang, and G. P. Wang, "Fabrication of two-dimensional metallodielectric quaiscrystals by single-beam holography," Appl. Phys. Lett. 88, 251104 (2006).
    [CrossRef]
  12. Y. Yang and G. P. Wang, "Realization of periodic and quasiperiodic microstructures with sub-diffraction-limit feature sizes by far-field holographic lithography," Appl. Phys. Lett. 89, 111104 (2006).
    [CrossRef]
  13. K. M. Leung and Y. F. Liu, "Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
    [CrossRef] [PubMed]
  14. M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
    [CrossRef]
  15. P. R. Villeneuve and M. Piche, "Photonic bandgaps: What is best numerical representation of periodic structures," J. Mod. Opt. 41, 241-256 (1994).
    [CrossRef]
  16. V. Kuzmiak, A. A. Maradudin and F. Pincemin, "Photonic band structures of two -dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).
    [CrossRef]
  17. C. M. Anderson and K. P. Giapis, "Large two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2951 (1996).
    [CrossRef] [PubMed]
  18. Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2576 (1998).
    [CrossRef]
  19. J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
    [CrossRef]
  20. W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
    [CrossRef] [PubMed]

2006 (4)

K. Wang, "Light wave states in two-dimensional quasiperiodic media," Phys. Rev. B 73, 235122 (2006).
[CrossRef]

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
[CrossRef]

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

Y. Yang and G. P. Wang, "Realization of periodic and quasiperiodic microstructures with sub-diffraction-limit feature sizes by far-field holographic lithography," Appl. Phys. Lett. 89, 111104 (2006).
[CrossRef]

2005 (1)

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]

2003 (1)

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

2001 (1)

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]

2000 (4)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

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]

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

1999 (2)

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]

1998 (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]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2576 (1998).
[CrossRef]

1996 (1)

C. M. Anderson and K. P. Giapis, "Large two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2951 (1996).
[CrossRef] [PubMed]

1994 (2)

P. R. Villeneuve and M. Piche, "Photonic bandgaps: What is best numerical representation of periodic structures," J. Mod. Opt. 41, 241-256 (1994).
[CrossRef]

V. Kuzmiak, A. A. Maradudin and F. Pincemin, "Photonic band structures of two -dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).
[CrossRef]

1991 (1)

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
[CrossRef]

1990 (1)

K. M. Leung and Y. F. Liu, "Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Abram, R. A.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Anderson, C. M.

C. M. Anderson and K. P. Giapis, "Large two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2951 (1996).
[CrossRef] [PubMed]

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]

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, 740-743 (2000).
[CrossRef] [PubMed]

Beggs, D. M.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
[CrossRef]

Brand, S.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

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, 993-996 (2005).
[CrossRef] [PubMed]

Chan, C. T.

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

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]

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

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]

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]

Chan, Y. C.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

Chan, Y. S.

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]

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, 740-743 (2000).
[CrossRef] [PubMed]

Cheng, 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]

Cheng, S. S. M.

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]

DeLa Rue, R.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Giapis, K. P.

C. M. Anderson and K. P. Giapis, "Large two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2951 (1996).
[CrossRef] [PubMed]

Gu, B. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2576 (1998).
[CrossRef]

Jin, C.

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]

Kaliteevski, M. A.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
[CrossRef]

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Kam, C. H.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

Krauss, T. F.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin and F. Pincemin, "Photonic band structures of two -dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).
[CrossRef]

Lam, Y. L.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

Lei, X. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

Leung, K. M.

K. M. Leung and Y. F. Liu, "Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Li, L.

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]

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]

Li, Z. Y.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2576 (1998).
[CrossRef]

Liu, Y. F.

K. M. Leung and Y. F. Liu, "Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

Liu, Z. Y.

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]

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]

Man, W.

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]

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin and F. Pincemin, "Photonic band structures of two -dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).
[CrossRef]

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
[CrossRef]

Megens, M.

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]

Millar, P.

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

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, 740-743 (2000).
[CrossRef] [PubMed]

Ng, C. Y.

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

Ng, S. L.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[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, 740-743 (2000).
[CrossRef] [PubMed]

Piche, M.

P. R. Villeneuve and M. Piche, "Photonic bandgaps: What is best numerical representation of periodic structures," J. Mod. Opt. 41, 241-256 (1994).
[CrossRef]

Pincemin, F.

V. Kuzmiak, A. A. Maradudin and F. Pincemin, "Photonic band structures of two -dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).
[CrossRef]

Plihal, M.

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
[CrossRef]

Que, W. X.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

Roper, D. T.

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
[CrossRef]

Sheng, P.

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

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[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, 993-996 (2005).
[CrossRef] [PubMed]

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. T.

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

Tam, W. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

P. R. Villeneuve and M. Piche, "Photonic bandgaps: What is best numerical representation of periodic structures," J. Mod. Opt. 41, 241-256 (1994).
[CrossRef]

Wang, G. P.

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

Y. Yang and G. P. Wang, "Realization of periodic and quasiperiodic microstructures with sub-diffraction-limit feature sizes by far-field holographic lithography," Appl. Phys. Lett. 89, 111104 (2006).
[CrossRef]

Wang, K.

K. Wang, "Light wave states in two-dimensional quasiperiodic media," Phys. Rev. B 73, 235122 (2006).
[CrossRef]

Wang, X.

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

Wang, Z. L.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

Yang, G. Z.

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2576 (1998).
[CrossRef]

Yang, Y.

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

Y. Yang and G. P. Wang, "Realization of periodic and quasiperiodic microstructures with sub-diffraction-limit feature sizes by far-field holographic lithography," Appl. Phys. Lett. 89, 111104 (2006).
[CrossRef]

Zhang, D.

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, H.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

Zhang, S.

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

Zhang, W. Y.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

Zhang, X.

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]

Zhang, Z. Q.

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]

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]

Zheng, D. G.

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

Zhou, Y.

J. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

Zoorob, M. E.

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]

Adv. Mater. (1)

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

Appl. Phys. Lett. (4)

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

Y. Yang and G. P. Wang, "Realization of periodic and quasiperiodic microstructures with sub-diffraction-limit feature sizes by far-field holographic lithography," Appl. Phys. Lett. 89, 111104 (2006).
[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. Zhou, Y. Zhou, S. L. Ng, H. Zhang, W. X. Que, Y. L. Lam, Y. C. Chan, and C. H. Kam, "Three-dimensional photonic band gap structure of a polymer-metal composite," Appl. Phys. Lett. 76, 3337-3339 (2000).
[CrossRef]

J. Mod. Opt. (2)

D. T. Roper, D. M. Beggs, M. A. Kaliteevski, S. Brand and R. A. Abram, "Properties of two-dimensional photonic crystals with octagonal quasicrystalline unit cells," J. Mod. Opt. 53, 407-416 (2006).
[CrossRef]

P. R. Villeneuve and M. Piche, "Photonic bandgaps: What is best numerical representation of periodic structures," J. Mod. Opt. 41, 241-256 (1994).
[CrossRef]

Nanotechnology (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, T. F. Krauss, R. DeLa Rue, and P. Millar, "Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure," Nanotechnology 11, 274-280 (2000).
[CrossRef]

Nature (2)

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]

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]

Phys. Rev. B (5)

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]

K. Wang, "Light wave states in two-dimensional quasiperiodic media," Phys. Rev. B 73, 235122 (2006).
[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]

V. Kuzmiak, A. A. Maradudin and F. Pincemin, "Photonic band structures of two -dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).
[CrossRef]

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B 44, 8565-8571 (1991).
[CrossRef]

Phys. Rev. Lett. (5)

W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, " Robust photonic band gap from tunable scatterers," Phys. Rev. Lett. 84, 2853-2856 (2000).
[CrossRef] [PubMed]

C. M. Anderson and K. P. Giapis, "Large two-dimensional photonic band gaps," Phys. Rev. Lett. 77, 2949-2951 (1996).
[CrossRef] [PubMed]

Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574-2576 (1998).
[CrossRef]

K. M. Leung and Y. F. Liu, "Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media," Phys. Rev. Lett. 65, 2646-2649 (1990).
[CrossRef] [PubMed]

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]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(color online) Scheme of the proposed 2D PC structures constructed with a portion of 12-fold symmetric PQ (orange circles). The primitive cell (dark diamonds) included seven cylinders is defined by two primitive translation vectors a1 and a2 .Six cylinders surrounded the central one are at positions u1, -u1,u2, -u2 ,u3 and -u3 , respectively.

Fig. 2.
Fig. 2.

(color online) Calculated PBSs of the proposed 2D PCs constructed with a portion of 12-fold symmetric PQ with dielectric cylinders (ε a =13 and R/a =0.35) in air (ε b =1) for (a) H- and (b) E- polarized modes, respectively. The PBGs are indicated with pink shadow.

Fig. 3.
Fig. 3.

(color online) Calculated PBSs of the proposed 2D PCs constructed with a portion of 12-fold symmetric PQ with air-holes (ε a =1 and R/a =0.47) in a dielectric background (ε b =13) for E- polarization. The PBGs are indicated with pink shadow.

Fig. 4.
Fig. 4.

(color online) Calculated PBSs of the proposed 2D PCs constructed with a portion of 12-fold symmetric PQ with metal cylinders (R/a =0.45) in air for E- polarization. Two large PBGs are indicated with pink shadow.

Equations (5)

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

det ( κ ω 2 c 2 ) = 0
ε ( G ) = f ε a + ( 1 f ) ε b , G = 0
ε ( G ) = 2 ( ε a ε b ) ( 1 + 2 i = 1 3 cos ( G u i ) ) f 0 J 1 ( GR ) ( GR ) , G 0
ε ( G ) = 1 f ω p 2 ω 2 , G = 0
ε ( G ) = 2 ( ω p 2 ω 2 ) ( 1 + 2 i = 1 3 cos ( G u i ) ) f 0 J 1 ( GR GR ) , G 0

Metrics