Abstract

We present a theoretical study of new two-dimensional photonic crystals based on Archimedean-like tilings. Three structures are considered: a square lattice with a 4-atom unit cell and triangular lattices with 7- and 13-atom unit cells. A 12-fold local rotational symmetry is obtained for the triangular lattices and is approached for the square lattice. Wide photonic bandgaps can then be achieved, with very weak bandwidth dependence 1% on the wave-propagation direction. The complete bandgap frequency is shown to depend on the atomic bond length and not on the crystal period. This new class of periodic photonic crystals is a simple and attractive alternative to photonic quasi crystals.

© 2000 Optical Society of America

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References

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  1. Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
    [Crossref]
  2. M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
    [Crossref]
  3. S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, Phys. Rev. B 59, 4091 (1999).
    [Crossref]
  4. M. Senechal, Quasicrystals and Geometry (Cambridge U. Press, Cambridge, 1995).
  5. P. Pearce, Structure in Nature Is a Strategy for Design (MIT Press, Cambridge, Mass., 1978).
  6. K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
    [Crossref] [PubMed]

2000 (1)

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
[Crossref]

1999 (1)

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, Phys. Rev. B 59, 4091 (1999).
[Crossref]

1998 (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[Crossref] [PubMed]

Baumeberg, J. J.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
[Crossref]

Chan, C. T.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, Phys. Rev. B 59, 4091 (1999).
[Crossref]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[Crossref] [PubMed]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

Charleton, M. D. B.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
[Crossref]

Cheng, S. S. M.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, Phys. Rev. B 59, 4091 (1999).
[Crossref]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[Crossref] [PubMed]

Li, L. M.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, Phys. Rev. B 59, 4091 (1999).
[Crossref]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

Netti, M. C.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
[Crossref]

Parker, G. J.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
[Crossref]

Pearce, P.

P. Pearce, Structure in Nature Is a Strategy for Design (MIT Press, Cambridge, Mass., 1978).

Senechal, M.

M. Senechal, Quasicrystals and Geometry (Cambridge U. Press, Cambridge, 1995).

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[Crossref] [PubMed]

Zhang, Z. Q.

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, Phys. Rev. B 59, 4091 (1999).
[Crossref]

Zoorob, M. E.

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
[Crossref]

Mater. Sci. Eng. B (1)

M. E. Zoorob, M. D. B. Charleton, G. J. Parker, J. J. Baumeberg, and M. C. Netti, Mater. Sci. Eng. B 74, 1/3168 (2000).
[Crossref]

Phys. Rev. B (1)

S. S. M. Cheng, L. M. Li, C. T. Chan, and Z. Q. Zhang, Phys. Rev. B 59, 4091 (1999).
[Crossref]

Phys. Rev. Lett. (2)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[Crossref]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
[Crossref] [PubMed]

Other (2)

M. Senechal, Quasicrystals and Geometry (Cambridge U. Press, Cambridge, 1995).

P. Pearce, Structure in Nature Is a Strategy for Design (MIT Press, Cambridge, Mass., 1978).

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Figures (3)

Fig. 1
Fig. 1

(left) Semiregular (Archimedean-like) photonic crystals and (right) their associated Brillouin zones. (a) Square lattice with a 4-atom unit cell. (b) Triangular lattice with a 7-atom unit cell. (c) Triangular lattice with a 13-atom unit cell. For (left) each crystal, the lattice mesh is indicated by thick dashed lines, and atomic bonds are represented by thin solid lines. The thick solid lines in (right) the reciprocal lattices correspond to the crystal directions probed in the band diagram calculations (see Fig. 3, below).

Fig. 2
Fig. 2

Diffraction pattern calculated for the Archimedean-like tiling of Fig. 1(a). Inset, diffraction pattern calculated for a regular square lattice with atomic bonds of the same length a. Circles of radius nπ/a (where n is an integer) serve as guides for the eye.

Fig. 3
Fig. 3

Band diagrams of the Archimedean-like photonic crystals shown in Fig. 1 calculated for TE and TM polarizations: (a) Square lattice with a 4-atom unit cell. (b) Triangular lattice with a 7-atom unit cell. (c) Triangular lattice with a 13-atom unit cell. The photonic structures consist of low-permittivity =1 cylinders (pores) in a high-permittivity =12 dielectric material. In the three cases the air filling is 75%. The gray bars show the complete bandgaps.

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