Abstract

The probability to realize a full photonic band gap in two-dimensional birefringent photonic crystals can be readily manipulated by introducing symmetry reduction or air holes in the crystal elements. The results lie in either creation of new band gaps or enlargement of existing band gaps. In particular, a combination of the two processes produces an effect much stronger than a simple summation of their individual contributions. Materials with both relatively low refractive index (rutile) and high refractive index (tellurium) were considered. The combined effect of introduction of symmetry reduction and air holes resulted in a maximum enlargement of the band gaps by 8.4% and 20.2%, respectively, for the two materials.

© 2008 Optical Society of America

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References

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  1. S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
    [CrossRef] [PubMed]
  2. S. A. Rinnie, F. G. Santamaria, and P. V. Braun, "Embedded cavities and waveguides in three dimensional silicon photonic crystal," Nat. Photonics 8, 52 (2008).
    [CrossRef]
  3. J. C. Knight, "Photonic crystal fibres," Nature (London) 424, 6950 (2003).
    [CrossRef]
  4. S. T. Huntington, B. C. Gibson, J. Canning, K. Digweed-Lyytik¨ainen, J. D. Love, and V. Steblina, "A fractal-based fibre for ultra-high throughput optical probes," Opt. Express 15, 2468 (2007).
    [CrossRef] [PubMed]
  5. Y. Akahane, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425, 944 (2003),
    [CrossRef]
  6. H. Takano, B. S. Song, T. Asano, and S. Noda, "Highly efficient multi-channel drop filter in a two dimensional hetero photonic crystal," Opt. Express 14, 3491 (2006).
    [CrossRef] [PubMed]
  7. D. L. Bullock, C. Shih, and R. S. Marguilies, "Photonic band structure investigation of two-dimensional Bragg reflector mirrors for semiconductor laser mode control," J. Opt. Soc. Am. B 10, 399 (1993).
    [CrossRef]
  8. S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).
  9. D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134 (1996).
    [CrossRef]
  10. Z. Y. Li, B. Y. Gu, and G. Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett. 81, 2574 (1998).
    [CrossRef]
  11. S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).
  12. C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 40, 2949 (1996).
    [CrossRef]
  13. T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
    [CrossRef]
  14. N. Malkova, S. Kim, T. Dilazaro, and V. Gopalon, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B 67, 125203 (2003).
    [CrossRef]
  15. K. P. Chang and S. L. Yang, "Photonic band gap of two-dimensional triangular photonic crystals with broken structural and rotational symmetries," J. Appl. Phys. 100, 073104 (2006).
    [CrossRef]
  16. T. Pan and Z. Y. Li, "The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals," Solid State Commun. 128, 187 (2003).
    [CrossRef]
  17. T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
    [CrossRef]
  18. T. Pan, F. Zhuang, and Z. Y. Li, "Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods," Sol. State Comm. 129, 501 (2004).
    [CrossRef]
  19. B. Rezaei and M. Klafi, "Engineering absolute band gap in anisotropic hexagonal photonic crystals," Opt. Commun. 266, 159 (2006).
    [CrossRef]
  20. E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic Press, Inc., 1991).
  21. Y. Yamada, H. Uyama, S. Watanabe, and H. Nozoye, "Deposition at low substrate temperatures of high-quality TiO2 films by radical beam-assisted evaporation," Appl. Opt. 38, 6638 (1999).
    [CrossRef]
  22. K. Sakoda, ed., Optical Properties of Photonic Crystals (Springer, 2001).
  23. In fact, it is more appropriate to talk about Crystal Systems instead of Bravais Lattices. Indeed, the symmetry level of a lattice with translational invariance is dictated by the corresponding crystal system. However we have chosen to use the Bravais lattice terminology to avoid confusion in the text. Besides, this approximation can work well if we consider that the fourteen Bravais lattices are intimately related to the seven crystal systems that are defined in three dimensions.

2008

S. A. Rinnie, F. G. Santamaria, and P. V. Braun, "Embedded cavities and waveguides in three dimensional silicon photonic crystal," Nat. Photonics 8, 52 (2008).
[CrossRef]

2007

2006

H. Takano, B. S. Song, T. Asano, and S. Noda, "Highly efficient multi-channel drop filter in a two dimensional hetero photonic crystal," Opt. Express 14, 3491 (2006).
[CrossRef] [PubMed]

K. P. Chang and S. L. Yang, "Photonic band gap of two-dimensional triangular photonic crystals with broken structural and rotational symmetries," J. Appl. Phys. 100, 073104 (2006).
[CrossRef]

B. Rezaei and M. Klafi, "Engineering absolute band gap in anisotropic hexagonal photonic crystals," Opt. Commun. 266, 159 (2006).
[CrossRef]

2005

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).

2004

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
[CrossRef]

T. Pan, F. Zhuang, and Z. Y. Li, "Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods," Sol. State Comm. 129, 501 (2004).
[CrossRef]

2003

S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalon, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B 67, 125203 (2003).
[CrossRef]

T. Pan and Z. Y. Li, "The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals," Solid State Commun. 128, 187 (2003).
[CrossRef]

Y. Akahane, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425, 944 (2003),
[CrossRef]

J. C. Knight, "Photonic crystal fibres," Nature (London) 424, 6950 (2003).
[CrossRef]

1999

1998

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

1996

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 40, 2949 (1996).
[CrossRef]

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134 (1996).
[CrossRef]

1993

Akahane, Y.

Y. Akahane, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425, 944 (2003),
[CrossRef]

Alcubilla, R.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
[CrossRef]

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
[CrossRef]

Anderson, C. M.

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 40, 2949 (1996).
[CrossRef]

Asano, T.

H. Takano, B. S. Song, T. Asano, and S. Noda, "Highly efficient multi-channel drop filter in a two dimensional hetero photonic crystal," Opt. Express 14, 3491 (2006).
[CrossRef] [PubMed]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).

Bertho, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134 (1996).
[CrossRef]

Braun, P. V.

S. A. Rinnie, F. G. Santamaria, and P. V. Braun, "Embedded cavities and waveguides in three dimensional silicon photonic crystal," Nat. Photonics 8, 52 (2008).
[CrossRef]

Bullock, D. L.

Canning, J.

Cassagne, D.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134 (1996).
[CrossRef]

Chang, K. P.

K. P. Chang and S. L. Yang, "Photonic band gap of two-dimensional triangular photonic crystals with broken structural and rotational symmetries," J. Appl. Phys. 100, 073104 (2006).
[CrossRef]

Chen, X. S.

S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).

Digweed-Lyytik¨ainen, K.

Dilazaro, T.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalon, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Giapis, K. P.

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 40, 2949 (1996).
[CrossRef]

Gibson, B. C.

Gopalon, V.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalon, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B 67, 125203 (2003).
[CrossRef]

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 (1998).
[CrossRef]

Huntington, S. T.

Imada, M.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Jouanin, C.

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134 (1996).
[CrossRef]

Kim, S.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalon, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Kitagawa, H.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).

Klafi, M.

B. Rezaei and M. Klafi, "Engineering absolute band gap in anisotropic hexagonal photonic crystals," Opt. Commun. 266, 159 (2006).
[CrossRef]

Knight, J. C.

J. C. Knight, "Photonic crystal fibres," Nature (London) 424, 6950 (2003).
[CrossRef]

Li, Z. Y.

T. Pan, F. Zhuang, and Z. Y. Li, "Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods," Sol. State Comm. 129, 501 (2004).
[CrossRef]

T. Pan and Z. Y. Li, "The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals," Solid State Commun. 128, 187 (2003).
[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 (1998).
[CrossRef]

Love, J. D.

Lu, W.

S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).

Malkova, N.

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalon, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Marguilies, R. S.

Marsal, L. F.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
[CrossRef]

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
[CrossRef]

Noda, S.

H. Takano, B. S. Song, T. Asano, and S. Noda, "Highly efficient multi-channel drop filter in a two dimensional hetero photonic crystal," Opt. Express 14, 3491 (2006).
[CrossRef] [PubMed]

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Nozoye, H.

Ogawa, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Okano, M.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Pallares, J.

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
[CrossRef]

Pallarès, J.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
[CrossRef]

Pan, T.

T. Pan, F. Zhuang, and Z. Y. Li, "Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods," Sol. State Comm. 129, 501 (2004).
[CrossRef]

T. Pan and Z. Y. Li, "The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals," Solid State Commun. 128, 187 (2003).
[CrossRef]

Rezaei, B.

B. Rezaei and M. Klafi, "Engineering absolute band gap in anisotropic hexagonal photonic crystals," Opt. Commun. 266, 159 (2006).
[CrossRef]

Rinnie, S. A.

S. A. Rinnie, F. G. Santamaria, and P. V. Braun, "Embedded cavities and waveguides in three dimensional silicon photonic crystal," Nat. Photonics 8, 52 (2008).
[CrossRef]

Rodriguez, A.

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
[CrossRef]

Rodríguez, A.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
[CrossRef]

Santamaria, F. G.

S. A. Rinnie, F. G. Santamaria, and P. V. Braun, "Embedded cavities and waveguides in three dimensional silicon photonic crystal," Nat. Photonics 8, 52 (2008).
[CrossRef]

Shen, X. C.

S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).

Shih, C.

Song, B. S.

Steblina, V.

Takano, H.

Takayama, S.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).

Tanaka, Y.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).

Trifonov, T.

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
[CrossRef]

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
[CrossRef]

Uyama, H.

Wang, S. W.

S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).

Watanabe, S.

Yamada, Y.

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 (1998).
[CrossRef]

Yang, S. L.

K. P. Chang and S. L. Yang, "Photonic band gap of two-dimensional triangular photonic crystals with broken structural and rotational symmetries," J. Appl. Phys. 100, 073104 (2006).
[CrossRef]

Yoshimoto, S.

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Zhou, M.

S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).

Zhuang, F.

T. Pan, F. Zhuang, and Z. Y. Li, "Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods," Sol. State Comm. 129, 501 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. Takayama, H. Kitagawa, Y. Tanaka, T. Asano, and S. Noda, "Experimental demonstration of complete photonic band gap in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 87, 061107 (2005).

Int. J. Infrared Millim. Waves

S. W. Wang, W. Lu, X. S. Chen, M. Zhou, and X. C. Shen, "Photonic band gap in two-dimensional anisotropic photonic crystal with rectangular bars," Int. J. Infrared Millim. Waves 24, 963 (2003).

J. Appl. Phys.

K. P. Chang and S. L. Yang, "Photonic band gap of two-dimensional triangular photonic crystals with broken structural and rotational symmetries," J. Appl. Phys. 100, 073104 (2006).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

S. A. Rinnie, F. G. Santamaria, and P. V. Braun, "Embedded cavities and waveguides in three dimensional silicon photonic crystal," Nat. Photonics 8, 52 (2008).
[CrossRef]

Nature (London)

J. C. Knight, "Photonic crystal fibres," Nature (London) 424, 6950 (2003).
[CrossRef]

Y. Akahane, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425, 944 (2003),
[CrossRef]

Opt. Commun.

B. Rezaei and M. Klafi, "Engineering absolute band gap in anisotropic hexagonal photonic crystals," Opt. Commun. 266, 159 (2006).
[CrossRef]

Opt. Express

Phys. Rev. B

D. Cassagne, C. Jouanin, and D. Bertho, "Hexagonal photonic-band-gap structures," Phys. Rev. B 53, 7134 (1996).
[CrossRef]

T. Trifonov, L. F. Marsal, A. Rodriguez, J. Pallares, and R. Alcubilla, "Analysis of photonic band gap in twodimensional photonic crystals with rods covered by a thin interfacial layer," Phys. Rev. B 70, 195108 (2004).
[CrossRef]

T. Trifonov, L. F. Marsal, A. Rodríguez, J. Pallarès, and R. Alcubilla, "Effects of symmetry reduction in twodimensional square and triangular lattices," Phys. Rev. B 69, 235112 (2004).
[CrossRef]

N. Malkova, S. Kim, T. Dilazaro, and V. Gopalon, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B 67, 125203 (2003).
[CrossRef]

Phys. Rev. Lett.

C. M. Anderson and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett. 40, 2949 (1996).
[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 (1998).
[CrossRef]

Science

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, "Control of Light Emission by 3D Photonic Crystals," Science 305, 227-229 (2004).
[CrossRef] [PubMed]

Sol. State Comm.

T. Pan, F. Zhuang, and Z. Y. Li, "Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods," Sol. State Comm. 129, 501 (2004).
[CrossRef]

Solid State Commun.

T. Pan and Z. Y. Li, "The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals," Solid State Commun. 128, 187 (2003).
[CrossRef]

Other

E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic Press, Inc., 1991).

K. Sakoda, ed., Optical Properties of Photonic Crystals (Springer, 2001).

In fact, it is more appropriate to talk about Crystal Systems instead of Bravais Lattices. Indeed, the symmetry level of a lattice with translational invariance is dictated by the corresponding crystal system. However we have chosen to use the Bravais lattice terminology to avoid confusion in the text. Besides, this approximation can work well if we consider that the fourteen Bravais lattices are intimately related to the seven crystal systems that are defined in three dimensions.

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Figures (4)

Fig. 1.
Fig. 1.

The geometry and relevant parameters utilized in the simulations. (a) A configuration with symmetry reduction. (b) A configuration with air holes and no symmetry reduction. (c) Both symmetry reduction and air holes considered at the same time.

Fig. 2.
Fig. 2.

A comparison of the ratio between the band-width and band-center for configurations with and without symmetry reduction for (a) rutile and (b) tellurium. The symmetry reduction (shown by blue circles) for rutile shows a full band gap for f ranging between 0.1 and 0.5, which is absent when there is no symmetry reduction. For tellurium, the symmetry reduction increases the band gap for f smaller than 0.3. The black dotted lines show comparisons with corresponding isotropic hexagonal crystals. The red triangles show the combined effect of symmetry reduction and air holes in hexagonal photonic crystals. The values of the radius ratios are chosen to maximize the gaps for every value of f.

Fig. 3.
Fig. 3.

Dispersion curves for rutile photonic crystal at filling ratio f = 0.3 for configurations (a) without and (b) with symmetry reduction. It is evident how the symmetry reduction can break degenerations in the band structure so to produce a band gap. In turn it can lead to overlap between TE and TM gaps. Moreover, symmetry reduction can also have the negative effect of reducing the width of existing gaps, as shown in the TM band structure.

Fig. 4.
Fig. 4.

Dispersion curves for tellurium photonic crystal at filling ratio f = 0.4 for configurations (a) without and (b) with symmetry reduction. When the degeneration is broken, the gaps, especially for TM polarization, tend to shrink. It reduces the overlap of the band gaps.

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