Abstract

We discuss the simultaneous existence of phononic and photonic band gaps in a periodic array of holes drilled in a Si membrane. We investigate in detail both the centered square lattice and the boron nitride (BN) lattice with two atoms per unit cell which include the simple square, triangular and honeycomb lattices as particular cases. We show that complete phononic and photonic band gaps can be obtained from the honeycomb lattice as well as BN lattices close to honeycomb. Otherwise, all investigated structures present the possibility of a complete phononic gap together with a photonic band gap of a given symmetry, odd or even, depending on the geometrical parameters.

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    [CrossRef]
  5. Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
    [CrossRef] [PubMed]
  6. J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
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  7. L. Fok, M. Ambati, and Z. Xiang, “Acoustic Metamaterials,” MRS Bull. 33, 931 (2008).
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  8. J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
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  9. A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
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  12. J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
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  13. Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
    [CrossRef]
  14. T. T. Wu, Z. G. Huang, T.-C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
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  15. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10(2), 283 (1993).
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  16. S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
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  17. S. Shi, C. Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A 21(9), 1769 (2004).
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  18. S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
    [CrossRef]
  19. T.-I. Weng and G. Y. Guo, “Band structure of honeycomb photonic crystal slabs,” J. Appl. Phys. 99(9), 093102 (2006).
    [CrossRef]
  20. M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
    [CrossRef] [PubMed]
  21. P. Lacharmoise, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Optical cavity enhancement of light–sound interaction in acoustic phonon cavities,” Appl. Phys. Lett. 84(17), 3274 (2004).
    [CrossRef]
  22. M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
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  23. M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83(4), 595–600 (2006).
    [CrossRef]
  24. S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
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  25. S. Mohammadi, A. A. Eftekhar, and A. Adibi, “Large Simultaneous Band Gaps for Photonic and Phononic Crystal Slabs,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, p. CFY1 (Optical Society of America, 2008). http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2008-CFY1 .
  26. A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
    [CrossRef] [PubMed]
  27. G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particules,” Phys. Rev. B 73(3), 035115 (2006).
    [CrossRef]
  28. N. Stefanou, V. Yannopapas, and A. Modinos, “A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1-2), 189–196 (2000).
    [CrossRef]

2009 (2)

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[CrossRef]

2008 (5)

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

L. Fok, M. Ambati, and Z. Xiang, “Acoustic Metamaterials,” MRS Bull. 33, 931 (2008).
[CrossRef]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[CrossRef]

T. T. Wu, Z. G. Huang, T.-C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[CrossRef]

2006 (7)

T.-I. Weng and G. Y. Guo, “Band structure of honeycomb photonic crystal slabs,” J. Appl. Phys. 99(9), 093102 (2006).
[CrossRef]

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[CrossRef]

M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83(4), 595–600 (2006).
[CrossRef]

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[CrossRef]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef] [PubMed]

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44, e1209 (2006).
[CrossRef] [PubMed]

G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particules,” Phys. Rev. B 73(3), 035115 (2006).
[CrossRef]

2005 (1)

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

2004 (2)

P. Lacharmoise, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Optical cavity enhancement of light–sound interaction in acoustic phonon cavities,” Appl. Phys. Lett. 84(17), 3274 (2004).
[CrossRef]

S. Shi, C. Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A 21(9), 1769 (2004).
[CrossRef]

2002 (1)

M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
[CrossRef] [PubMed]

2000 (2)

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

N. Stefanou, V. Yannopapas, and A. Modinos, “A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1-2), 189–196 (2000).
[CrossRef]

1999 (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

1998 (1)

1993 (3)

E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10(2), 283 (1993).
[CrossRef]

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[CrossRef] [PubMed]

M. M. Sigalas and E. N. Economou, “Band structure of elastic waves in two dimensional systems,” Solid State Commun. 86(3), 141–143 (1993).
[CrossRef]

Adibi, A.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef] [PubMed]

Akimov, A. V.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Ambati, M.

L. Fok, M. Ambati, and Z. Xiang, “Acoustic Metamaterials,” MRS Bull. 33, 931 (2008).
[CrossRef]

Aoubiza, B.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef] [PubMed]

Baida, F. I.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[CrossRef]

Bayer, M.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Benchabane, S.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

Bernal, M. P.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[CrossRef]

Bonello, B.

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44, e1209 (2006).
[CrossRef] [PubMed]

Bruchhausen, A.

M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
[CrossRef] [PubMed]

Bucay, J.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Chan, C. T.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Charles, C.

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44, e1209 (2006).
[CrossRef] [PubMed]

Chen, C.

Choujaa, A.

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

Deymier, P. A.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[CrossRef]

Djafari-Rouhani, B.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[CrossRef]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[CrossRef] [PubMed]

Dobrzynski, L.

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[CrossRef] [PubMed]

Dubus, B.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Economou, E. N.

M. M. Sigalas and E. N. Economou, “Band structure of elastic waves in two dimensional systems,” Solid State Commun. 86(3), 141–143 (1993).
[CrossRef]

Fainstein, A.

P. Lacharmoise, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Optical cavity enhancement of light–sound interaction in acoustic phonon cavities,” Appl. Phys. Lett. 84(17), 3274 (2004).
[CrossRef]

M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
[CrossRef] [PubMed]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[CrossRef] [PubMed]

Fok, L.

L. Fok, M. Ambati, and Z. Xiang, “Acoustic Metamaterials,” MRS Bull. 33, 931 (2008).
[CrossRef]

Ganot, F.

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44, e1209 (2006).
[CrossRef] [PubMed]

Gantzounis, G.

G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particules,” Phys. Rev. B 73(3), 035115 (2006).
[CrossRef]

Golubev, V. G.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Guo, G. Y.

T.-I. Weng and G. Y. Guo, “Band structure of honeycomb photonic crystal slabs,” J. Appl. Phys. 99(9), 093102 (2006).
[CrossRef]

Halevi, P.

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[CrossRef] [PubMed]

Haus, H.

Hladky-Hennion, A. C.

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[CrossRef]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[CrossRef]

Hladky-Hennion, A.-C.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Hsu, J. C.

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[CrossRef]

Huang, Z. G.

T. T. Wu, Z. G. Huang, T.-C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[CrossRef]

Joannopoulos, J.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[CrossRef] [PubMed]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Jusserand, B.

P. Lacharmoise, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Optical cavity enhancement of light–sound interaction in acoustic phonon cavities,” Appl. Phys. Lett. 84(17), 3274 (2004).
[CrossRef]

M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
[CrossRef] [PubMed]

Kaplan, S. F.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Khelif, A.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef] [PubMed]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

Kolodziejski, L.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Kushwaha, M. S.

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[CrossRef] [PubMed]

Lacharmoise, P.

P. Lacharmoise, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Optical cavity enhancement of light–sound interaction in acoustic phonon cavities,” Appl. Phys. Lett. 84(17), 3274 (2004).
[CrossRef]

Larabi, H.

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

Laude, V.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[CrossRef]

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef] [PubMed]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

Liu, Z.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Maldovan, M.

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[CrossRef]

M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83(4), 595–600 (2006).
[CrossRef]

Mao, Y.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Modinos, A.

N. Stefanou, V. Yannopapas, and A. Modinos, “A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1-2), 189–196 (2000).
[CrossRef]

Mohammadi, S.

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef] [PubMed]

Muralidharan, K.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Pennec, Y.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[CrossRef]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

Pevtsov, A. B.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Prather, D. W.

Roussel, E.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Sadat-Saleh, S.

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[CrossRef]

Sheng, P.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Shi, S.

Sigalas, M. M.

M. M. Sigalas and E. N. Economou, “Band structure of elastic waves in two dimensional systems,” Solid State Commun. 86(3), 141–143 (1993).
[CrossRef]

Stefanou, N.

G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particules,” Phys. Rev. B 73(3), 035115 (2006).
[CrossRef]

N. Stefanou, V. Yannopapas, and A. Modinos, “A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1-2), 189–196 (2000).
[CrossRef]

Tamura, S.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Tanaka, Y.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Thierry-Mieg, V.

P. Lacharmoise, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Optical cavity enhancement of light–sound interaction in acoustic phonon cavities,” Appl. Phys. Lett. 84(17), 3274 (2004).
[CrossRef]

M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
[CrossRef] [PubMed]

Thomas, E. L.

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[CrossRef]

M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83(4), 595–600 (2006).
[CrossRef]

Trigo, M.

M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
[CrossRef] [PubMed]

Tsai, T.-C.

T. T. Wu, Z. G. Huang, T.-C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[CrossRef]

Vasseur, J. O.

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[CrossRef]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

Villeneuve, P.

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

Weng, T.-I.

T.-I. Weng and G. Y. Guo, “Band structure of honeycomb photonic crystal slabs,” J. Appl. Phys. 99(9), 093102 (2006).
[CrossRef]

Wu, T. C.

T. T. Wu, Z. G. Huang, T.-C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[CrossRef]

Wu, T. T.

T. T. Wu, Z. G. Huang, T.-C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[CrossRef]

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[CrossRef]

Xiang, Z.

L. Fok, M. Ambati, and Z. Xiang, “Acoustic Metamaterials,” MRS Bull. 33, 931 (2008).
[CrossRef]

Yablonovitch, E.

Yakovlev, D. R.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Yang, Z.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1-2), 189–196 (2000).
[CrossRef]

Zhang, X.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Zhu, Y. Y.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Appl. Phys. B (1)

M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83(4), 595–600 (2006).
[CrossRef]

Appl. Phys. Lett. (4)

P. Lacharmoise, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Optical cavity enhancement of light–sound interaction in acoustic phonon cavities,” Appl. Phys. Lett. 84(17), 3274 (2004).
[CrossRef]

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, H. Larabi, A. Khelif, A. Choujaa, S. Benchabane, and V. Laude, “Acoustic channel drop tunneling in a phononic crystal,” Appl. Phys. Lett. 87(26), 261912 (2005).
[CrossRef]

T. T. Wu, Z. G. Huang, T.-C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
[CrossRef]

Comput. Phys. Commun. (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1-2), 189–196 (2000).
[CrossRef]

J. Appl. Phys. (2)

S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
[CrossRef]

T.-I. Weng and G. Y. Guo, “Band structure of honeycomb photonic crystal slabs,” J. Appl. Phys. 99(9), 093102 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

MRS Bull. (1)

L. Fok, M. Ambati, and Z. Xiang, “Acoustic Metamaterials,” MRS Bull. 33, 931 (2008).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (6)

G. Gantzounis and N. Stefanou, “Layer-multiple-scattering method for photonic crystals of nonspherical particules,” Phys. Rev. B 73(3), 035115 (2006).
[CrossRef]

J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic-crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
[CrossRef]

J. Bucay, E. Roussel, J. O. Vasseur, P. A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, and B. Dubus, “Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: Theoretical and experimental study,” Phys. Rev. B 79(21), 214305 (2009).
[CrossRef]

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
[CrossRef]

Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[CrossRef] [PubMed]

M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
[CrossRef] [PubMed]

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[CrossRef] [PubMed]

Science (1)

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[CrossRef] [PubMed]

Solid State Commun. (1)

M. M. Sigalas and E. N. Economou, “Band structure of elastic waves in two dimensional systems,” Solid State Commun. 86(3), 141–143 (1993).
[CrossRef]

Ultrasonics (1)

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44, e1209 (2006).
[CrossRef] [PubMed]

Other (3)

For a comprehensive list of references on phononic crystals, see the phononic database at http://www.univ-lehavre.fr/recherche/lomc/phonon/PhononicDatabase1.html .

J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, and Y. Pennec, “Absolute band gaps in two-dimensional phononic crystal plates,” in Proceeding of IMECE 2006, ASME International Mechanical Engineering Congress and Exhibition, Chicago, Illinois, (5–10 Nov. 2006), pp13353.

S. Mohammadi, A. A. Eftekhar, and A. Adibi, “Large Simultaneous Band Gaps for Photonic and Phononic Crystal Slabs,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, p. CFY1 (Optical Society of America, 2008). http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2008-CFY1 .

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Figures (7)

Fig. 1
Fig. 1

(a) Representation of the unit cell for the numerical calculations. Centered square (b) and Boron Nitride (BN) (c) lattices with two atoms per unit cell together with the corresponding Brillouin zones. hSi and hair are respectively the thickness of the Si slab and air in the super-cell considered in the course of the PWE computation. r1 and r2 are the radii of two types of holes in the unit cell of the lattice with period a.

Fig. 2
Fig. 2

Photonic dispersion curves for hair/a = 1.4 (a) hair/a = 7.4 (b) in comparison with hair/a = 3.4 in the ΓM direction of the Brillouin zone for a silicon slab of holes in a square lattice for the geometrical parameters hSi/a = 0.6 and r/a = 0.43. The blue solid line delimits the light cone.

Fig. 3
Fig. 3

Photonic dispersion curves for a silicon slab of holes in a square lattice for the geometrical parameters hSi/a = 0.6 and r/a = 0.43 computed with (a) the layered multiple (LMS) method and (b) the plane wave expansion (PWE) method.

Fig. 4
Fig. 4

Simple square lattice: evolution of phononic and photonic gaps of even (red) and odd (blue) symmetries as a function of the filling factor f for different values of the thickness of the silicon slab hSi/a. The grey areas correspond to absolute band gaps.

Fig. 5
Fig. 5

Square lattice with two cylinders per unit cell: evolution of the phononic (a) and photonic (b) band gaps according to the symmetries even (red) and odd (blue) as a function of α = r1/r2, assuming the geometrical parameters hSi/a = 0.6 and f = 0.65.

Fig. 6
Fig. 6

Honeycomb lattice: evolution of the phononic and photonic even (red) and odd (blue) gaps as a function of the filling factor f for different values of the thickness of the silicon slab hSi/a. The grey areas correspond to absolute band gaps.

Fig. 7
Fig. 7

Boron Nitride lattice: Phononic and photonic band gaps with f = 0.45 and for two thicknesses hSi/a of the slab. The odd (blue) and even (red) modes are shown separately. The grey areas represent the domain of α where there are complete phononic and photonic gaps of both symmetries.

Tables (1)

Tables Icon

Table 1 Summary of the most suitable phononic and photonic crystals and the corresponding band gaps frequencies.

Equations (2)

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

f = f 1 + f 2 = π ( r 1 2 + r 2 2 ) a ²
f = f 1 + f 2 = π ( r 1 2 + r 2 2 ) a 2 3 2

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