Abstract

We demonstrate theoretically that photons and acoustic phonons can be simultaneously guided and slowed down in specially designed nanostructures. Phoxonic crystal waveguides presenting simultaneous phononic and photonic band gaps were designed in perforated silicon membranes that can be conveniently obtained using silicon-on-insulator technology. Geometrical parameters for simultaneous photonic and phononic band gaps were first chosen for optical wavelengths around 1550 nm, based on the finite element analysis of a perfect phoxonic crystal of circular holes. A plain core waveguide was then defined, and simultaneous slow light and elastic guided modes were identified for some waveguide width. Joint guidance of light and elastic waves is predicted with group velocities as low as c/25 and 180 m/s, respectively.

© 2011 OSA

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  1. J. Joannopoulos and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008).
  2. M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71, 2022–2025 (1993).
    [CrossRef] [PubMed]
  3. M. Maldovan and E. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88, 251907 (2006).
    [CrossRef]
  4. M. Maldovan and E. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B: Lasers and Optics 83, 595–600 (2006).
    [CrossRef]
  5. A. Akimov, Y. Tanaka, A. Pevtsov, S. Kaplan, V. Golubev, S. Tamura, D. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101, 033902 (2008).
    [CrossRef] [PubMed]
  6. S. Sadat-Saleh, S. Benchabane, F. Baida, M. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106, 074912 (2009).
    [CrossRef]
  7. N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96, 231917 (2010).
    [CrossRef]
  8. S. Mohammadi, A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18, 9164–9172 (2010).
    [CrossRef] [PubMed]
  9. Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
    [CrossRef] [PubMed]
  10. A. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18, 14926–14943 (2010).
    [CrossRef] [PubMed]
  11. Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
    [CrossRef]
  12. A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude, “Complete band gaps in two-dimensional phononic crystal slabs,” Phys. Rev. E 74, 046610 (2006).
    [CrossRef]
  13. M. I. Hussein, “Reduced bloch mode expansion for periodic media band structure calculations,” Proc. R. Soc. London, Ser. A 465, 2825–2848 (2009).
    [CrossRef]
  14. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [CrossRef]
  15. J. Jin, The finite element method in electromagnetics , 2nd ed. (Wiley, 2002).
  16. T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
    [CrossRef]
  17. V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, “Evanescent Bloch waves and the complex band structure of phononic crystals,” Phys. Rev. B 80, 092301 (2009).
    [CrossRef]
  18. V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
    [CrossRef]
  19. P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
    [CrossRef]

2010

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96, 231917 (2010).
[CrossRef]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

S. Mohammadi, A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18, 9164–9172 (2010).
[CrossRef] [PubMed]

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

A. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18, 14926–14943 (2010).
[CrossRef] [PubMed]

2009

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

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, “Evanescent Bloch waves and the complex band structure of phononic crystals,” Phys. Rev. B 80, 092301 (2009).
[CrossRef]

M. I. Hussein, “Reduced bloch mode expansion for periodic media band structure calculations,” Proc. R. Soc. London, Ser. A 465, 2825–2848 (2009).
[CrossRef]

2008

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

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

2006

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

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

M. Maldovan and E. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B: Lasers and Optics 83, 595–600 (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 74, 046610 (2006).
[CrossRef]

2005

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

1999

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

1993

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

Achaoui, Y.

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, “Evanescent Bloch waves and the complex band structure of phononic crystals,” Phys. Rev. B 80, 092301 (2009).
[CrossRef]

Adibi, A.

S. Mohammadi, A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18, 9164–9172 (2010).
[CrossRef] [PubMed]

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

Aitchison, J. S.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Akimov, A.

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

Akjouj, A.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[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 74, 046610 (2006).
[CrossRef]

Baida, F.

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

Bayer, M.

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

Benchabane, S.

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

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

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, “Evanescent Bloch waves and the complex band structure of phononic crystals,” Phys. Rev. B 80, 092301 (2009).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Bernal, M.

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

Bou Matar, O.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Dainese, P.

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

Djafari Rouhani, B.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Djafari-Rouhani, B.

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

Dudley, J. M.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Eftekhar, A.

El Boudouti, E.

El Boudouti, E. H.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

El Hassouani, Y.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

Fan, S.

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

Fragnito, H.

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

Golubev, V.

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

Halevi, P.

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

Hussein, M. I.

M. I. Hussein, “Reduced bloch mode expansion for periodic media band structure calculations,” Proc. R. Soc. London, Ser. A 465, 2825–2848 (2009).
[CrossRef]

Jin, J.

J. Jin, The finite element method in electromagnetics , 2nd ed. (Wiley, 2002).

Joannopoulos, J.

J. Joannopoulos and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008).

Joannopoulos, J. D.

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

Johnson, S. G.

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

Joly, N.

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

Kaplan, S.

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

Khelif, A.

S. Mohammadi, A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18, 9164–9172 (2010).
[CrossRef] [PubMed]

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, “Evanescent Bloch waves and the complex band structure of phononic crystals,” Phys. Rev. B 80, 092301 (2009).
[CrossRef]

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (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 74, 046610 (2006).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Kibler, B.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Knight, J.

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 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, 2022–2025 (1993).
[CrossRef] [PubMed]

Larabi, H.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Laude, V.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, “Evanescent Bloch waves and the complex band structure of phononic crystals,” Phys. Rev. B 80, 092301 (2009).
[CrossRef]

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

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (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 74, 046610 (2006).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Li, C.

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Maillotte, H.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Maldovan, M.

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

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

Martinez, A.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

Mohammadi, S.

S. Mohammadi, A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18, 9164–9172 (2010).
[CrossRef] [PubMed]

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

Mojahedi, M.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Mussot, A.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Nair, S. V.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Painter, O.

Papanikolaou, N.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96, 231917 (2010).
[CrossRef]

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

Pennec, Y.

Y. Pennec, B. Rouhani, E. El Boudouti, C. Li, Y. El Hassouani, J. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18, 14301–14310 (2010).
[CrossRef] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

Pevtsov, A.

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

Psarobas, I.

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96, 231917 (2010).
[CrossRef]

Rouhani, B.

Ruda, H. E.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Russell, P.

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

Sadat-Saleh, S.

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

Safavi-Naeini, A.

Stefanou, N.

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96, 231917 (2010).
[CrossRef]

Sylvestre, T.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Tamura, S.

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

Tanaka, Y.

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

Thomas, E.

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

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

Vasseur, J.

Villeneuve, P. R.

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

Wheeler, M. S.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Wiederhecker, G.

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

Wilm, M.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Winn, J.

J. Joannopoulos and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008).

Xu, T.

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

Yakovlev, D.

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

Appl. Phys. B: Lasers and Optics

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

Appl. Phys. Lett.

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96, 231917 (2010).
[CrossRef]

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

T. Xu, M. S. Wheeler, S. V. Nair, H. E. Ruda, M. Mojahedi, and J. S. Aitchison, “Highly confined mode above the light line in a two-dimensional photonic crystal slab,” Appl. Phys. Lett. 93, 241105 (2008).
[CrossRef]

J. Appl. Phys.

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

Nat. Phys.

P. Dainese, P. Russell, N. Joly, J. Knight, G. Wiederhecker, H. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2, 388–392 (2006).
[CrossRef]

Opt. Express

Phys. Rev. B

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

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82, 155405 (2010).
[CrossRef]

V. Laude, Y. Achaoui, S. Benchabane, and A. Khelif, “Evanescent Bloch waves and the complex band structure of phononic crystals,” Phys. Rev. B 80, 092301 (2009).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
[CrossRef]

Phys. Rev. E

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

Phys. Rev. Lett.

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

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

Proc. R. Soc. London, Ser. A

M. I. Hussein, “Reduced bloch mode expansion for periodic media band structure calculations,” Proc. R. Soc. London, Ser. A 465, 2825–2848 (2009).
[CrossRef]

Other

J. Joannopoulos and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2008).

J. Jin, The finite element method in electromagnetics , 2nd ed. (Wiley, 2002).

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Figures (6)

Fig. 1
Fig. 1

Examples of unit-cells used in the analysis of phoxonic crystal slab structures. Two-dimensional periodic boundary conditions are applied at the lateral sides of the unit-cells. (a) For elastic waves, only the solid part (silicon) needs to be meshed. Traction-free boundary conditions are applied at the top and the bottom surfaces. (b) For photonic modes, the vacuum or air inside the holes and surrounding the slab needs to be taken into account. Free boundary conditions are applied at the top and the bottom surfaces of the air region, resulting in an artificial truncation of the computation domain. (c) First irreducible Brillouin zone showing the highest symmetry points.

Fig. 2
Fig. 2

(a) Phononic band structure for a periodic array of circular holes in a silicon slab with parameters a = 651 nm, h = 390 nm, and r = 280 nm. A complete band gap appears around 5 GHz. (b)–(g) Modal distribution of the displacements for the first six modes at the M point of the first Brillouin zone. The color bar is for the modulus of the total displacement while the deformation of the mesh is proportional to the algebraic displacements.

Fig. 3
Fig. 3

(a) Photonic band structure for a periodic array of circular holes in a silicon slab with parameters a = 651 nm, h = 390 nm, and r = 280 nm. The left vertical axis is in units of the reduced frequency, ωa/2πc = a/λ. The two photonic band gaps for guided waves appear in white. (b)–(g) Modal distribution of the modulus of the magnetic field vector H (a.u.) for the reduced wavevector value k x a/2π = k y a/2π = 0.3, somewhat midway along the ΓM direction, for the first six even modes.

Fig. 4
Fig. 4

Phononic band structure of a solid core phoxonic crystal waveguide defined along the ΓX direction in a square-lattice phoxonic crystal slab. In the supercell computation, three rows of holes surround a central solid core of width (a) w = a and (b) w = 0.9a. The complete phononic band gap appears in white. The band supporting guided waves with the lowest group velocity is shown as a solid line. (c)–(e) Modal distributions of the displacements for three particular eigenmodes with k x a/2π = 0.3. The color bar is for the modulus of the total displacement while the deformation of the mesh is proportional to the algebraic displacements.

Fig. 5
Fig. 5

Photonic band structure for waves in a solid core phoxonic crystal waveguide defined along the ΓX direction in a square-lattice phoxonic crystal slab. In the supercell computation, three rows of holes surround a central solid core of width (a) w = a and (b) w = 0.9a. Two photonic band gaps for guided waves appear in white. The bands supporting waves latterally guided by the photonic band gap effect are shown with solid lines. (c),(d) Modal distribution for two of these eigenmodes. The modulus of the magnetic field vector H is presented for the reduced wavevector value kxa/2π = 0.45.

Fig. 6
Fig. 6

(a) Dependence of the group index and of the reduced frequency with reduced wave vector, for the guided photonic mode labeled “c” in Fig. 5. (b) Dependence of the group velocity and of the frequency with reduced wave vector, for the guided phononic mode labeled “c” in Fig. 4.

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