Abstract

We demonstrate planar structures that can provide simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical (or phoxonic) crystal slabs. Different phoxonic crystal (PxC) structures, composed of square, hexagonal (honeycomb), or triangular arrays of void cylindrical holes embedded in silicon (Si) slabs with a finite thickness, are investigated. Photonic band gap (PtBG) maps and the complete phononic band gap (PnBG) maps of PxC slabs with different radii of the holes and thicknesses of the slabs are calculated using a three-dimensional plane wave expansion code. Simultaneous phononic and photonic band gaps with band gap to midgap ratios of more than 10% are shown to be readily obtainable with practical geometries in both square and hexagonal lattices, but not for the triangular lattice.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
    [CrossRef] [PubMed]
  2. M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
    [CrossRef]
  3. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
    [CrossRef] [PubMed]
  4. M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol. 19(12), 1970–1975 (2001).
    [CrossRef]
  5. M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. 158(2), 377–382 (1992).
    [CrossRef]
  6. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
    [CrossRef] [PubMed]
  7. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
    [CrossRef] [PubMed]
  8. 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), 033902–033905 (2008).
    [CrossRef] [PubMed]
  9. P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
    [CrossRef]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
    [CrossRef]
  15. S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
    [CrossRef]
  16. S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “Demonstration of large complete phononic band gaps and waveguiding in high-frequency silicon phononic crystal slabs,” in Proceedings of 2008 IEEE International Frequency Control Symposium, 2008 IEEE International Frequency Control Symposium, FCS (IEEE, 2008), 768–772.
  17. R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
    [CrossRef]
  18. S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . 94, 051906–1 (2009).
  19. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
    [CrossRef] [PubMed]
  20. M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
    [CrossRef]
  21. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999).
    [CrossRef]
  22. W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials I. Scalar case,” J. Comput. Phys. 150(2), 468–481 (1999).
    [CrossRef]
  23. L. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38(7), 891–898 (2002).
    [CrossRef]

2009 (3)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

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]

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . 94, 051906–1 (2009).

2008 (3)

S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
[CrossRef]

R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
[CrossRef]

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), 033902–033905 (2008).
[CrossRef] [PubMed]

2007 (1)

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[CrossRef]

2006 (4)

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]

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (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]

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]

2005 (1)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

2003 (1)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

2002 (1)

L. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38(7), 891–898 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[CrossRef]

1999 (2)

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

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials I. Scalar case,” J. Comput. Phys. 150(2), 468–481 (1999).
[CrossRef]

1994 (1)

M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
[CrossRef]

1992 (1)

M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. 158(2), 377–382 (1992).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

1987 (1)

E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Adibi, A.

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . 94, 051906–1 (2009).

S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
[CrossRef]

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[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]

Agio, M.

L. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38(7), 891–898 (2002).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[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), 033902–033905 (2008).
[CrossRef] [PubMed]

Andreani, L.

L. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38(7), 891–898 (2002).
[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]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Axmann, W.

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials I. Scalar case,” J. Comput. Phys. 150(2), 468–481 (1999).
[CrossRef]

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), 033902–033905 (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]

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]

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Carmon, T.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Dainese, P.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[CrossRef]

Djafari-Rouhani, B.

M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
[CrossRef]

Dobrzynski, L.

M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
[CrossRef]

Doll, T.

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[CrossRef]

Economou, E. N.

M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. 158(2), 377–382 (1992).
[CrossRef]

Eftekhar, A. A.

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . 94, 051906–1 (2009).

S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
[CrossRef]

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[CrossRef]

Eichenfield, M.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

El-Kady, I. F.

R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
[CrossRef]

Fan, S. H.

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

Fleming, J. G.

R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
[CrossRef]

Fragnito, H. L.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[CrossRef]

Gmitter, T.

E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

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), 033902–033905 (2008).
[CrossRef] [PubMed]

Halevi, P.

M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
[CrossRef]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Hunt, W. D.

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . 94, 051906–1 (2009).

S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
[CrossRef]

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[CrossRef]

Joannopoulos, J. D.

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

Johnson, S. G.

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

Joly, N.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[CrossRef]

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), 033902–033905 (2008).
[CrossRef] [PubMed]

Khelif, A.

S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
[CrossRef]

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[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]

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[CrossRef]

Kippenberg, T. J.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

Knight, J. C.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[CrossRef]

Kolodziejski, L. A.

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

Koshiba, M.

Kuchment, P.

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials I. Scalar case,” J. Comput. Phys. 150(2), 468–481 (1999).
[CrossRef]

Kushwaha, M.

M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
[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]

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 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 Stat. Nonlin. Soft Matter Phys. 74(4), 046610 (2006).
[CrossRef]

Leung, K.

E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Loncar, M.

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[CrossRef]

Maldovan, M.

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]

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]

Martinez, G.

M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
[CrossRef]

Mohammadi, S.

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . 94, 051906–1 (2009).

S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
[CrossRef]

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[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]

Moubchir, H.

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[CrossRef]

Nedeljkovi, D.

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Olsson, R. H.

R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
[CrossRef]

Painter, O.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Pearsall, T. P.

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[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), 033902–033905 (2008).
[CrossRef] [PubMed]

Rokhsari, H.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

Russell, P. S. J.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[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]

Scherer, A.

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[CrossRef]

Sigalas, M. M.

M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. 158(2), 377–382 (1992).
[CrossRef]

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Su, M. F.

R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
[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), 033902–033905 (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), 033902–033905 (2008).
[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]

Tuck, M. R.

R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
[CrossRef]

Vahala, K. J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

Villeneuve, P. R.

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

Vuckovic, J.

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[CrossRef]

Westafer, R.

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[CrossRef]

Wiederhecker, G. S.

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

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), 033902–033905 (2008).
[CrossRef] [PubMed]

Yang, L.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[CrossRef] [PubMed]

,” Appl. Phys. Lett (1)

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a two-dimensional phononic crystal slab,” Appl. Phys. Lett . 94, 051906–1 (2009).

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. (3)

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]

S. Mohammadi, A. A. Eftekhar, A. Khelif, W. D. Hunt, and A. Adibi, “Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates,” Appl. Phys. Lett. 92(22), 221905 (2008).
[CrossRef]

M. Loncar, D. Nedeljkovi, T. Doll, J. Vuckovic, A. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77(13), 1937–1939 (2000).
[CrossRef]

Electron. Lett. (1)

S. Mohammadi, A. A. Eftekhar, A. Khelif, H. Moubchir, R. Westafer, W. D. Hunt, and A. Adibi, “Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates,” Electron. Lett. 43(16), 898–899 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. Andreani and M. Agio, “Photonic bands and gap maps in a photonic crystal slab,” IEEE J. Quantum Electron. 38(7), 891–898 (2002).
[CrossRef]

J. Appl. Phys. (1)

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]

J. Comput. Phys. (1)

W. Axmann and P. Kuchment, “An efficient finite element method for computing spectra of photonic and acoustic band-gap materials I. Scalar case,” J. Comput. Phys. 150(2), 468–481 (1999).
[CrossRef]

J. Lightwave Technol. (1)

J. Sound Vibrat. (1)

M. M. Sigalas and E. N. Economou, “Elastic and Acoustic-Wave Band-Structure,” J. Sound Vibrat. 158(2), 377–382 (1992).
[CrossRef]

Nat. Phys. (1)

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibres,” Nat. Phys. 2(6), 388–392 (2006).
[CrossRef]

Nature (2)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Phys. Rev. B (2)

M. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Phys. Rev. B 49(4), 2313–2322 (1994).
[CrossRef]

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

Phys. Rev. Lett. (4)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[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), 033902–033905 (2008).
[CrossRef] [PubMed]

E. Yablonovitch, T. Gmitter, and K. Leung, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[CrossRef] [PubMed]

Sens. Actuators A Phys. (1)

R. H. Olsson, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, “Microfabricated VHF acoustic crystals and waveguides,” Sens. Actuators A Phys. 145-146, 87–93 (2008).
[CrossRef]

Other (1)

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “Demonstration of large complete phononic band gaps and waveguiding in high-frequency silicon phononic crystal slabs,” in Proceedings of 2008 IEEE International Frequency Control Symposium, 2008 IEEE International Frequency Control Symposium, FCS (IEEE, 2008), 768–772.

Cited By

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

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Band structure of in-plane elastic waves propagating in a 2D square-lattice PnC of infinitely long void holes in Si. A schematic of the cross section of the structures is shown in the inset. In this figure, a is the lattice constant (or distance between the centers of the nearest holes) and r is the radius of the holes. The band structure associates with a structure with r/a = 0.45. (b) Band structure of elastic waves for square lattice of void holes in a Si slab with a finite thickness. A schematic of the structures is shown in the inset, where a is the lattice constant, r is the radius of the holes, and d is the slab thickness. The band structure is calculated for r/a = 0.45 and d/a = 0.5 [‎14]. (c), (d) Band structure of in-plane-propagating optical modes in the 2D PxC explained in (a) and (b), respectively. The radiation optical modes above the light line are not depicted in (d).

Fig. 2
Fig. 2

PnBG maps of the square-lattice PxC slab structure with (a) a constant normalized thickness of d/a = 0.5 as a function of the normalized radius (r/a), and (b) a constant normalized radius of r/a = 0.45 and as a function of normalized thickness (d/a) [14]. (c), (d) PtBG maps of the PxC structure for even and odd optical modes for the same structures as in (a) and (b), respectively. The numbers near each PtBG region show the band numbers between which the PtBGs appear. The schematic of the associated PxC structure is shown in the inset of (a) for reference.

Fig. 3
Fig. 3

PnBG maps of the hexagonal-lattice PxC slab structure with (a) a constant normalized thickness of d/a = 1 as a function of the normalized radius (r/a) and (b) a constant normalized radius of r/a = 0.45 and as a function of the normalized slab thickness (d/a) [‎14]. (c), (d) PtBG maps of the PxC structure for even and odd optical modes for the same geometrical parameters as in (a) and (b), respectively. The numbers near each PtBG region show the band numbers between which the PtBGs appear. The schematic of the hexagonal PxC structure is shown in the inset of (a) for reference.

Equations (2)

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

× [ 1 ε × H ] = ω 2 c 2 H ,
( c s u ) = ρ ω 2 u ,

Metrics