Abstract

In this paper we study and design quasi-2D optomechanical crystals, waveguides, and resonant cavities formed from patterned slabs. Two-dimensional periodicity allows for in-plane pseudo-bandgaps in frequency where resonant optical and mechanical excitations localized to the slab are forbidden. By tailoring the unit cell geometry, we show that it is possible to have a slab crystal with simultaneous optical and mechanical pseudo-bandgaps, and for which optical waveguiding is not compromised. We then use these crystals to design optomechanical cavities in which strongly interacting, co-localized photonic-phononic resonances occur. A resonant cavity structure formed by perturbing a “linear defect” waveguide of optical and acoustic waves in a silicon optomechanical crystal slab is shown to support an optical resonance at wavelength λ 0 ≈ 1.5 µm and a mechanical resonance of frequency ωm/2π ≈ 9.5 GHz. These resonances, due to the simultaneous pseudo-bandgap of the waveguide structure, are simulated to have optical and mechanical radiation-limited Q-factors greater than 107. The optomechanical coupling of the optical and acoustic resonances in this cavity due to radiation pressure is also studied, with a quantum conversion rate, corresponding to the scattering rate of a single cavity photon via a single cavity phonon, calculated to be g/2π = 292 kHz.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172–1176 (2008).
    [CrossRef] [PubMed]
  2. I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009).
    [CrossRef]
  3. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
    [CrossRef] [PubMed]
  4. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic crystal optomechanical cavity,” Nature 459, 550–555 (2009).
    [CrossRef] [PubMed]
  5. M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
    [CrossRef] [PubMed]
  6. Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
    [CrossRef] [PubMed]
  7. G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
    [CrossRef] [PubMed]
  8. J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
    [CrossRef] [PubMed]
  9. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
    [CrossRef] [PubMed]
  10. M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 20078–20098 (2009).
    [CrossRef] [PubMed]
  11. O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082 (1999).
    [CrossRef]
  12. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  13. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001).
    [CrossRef]
  14. H. Takano, B.-S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
    [CrossRef] [PubMed]
  15. B.-S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Multichannel add/drop filter based on in-plane hetero photonic crystals,” J. Lightwave Technol. 23, 1449–1455 (2005).
    [CrossRef]
  16. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
    [CrossRef] [PubMed]
  17. R. H. OlssonIII, and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol. 20, 012002 (2009).
    [CrossRef]
  18. J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
    [CrossRef]
  19. J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
    [CrossRef]
  20. K.-B. Gu, C.-L. Chang, J.-C. Shieh, and W.-P. Shih, “Design and fabrication of 2d phononic crystals in surface acoustic wave micro devices,” in “Micro Electro Mechanical Systems, 2006. MEMS 2006 Istanbul. 19th IEEE International Conference on,” (2006), pp. 686–689.
  21. 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, 221905 (2008).
    [CrossRef]
  22. M. Maldovan, and E. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83, 595–600 (2006).
    [CrossRef]
  23. T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
    [CrossRef] [PubMed]
  24. M. Maldovan, and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88, 251907 (2006).
    [CrossRef]
  25. 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 (2009).
    [CrossRef]
  26. S. Mohammadi, A. Eftekhar, and A. Adibi, “Large simultaneous band gaps for photonic and phononic crystal slabs,” in “Lasers and Electro-Optics, 2008 and 2008 Conference on Quantum Electronics and Laser Science. CLEO/QELS 2008. Conference on,” (2008), pp. 1–2.
  27. 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]
  28. M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
    [CrossRef] [PubMed]
  29. V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 045107 (2005).
    [CrossRef]
  30. 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, 388–392 (2006).
    [CrossRef]
  31. A. Brenn, G. Wiederhecker, M. Kang, H. Hundertmark, N. Joly, and P. St. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009).
    [CrossRef]
  32. M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (2009).
    [CrossRef]
  33. V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
    [CrossRef]
  34. C. Kittel, Introduction to Solid State Physics (John Wiley, 2005).
  35. COMSOL Multphysics3.5 (2009).
  36. S. Nemat-Nasser and M. Hori, Micromechanics: overall properties of heterogeneous materials (North-Holland, 1993).
  37. C. Mei, J. Auriault and C. Ng, “Some applications of the homogenization theory,” Adv. Appl. Mech. 32, 278–348 (1996).
  38. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [CrossRef] [PubMed]
  39. A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 82, 4488–4492 (2000).
    [CrossRef]
  40. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
    [CrossRef]
  41. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
    [CrossRef]
  42. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
    [CrossRef]
  43. P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
    [CrossRef]
  44. P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
    [CrossRef] [PubMed]
  45. R. W. Boyd, Nonlinear Optics, 3ed (Academic Press, 2008).
  46. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
    [CrossRef]
  47. G. Wannier, “Dynamics of band electrons in electric and magnetic fields,” Rev. Mod. Phys. 34, 645–655 (1962).
    [CrossRef]
  48. M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
    [CrossRef]
  49. E. Istrate, M. Charbonneau-Lefort, and E. Sargent, “Theory of photonic crystal heterostructures,” Phys. Rev. B 66, 075121 (2002).
    [CrossRef]
  50. O. Painter, K. Srinivasan, and P. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
    [CrossRef]
  51. D. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” arXiv:1006.3829 (2010).
  52. . P. Rabl, S. J. Kolkowitz, F. H. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, “A quantum spin transducer based on nano electro-mechanical resonator arrays,” arXiv:0908.0316v1 (2009).
  53. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
    [CrossRef]

2010

2009

A. Brenn, G. Wiederhecker, M. Kang, H. Hundertmark, N. Joly, and P. St. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009).
[CrossRef]

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[CrossRef]

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (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 (2009).
[CrossRef]

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009).
[CrossRef]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
[CrossRef] [PubMed]

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

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 20078–20098 (2009).
[CrossRef] [PubMed]

R. H. OlssonIII, and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol. 20, 012002 (2009).
[CrossRef]

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
[CrossRef]

2008

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, 221905 (2008).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

2007

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

2006

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

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

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, 388–392 (2006).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

H. Takano, B.-S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[CrossRef] [PubMed]

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

2005

T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
[CrossRef] [PubMed]

B.-S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Multichannel add/drop filter based on in-plane hetero photonic crystals,” J. Lightwave Technol. 23, 1449–1455 (2005).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

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

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
[CrossRef]

2003

O. Painter, K. Srinivasan, and P. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[CrossRef]

2002

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
[CrossRef]

E. Istrate, M. Charbonneau-Lefort, and E. Sargent, “Theory of photonic crystal heterostructures,” Phys. Rev. B 66, 075121 (2002).
[CrossRef]

2001

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

2000

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 82, 4488–4492 (2000).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

1999

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

1998

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

1996

C. Mei, J. Auriault and C. Ng, “Some applications of the homogenization theory,” Adv. Appl. Mech. 32, 278–348 (1996).

1962

G. Wannier, “Dynamics of band electrons in electric and magnetic fields,” Rev. Mod. Phys. 34, 645–655 (1962).
[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]

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 (2009).
[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, 221905 (2008).
[CrossRef]

Akahane, Y.

B.-S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Multichannel add/drop filter based on in-plane hetero photonic crystals,” J. Lightwave Technol. 23, 1449–1455 (2005).
[CrossRef]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
[CrossRef]

Allard, M.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Asano, T.

Auriault, J.

C. Mei, J. Auriault and C. Ng, “Some applications of the homogenization theory,” Adv. Appl. Mech. 32, 278–348 (1996).

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

Baets, R.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

Barclay, P.

O. Painter, K. Srinivasan, and P. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Barclay, P. E.

Benchabane, S.

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

Brenn, A.

A. Brenn, G. Wiederhecker, M. Kang, H. Hundertmark, N. Joly, and P. St. J. Russell, “Influence of air-filling fraction on forward Raman-like scattering by transversely trapped acoustic resonances in photonic crystal fibers,” J. Opt. Soc. Am. B 26, 1641–1648 (2009).
[CrossRef]

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[CrossRef]

Bretagne, A.

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
[CrossRef]

Caballero, D.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[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, 550–555 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
[CrossRef] [PubMed]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

Chan, J.

Charbonneau-Lefort, M.

E. Istrate, M. Charbonneau-Lefort, and E. Sargent, “Theory of photonic crystal heterostructures,” Phys. Rev. B 66, 075121 (2002).
[CrossRef]

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

Chutinan, A.

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 82, 4488–4492 (2000).
[CrossRef]

Dainese, P.

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

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, 388–392 (2006).
[CrossRef]

Dapkus, P. D.

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082 (1999).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

De Vlaminck, I.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

Deymier, P. A.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

Djafari-Rouhani, B.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

Dubus, B.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

Dudley, J.

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

Duval, F.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

Eftekhar, A.

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 (2009).
[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, 221905 (2008).
[CrossRef]

Eichenfield, M.

El-Kady, I.

R. H. OlssonIII, and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol. 20, 012002 (2009).
[CrossRef]

Fan, S.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Favero, I.

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009).
[CrossRef]

Fink, M.

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
[CrossRef]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Fragnito, H. L.

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

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, 388–392 (2006).
[CrossRef]

Fytas, G.

T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
[CrossRef] [PubMed]

Galvez, F.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

Gorishnyy, T.

T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
[CrossRef] [PubMed]

Hammerer, K.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
[CrossRef]

Hladky-Hennion, A.-C.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

Hochberg, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

Hundertmark, H.

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 (2009).
[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, 221905 (2008).
[CrossRef]

Husain, A.

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Istrate, E.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
[CrossRef]

E. Istrate, M. Charbonneau-Lefort, and E. Sargent, “Theory of photonic crystal heterostructures,” Phys. Rev. B 66, 075121 (2002).
[CrossRef]

Jiang, X.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Joly, N.

Kang, M.

Kang, M. S.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[CrossRef]

Karrai, K.

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009).
[CrossRef]

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]

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, 221905 (2008).
[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, 388–392 (2006).
[CrossRef]

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

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

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082 (1999).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[CrossRef] [PubMed]

Kira, G.

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, 388–392 (2006).
[CrossRef]

Kuramochi, E.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

Lagae, L.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

Laude, V.

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, 388–392 (2006).
[CrossRef]

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

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

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Leroy, V.

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
[CrossRef]

Li, M.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

Lin, Q.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

Lipson, M.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

Llinares, J.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Loncar, M.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Lukin, M.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
[CrossRef]

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Maes, B.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

Maillotte, H.

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. 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 complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B 83, 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, 251907 (2006).
[CrossRef]

T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
[CrossRef] [PubMed]

Martinez-Sala, R.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Mei, C.

C. Mei, J. Auriault and C. Ng, “Some applications of the homogenization theory,” Adv. Appl. Mech. 32, 278–348 (1996).

Meseguer, F.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Mitsugi, S.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[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]

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 (2009).
[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, 221905 (2008).
[CrossRef]

Mussot, A.

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

Nazarkin, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[CrossRef]

Ng, C.

C. Mei, J. Auriault and C. Ng, “Some applications of the homogenization theory,” Adv. Appl. Mech. 32, 278–348 (1996).

Noda, S.

H. Takano, B.-S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[CrossRef] [PubMed]

B.-S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Multichannel add/drop filter based on in-plane hetero photonic crystals,” J. Lightwave Technol. 23, 1449–1455 (2005).
[CrossRef]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
[CrossRef]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 82, 4488–4492 (2000).
[CrossRef]

Notomi, M.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082 (1999).
[CrossRef]

Olsson, R. H.

R. H. OlssonIII, and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol. 20, 012002 (2009).
[CrossRef]

Painter, O.

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 20078–20098 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

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

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
[CrossRef] [PubMed]

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[CrossRef]

O. Painter, K. Srinivasan, and P. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Painter, O. J.

Pennec, Y.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

Pernice, W. H. P.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

Poon, J.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Rabl, P.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
[CrossRef]

Roels, J.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

Rosenberg, J.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

Rubio, C.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Russell, P. S. J.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (2009).
[CrossRef]

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

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, 388–392 (2006).
[CrossRef]

Russell, P. St. J.

Safavi-Naeini, A. H.

Sanchez-Dehesa, J.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Sanchez-Perez, J. V.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Sargent, E.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
[CrossRef]

E. Istrate, M. Charbonneau-Lefort, and E. Sargent, “Theory of photonic crystal heterostructures,” Phys. Rev. B 66, 075121 (2002).
[CrossRef]

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP,” J. Lightwave Technol. 17, 2082 (1999).
[CrossRef]

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Song, B.-S.

Srinivasan, K.

P. E. Barclay, K. Srinivasan, and O. Painter, “Design of photonic crystal waveguides for evanescent coupling to optical fiber tapers and integration with high-Q cavities,” J. Opt. Soc. Am. B 20, 2274–2284 (2003).
[CrossRef]

O. Painter, K. Srinivasan, and P. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

Sylvestre, T.

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

Tabeling, P.

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
[CrossRef]

Takano, H.

Tanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

Tanaka, Y.

Tang, H. X.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

Taniyama, H.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

Thomas, E.

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

T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
[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, 251907 (2006).
[CrossRef]

Tourin, A.

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
[CrossRef]

Ullal, C.

T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
[CrossRef] [PubMed]

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, 550–555 (2009).
[CrossRef] [PubMed]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 20078–20098 (2009).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[CrossRef] [PubMed]

Van Thourhout, D.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

Vasseur, J. O.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

Vuckovic, J.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

Wallquist, M.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
[CrossRef]

Wannier, G.

G. Wannier, “Dynamics of band electrons in electric and magnetic fields,” Rev. Mod. Phys. 34, 645–655 (1962).
[CrossRef]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Wiederhecker, G.

Wiederhecker, G. S.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

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, 388–392 (2006).
[CrossRef]

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

Willaime, H.

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
[CrossRef]

Wilm, M.

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

Xiong, C.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Zoller, P.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
[CrossRef]

Adv. Appl. Mech.

C. Mei, J. Auriault and C. Ng, “Some applications of the homogenization theory,” Adv. Appl. Mech. 32, 278–348 (1996).

Appl. Phys. B

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

Appl. Phys. Lett.

M. Maldovan, and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88, 251907 (2006).
[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 (2009).
[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, 221905 (2008).
[CrossRef]

V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, and A. Tourin, “Design and characterization of bubble phononic crystals,” Appl. Phys. Lett. 95, 171904 (2009).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

J. Appl. Phys.

J. O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval, B. Dubus, Y. Pennec, and P. A. Deymier, “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904 (2007).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Meas. Sci. Technol.

R. H. OlssonIII, and I. El-Kady, “Microfabricated phononic crystal devices and applications,” Meas. Sci. Technol. 20, 012002 (2009).
[CrossRef]

Nat. Mater.

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
[CrossRef]

Nat. Nanotechnol.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4, 510–513 (2009).
[CrossRef] [PubMed]

Nat. Photonics

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3, 201–205 (2009).
[CrossRef]

Nat. Phys.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial raman oscillators,” Nat. Phys. 5, 276–280 (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, 388–392 (2006).
[CrossRef]

Nature

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

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

Opt. Express

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 20078–20098 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17, 3802–3817 (2009).
[CrossRef] [PubMed]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687 (2005).
[CrossRef] [PubMed]

H. Takano, B.-S. Song, T. Asano, and S. Noda, “Highly efficient multi-channel drop filter in a two-dimensional hetero photonic crystal,” Opt. Express 14, 3491–3496 (2006).
[CrossRef] [PubMed]

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]

P. Dainese, P. S. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like light scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141–4150 (2006).
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

Phys. Rev. B

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 82, 4488–4492 (2000).
[CrossRef]

S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212–8222 (2000).
[CrossRef]

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, and E. Sargent, “Photonic crystal heterostructures: waveguiding phenomena and methods of solution in an envelope function picture,” Phys. Rev. B 65, 125318 (2002).
[CrossRef]

E. Istrate, M. Charbonneau-Lefort, and E. Sargent, “Theory of photonic crystal heterostructures,” Phys. Rev. B 66, 075121 (2002).
[CrossRef]

O. Painter, K. Srinivasan, and P. Barclay, “Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals,” Phys. Rev. B 68, 035214 (2003).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. 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

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity qed,” Phys. Rev. E 65, 016608 (2001).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Phys. Rev. Lett.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, “Sound attenuation by a two-dimensional array of rigid cylinders,” Phys. Rev. Lett. 80, 5325–5328 (1998).
[CrossRef]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97, 023903 (2006).
[CrossRef] [PubMed]

T. Gorishnyy, C. Ullal, M. Maldovan, G. Fytas, and E. Thomas, “Hypersonic phononic crystals,” Phys. Rev. Lett. 94, 115501 (2005).
[CrossRef] [PubMed]

Phys. Scr. T

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T 137, 014001 (2009).
[CrossRef]

Rev. Mod. Phys.

G. Wannier, “Dynamics of band electrons in electric and magnetic fields,” Rev. Mod. Phys. 34, 645–655 (1962).
[CrossRef]

Science

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[CrossRef] [PubMed]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Other

K.-B. Gu, C.-L. Chang, J.-C. Shieh, and W.-P. Shih, “Design and fabrication of 2d phononic crystals in surface acoustic wave micro devices,” in “Micro Electro Mechanical Systems, 2006. MEMS 2006 Istanbul. 19th IEEE International Conference on,” (2006), pp. 686–689.

S. Mohammadi, A. Eftekhar, and A. Adibi, “Large simultaneous band gaps for photonic and phononic crystal slabs,” in “Lasers and Electro-Optics, 2008 and 2008 Conference on Quantum Electronics and Laser Science. CLEO/QELS 2008. Conference on,” (2008), pp. 1–2.

C. Kittel, Introduction to Solid State Physics (John Wiley, 2005).

COMSOL Multphysics3.5 (2009).

S. Nemat-Nasser and M. Hori, Micromechanics: overall properties of heterogeneous materials (North-Holland, 1993).

D. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” arXiv:1006.3829 (2010).

. P. Rabl, S. J. Kolkowitz, F. H. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, “A quantum spin transducer based on nano electro-mechanical resonator arrays,” arXiv:0908.0316v1 (2009).

R. W. Boyd, Nonlinear Optics, 3ed (Academic Press, 2008).

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 (10)

Fig. 1.
Fig. 1.

Band diagram for a simple (a) spring-mass system and (b) its quasi-1D nanomechanical analogue. The nanomechanical structure band diagram is plotted for a silicon structure with (d,h,w,a) = (220,200,100,500) nm. In (b) waveguide bands are plotted as (oe-18-14-14926-i001.jpg), (oe-18-14-14926-i002.jpg), (oe-18-14-14926-i003.jpg) and (oe-18-14-14926-i004.jpg) for vibrational modes with (σyz ) symmetry of (+,+), (−,−), (−,+) and (+,−) respectively. Here, σy is a mirror plane symmetry of the structure about the y-axis. σz is the corresponding vertical mirror symmetry about the z-axis.

Fig. 2.
Fig. 2.

The tight-binding bands of symmetry (σyz ) = (+,+) are plotted for the quasi-1D nanomechanical system of Fig. 1(b), along with the unit cell solved for fixed and free boundary conditions. The E (O) symbol below the Bloch function plots designates σx = +(−) symmetry of the vibrational modes. We see that in every case where bands don’t mix, i.e. the bottom three bands, the E bands slope downwards in frequency from Γ to X, while the O band slopes upwards. In plots of the mechanical modes, color indicates the magnitude of the displacement field (blue no displacement, red large displacement) and the displacement of the structure has been exaggerated for viewing purposes.

Fig. 3.
Fig. 3.

(a) Photonic and (b) phononic bandstructure of the quasi-2D Si cross substrate shown schematically in (c) real space and (d) reciprocal space. The photonic bandstructure is for the even symmetry modes of the slab only. The band diagrams were calculated for a Si structure with parameters (d,h,w,a) = (220,200,100,500) nm. Notably, there is not even a photonic pseudo in-plane bandgap for the even vertical symmetry optical modes of the slab.

Fig. 4.
Fig. 4.

Phononic gap maps for a Si quasi-2D cross structure. The cross width is varied in (a) and the cross height is varied in (b). The nominal structure about which the variations are performed is characterized by parameters (d,h,w,a) = (220,200,100,500) nm. The lattice constant a is varied while keeping the ratios h/a = 0.8 and w/a = 0.2 constant in (a) and (b), respectively.

Fig. 5.
Fig. 5.

(a) Photonic and (b) phononic bandstructure of the quasi-2D Si snowflake substrate. Schematic of the snowflake slab substrate in (c) real space and (d) reciprocal space. The band diagrams were calculated for a Si structure with parameters (d,r,w,a) = (220,200,75,500) nm. For these parameters, there are large simultaneous phononic and photonic bandgaps.

Fig. 6.
Fig. 6.

Phononic (a,b) and photonic (c,d) gap maps for a quasi-2D snowflake substrate. The photonic gap maps are for the even vertical symmetry modes of the slab only. In (a,c) we vary the snowflake width and (b,d) the snowflake radius. The nominal structure about which the variations are performed is characterized by parameters (d,r,w,a) = (220,200,75,500) nm. The lattice constant a is varied while keeping the ratios r/a = 0.4 and w/a = 0.15 constant in (a,c) and (b,d), respectively.

Fig. 7.
Fig. 7.

(a) Schematic of a W1-like linear defect waveguide in the quasi-2D snowflake crystal slab structure. The central row of snowflake holes is completely removed along the x-direction (Γ-K in reciprocal space), and the remaining top and bottom pieces of the lattice are shifted by a value W towards each other (effectively a strip of 2W is removed from the center of the waveguide). A transverse radius variation of the snowflake holes is also applied. N WG d is the number of rows of holes which take part in forming this defect. The number rd represents the factor by which the radius of holes on the two rows neighbouring the center of the defect are reduced; i.e. the radius is changed to r × (1 − rd ), where r is the nominal radius. Rows going further out from the center of the waveguide have radii which scale quadratically to the nominal value of r. (b) Cavities are formed from this line-defect waveguide by a longitudinal modulation of the waveguide parameters. In this case, the rd scale factor is varied quadratically from 0 to a desired value at the cavity center along the length of the waveguide over a period of Nd lattice periods. The cavity structure shown here has rd = 0.4 at the cavity center, Nd = 10 and N WG d = 7.

Fig. 8.
Fig. 8.

(a) Photonic and (b) phononic waveguide bands for an optomechanical waveguide on a snowflake substrate with (d,r,w,a) = (220,210,75,500) nm, and a W1-like waveguide with properties W = 200 nm and rd = 0. The E and O symbols represent even and odd vector parity, respectively, of the zone boundary modes with respect to σy reflections for the optical and σx reflections for the mechanical modes. The same mode labels are used in Fig. 9. In (a), only the even vertical symmetry modes are shown (those including the fundamental TE-like modes, but not the fundamental TM-like modes). In (b), guided modes with different transverse symmetries (σyz ) are colored (oe-18-14-14926-i005.jpg), (oe-18-14-14926-i006.jpg) and (oe-18-14-14926-i007.jpg) for symmetries (+,+), (±,−), and (−,+), respectively. In both diagrams frequencies above and below the in-plane bandgap are colored light grey, and in (a) the light cone is region is colored dark grey. Above the light-line in (a), the leaky mode bands are colored red (oe-18-14-14926-i008.jpg). In both (a) and (b) we have highlighted the bandgap regions which will be relevant in the cavity design pursued below.

Fig. 9.
Fig. 9.

Tuning of the (a) X-point optical and (b) Γ-point mechanical waveguide modes of a W1-like waveguide in a snowflake substrate with parameters (d,r,w,a) = (220,210,75,500) nm. Tuning is shown versus both waveguide width W and snowflake radius r. In this case we have taken rd = 0, and N WG d = 1. See Fig. 7(a) for line-defect waveguide description. The E and O symbols represent respectively the even and odd vector parity of E(r) with respect to mirror reflection σy about the middle of the waveguide and Q(r) with respect to mirror reflection σx about the middle of each waveguide unit cell. In the optical field plots we show a snapshot in time of the y-polarization of the electric field (Ey (r)), with red and blue indicating positive and negative values of the field, respectively. In the mechanical mode plots, color indicates the magnitude of the displacement field (blue no displacement, and red large displacement), and the displacement of the structure has been exaggerated for viewing purposes.

Fig. 10.
Fig. 10.

Plots of the localized ultrahigh-Q resonances of an optomechanical cavity formed in a Si snowflake thin-film substrate with parameters (d,r,w,a) = (220,210,75,500) nm. (a) Optical field (Ey (r)) and (b) magnitude of the mechanical displacement field (Q(r)). (c) Zoom-in of the mechanical displacement field. In the optical field plot we show a snapshot in time of the y-polarization of the electric field, with red and blue indicating positive and negative values of the field, respectively. In the mechanical mode plots, color indicates the magnitude of the displacement field (blue no displacement, and red large displacement), and the displacement of the structure has been exaggerated for viewing purposes. The mechanical resonance is at a frequency of νm = 9.50 GHz, and the optical mode at a wavelength of λ 0 = 1.459 µm. The defect cavity design, with parameters (rd,Nd,N WG d ) = (0.03,14,5), is described in Fig. 7. The lowest-order optomechanical coupling between the photon and phonon cavity resonances is calculated to be g = 2π × 292 kHz.

Equations (14)

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

Q ( x + ) ( r b + a e x ) = + σ x Q ( x + ) ( r b ) ,
Q ( x ) ( r b + a e x ) = σ x Q ( x ) ( r b ) ,
Q Γ ( r + a e x ) = + Q Γ ( r ) ,
Q X ( r + a e x ) = Q X ( r ) .
e x · Q Γ ( x + ) ( r b ) = 0 ,
e x × Q X ( x + ) ( r b ) = 0 .
g = h ¯ 2 Ω ω o 2 ( Q ( r ) · n ) ( Δ ε E 2 Δ ( ε 1 ) D 2 ) d A ρ Q ( r ) 2 d 3 r ε ( r ) E ( r ) 2 d 3 r .
E ± ( r ) = E X ( r ) e ± i k X · r f e ( x ) ,
Q ( r ) = Q Γ ( r ) f m ( x ) ,
Q ( r ) 2 d r 1 a Δ Q Γ ( r ) 2 d 3 r f m ( x ) 2 dx .
g a g Δ f e f m f e f m f m f e f e ,
g Δ = h ¯ 2 Ω ω o 2 Δ ( Q Γ ( r ) · n ) ( Δ ε E X 2 Δ ( ε 1 ) D X 2 ) d A Δ ρ Q Γ ( r ) 2 d 3 r Δ ε ( r ) E X ( r ) 2 d 3 r .
f e f m f e = 1 ( 2 π ) 1 4 1 L m + 1 2 L e 2 L m .
g optimal 1 ( 4 π ) 1 4 g Δ a L e .

Metrics