Abstract

The limits of validity of the linear photoelastic model are investigated in a one-dimensional dual photonic-phononic cavity, formed by alternating layers of a chalcogenide glass and a polymer homogeneous and isotropic material, which supports both optical and acoustic resonant modes localized in the same region. It is shown that the linear-response regime breaks down when either the acoustic excitation increases or the first-order acousto-optic interaction coupling element vanishes by symmetry, giving rise to the manifestation of multiphonon absorption and emission processes by a photon. Our results provide a consistent interpretation of different aspects of the underlying physics relating to nonlinear acousto-optic interactions that can occur in such cavities.

© 2014 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Acousto-optic coupling in phoxonic crystal nanobeam cavities with plasmonic behavior

Jin-Chen Hsu, Tsung-Yi Lu, and Tzy-Rong Lin
Opt. Express 23(20) 25814-25826 (2015)

Acousto-optical interaction of surface acoustic and optical waves in a two-dimensional phoxonic crystal hetero-structure cavity

Tian-Xue Ma, Kui Zou, Yue-Sheng Wang, Chuanzeng Zhang, and Xiao-Xing Su
Opt. Express 22(23) 28443-28451 (2014)

High-efficiency acousto-optic coupling in phoxonic resonator based on silicon fishbone nanobeam cavity

Chien-Chang Chiu, Wei-Min Chen, Kuen-Wei Sung, and Fu-Li Hsiao
Opt. Express 25(6) 6076-6091 (2017)

References

  • View by:
  • |
  • |
  • |

  1. A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 2003).
  2. J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551 (1999).
    [Crossref]
  3. H. Ma, S. Qu, and Z. Xu, “Photonic crystals based on acousto-optic effects,” J. Appl. Phys. 103(10), 104904 (2008).
    [Crossref]
  4. J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79(5), 053821 (2009).
    [Crossref]
  5. J. C. Hsu, C. H. Lin, Y. C. Ku, and T. R. Lin, “Photonic band gaps induced by submicron acoustic plate waves in dielectric slab waveguides,” Opt. Lett. 38(20), 4050–4053 (2013).
    [Crossref] [PubMed]
  6. S. Krishnamurthy and P. V. Santos, “High-contrast optical modulation by surface acoustic waves,” Appl. Phys. Lett. 83(13), 2548–2550 (2003).
    [Crossref]
  7. X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
    [Crossref]
  8. N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
    [Crossref]
  9. C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34(6), 4129 (1986).
    [Crossref]
  10. N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
    [Crossref]
  11. J. -F. Robillard, A. Devos, I. Roch-Jeune, and P. A. Mante, “Collective acoustic modes in various two-dimensional crystals by ultrafast acoustics: Theory and experiment,” Phys. Rev. B 78(6), 064302 (2008).
    [Crossref]
  12. T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
    [Crossref]
  13. P. M. Walker, J. S. Sharp, A. V. Akimov, and A. J. Kent, “Coherent elastic waves in a one-dimensional polymer hypersonic crystal,” Appl. Phys. Lett. 97(7), 073106 (2010).
    [Crossref]
  14. A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
    [Crossref] [PubMed]
  15. D. J. Farmer, A. V. Akimov, N. A. Gippius, J. Bailey, J. S. Sharp, and A. J. Kent, “High-frequency acousto-optic effects in Bragg reflectors,” Opt. Express 22(12), 15218–15231 (2014).
    [Crossref] [PubMed]
  16. M. Trigo, A. Bruchhausen, A. Fainstein, B. Jusserand, and V. Thierry-Mieg, “Confinement of acoustical vibrations in a semiconductor planar phonon cavity,” Phys. Rev. Lett. 89(22), 227402 (2002).
    [Crossref] [PubMed]
  17. J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
    [Crossref]
  18. N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
    [Crossref] [PubMed]
  19. T. Gorishnyy, M. Maldovan, C. Ullal, and E. L. Thomas, “Sound ideas,” Phys. World 18(12), 24–29 (2005).
  20. I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
    [Crossref]
  21. N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
    [Crossref]
  22. E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
    [Crossref]
  23. J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
    [Crossref]
  24. M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B: Lasers and Optics 83(4), 595–600 (2006).
    [Crossref]
  25. 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]
  26. 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]
  27. D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
    [Crossref]
  28. T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
    [Crossref]
  29. Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
    [Crossref]
  30. S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
    [Crossref] [PubMed]
  31. Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
    [Crossref] [PubMed]
  32. N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96(23), 231917 (2010).
    [Crossref]
  33. T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
    [Crossref] [PubMed]
  34. V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
    [Crossref] [PubMed]
  35. Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
    [Crossref]
  36. J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
    [Crossref]
  37. T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, ”Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect,” J. Opt. 16(8), 085002 (2014).
    [Crossref]
  38. J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
    [Crossref] [PubMed]
  39. F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
    [Crossref]
  40. Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
    [Crossref]
  41. T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
    [Crossref]
  42. S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
    [Crossref]
  43. S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).
  44. L. Kipfstuhl, F. Guldner, J. Riedrich-Möller, and C. Becher, “Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond,” Opt. Express 22(10), 12410–12423 (2014).
    [Crossref] [PubMed]
  45. M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
    [Crossref]
  46. Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).
  47. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
    [Crossref] [PubMed]
  48. A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
    [Crossref] [PubMed]
  49. J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
    [Crossref] [PubMed]
  50. A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
    [Crossref] [PubMed]
  51. O. Matsuda and O. B. Wright, “Reflection and transmission of light in multilayers perturbed by picosecond strain pulse propagation,” J. Opt. Soc. Am. B 19(12), 3028–3041 (2002).
    [Crossref]
  52. E. Bormashenko, R. Pogreb, Z. Pogreb, and S. Sutovski, “Development of new near-infrared filters based on the sandwich polymer-chalcogenide glass-polymer composites,” Opt. Eng. 40(5), 661–662 (2001).
    [Crossref]
  53. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
    [Crossref] [PubMed]
  54. G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
    [Crossref]
  55. Y. Ohmachi and N. Uchida, “Vitreous As2Se3; Investigation of acousto-optical properties and application to infrared modulator,” J. Appl. Phys. 43(4), 1709–1712 (1972).
    [Crossref]
  56. M. E. Boyle and R. F. Cozzens, “Acousto-optic and linear electro-optic properties of organic polymeric materials,” Naval Research LabWashington DC, No. NRL-MR-6454 (1989).
  57. S. Jakobs, A. Petrov, and M. Eich, “Suppression of stimulated Brillouin scattering in integrated chalcogenide waveguides,” J. Opt. Soc. Am. B 31(2), 178–188 (2014).
    [Crossref]
  58. J. E. Mark, Polymer Data Handbook (Oxford University, 2009).
  59. N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49 (1998).
    [Crossref]
  60. N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1), 189 (2000).
    [Crossref]
  61. R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, ”A layer-multiple-scattering method for phononic crystals and heterostructures of such,” Comput. Phys. Commun. 166(3), 197–240 (2005).
    [Crossref]
  62. E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.
  63. K. Børkje, A. Nunnenkamp, J. D. Tenfel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
    [Crossref] [PubMed]
  64. C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
    [Crossref]

2014 (11)

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, ”Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect,” J. Opt. 16(8), 085002 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

S. Jakobs, A. Petrov, and M. Eich, “Suppression of stimulated Brillouin scattering in integrated chalcogenide waveguides,” J. Opt. Soc. Am. B 31(2), 178–188 (2014).
[Crossref]

L. Kipfstuhl, F. Guldner, J. Riedrich-Möller, and C. Becher, “Modeling of optomechanical coupling in a phoxonic crystal cavity in diamond,” Opt. Express 22(10), 12410–12423 (2014).
[Crossref] [PubMed]

D. J. Farmer, A. V. Akimov, N. A. Gippius, J. Bailey, J. S. Sharp, and A. J. Kent, “High-frequency acousto-optic effects in Bragg reflectors,” Opt. Express 22(12), 15218–15231 (2014).
[Crossref] [PubMed]

2013 (6)

K. Børkje, A. Nunnenkamp, J. D. Tenfel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

J. C. Hsu, C. H. Lin, Y. C. Ku, and T. R. Lin, “Photonic band gaps induced by submicron acoustic plate waves in dielectric slab waveguides,” Opt. Lett. 38(20), 4050–4053 (2013).
[Crossref] [PubMed]

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

2012 (5)

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
[Crossref]

2011 (5)

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

2010 (9)

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

P. M. Walker, J. S. Sharp, A. V. Akimov, and A. J. Kent, “Coherent elastic waves in a one-dimensional polymer hypersonic crystal,” Appl. Phys. Lett. 97(7), 073106 (2010).
[Crossref]

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96(23), 231917 (2010).
[Crossref]

S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, “Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs,” Opt. Express 18(9), 9164–9172 (2010).
[Crossref] [PubMed]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

2009 (4)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
[Crossref]

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79(5), 053821 (2009).
[Crossref]

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

2008 (3)

H. Ma, S. Qu, and Z. Xu, “Photonic crystals based on acousto-optic effects,” J. Appl. Phys. 103(10), 104904 (2008).
[Crossref]

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

J. -F. Robillard, A. Devos, I. Roch-Jeune, and P. A. Mante, “Collective acoustic modes in various two-dimensional crystals by ultrafast acoustics: Theory and experiment,” Phys. Rev. B 78(6), 064302 (2008).
[Crossref]

2007 (1)

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

2006 (2)

M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B: Lasers and Optics 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 (2)

T. Gorishnyy, M. Maldovan, C. Ullal, and E. L. Thomas, “Sound ideas,” Phys. World 18(12), 24–29 (2005).

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, ”A layer-multiple-scattering method for phononic crystals and heterostructures of such,” Comput. Phys. Commun. 166(3), 197–240 (2005).
[Crossref]

2003 (2)

G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
[Crossref]

S. Krishnamurthy and P. V. Santos, “High-contrast optical modulation by surface acoustic waves,” Appl. Phys. Lett. 83(13), 2548–2550 (2003).
[Crossref]

2002 (3)

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

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[Crossref] [PubMed]

O. Matsuda and O. B. Wright, “Reflection and transmission of light in multilayers perturbed by picosecond strain pulse propagation,” J. Opt. Soc. Am. B 19(12), 3028–3041 (2002).
[Crossref]

2001 (1)

E. Bormashenko, R. Pogreb, Z. Pogreb, and S. Sutovski, “Development of new near-infrared filters based on the sandwich polymer-chalcogenide glass-polymer composites,” Opt. Eng. 40(5), 661–662 (2001).
[Crossref]

2000 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1), 189 (2000).
[Crossref]

1999 (1)

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551 (1999).
[Crossref]

1998 (1)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49 (1998).
[Crossref]

1986 (1)

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34(6), 4129 (1986).
[Crossref]

1972 (1)

Y. Ohmachi and N. Uchida, “Vitreous As2Se3; Investigation of acousto-optical properties and application to infrared modulator,” J. Appl. Phys. 43(4), 1709–1712 (1972).
[Crossref]

Adibi, A.

Ahopelto, J.

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

Akimov, A. V.

D. J. Farmer, A. V. Akimov, N. A. Gippius, J. Bailey, J. S. Sharp, and A. J. Kent, “High-frequency acousto-optic effects in Bragg reflectors,” Opt. Express 22(12), 15218–15231 (2014).
[Crossref] [PubMed]

P. M. Walker, J. S. Sharp, A. V. Akimov, and A. J. Kent, “Coherent elastic waves in a one-dimensional polymer hypersonic crystal,” Appl. Phys. Lett. 97(7), 073106 (2010).
[Crossref]

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Akjouj, A.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Almpanis, E.

E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
[Crossref]

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Alzina, F.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Aspelmeyer, M.

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Assouar, M. B.

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[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]

Bailey, J.

Bayer, M.

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Becher, C.

Benchabane, S.

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[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]

Benoit, G.

G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[Crossref] [PubMed]

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]

Berstermann, T.

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Beugnot, J. C.

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Bombeck, M.

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Bonello, B.

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Børkje, K.

K. Børkje, A. Nunnenkamp, J. D. Tenfel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

Bormashenko, E.

E. Bormashenko, R. Pogreb, Z. Pogreb, and S. Sutovski, “Development of new near-infrared filters based on the sandwich polymer-chalcogenide glass-polymer composites,” Opt. Eng. 40(5), 661–662 (2001).
[Crossref]

Boyle, M. E.

M. E. Boyle and R. F. Cozzens, “Acousto-optic and linear electro-optic properties of organic polymeric materials,” Naval Research LabWashington DC, No. NRL-MR-6454 (1989).

Bria, D.

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Bruchhausen, A.

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

Brüggemann, C.

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Butt, H.-J.

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Castro-Garay, P.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Cervantes-González, J. C.

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79(5), 053821 (2009).
[Crossref]

Chan, J.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Chang, D. E.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Chavez, E.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Chen, Y.

X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
[Crossref]

Chiu, C. C.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Courjal, N.

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

Cozzens, R. F.

M. E. Boyle and R. F. Cozzens, “Acousto-optic and linear electro-optic properties of organic polymeric materials,” Naval Research LabWashington DC, No. NRL-MR-6454 (1989).

Dahdah, J.

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

Davis, J. P.

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

Devos, A.

J. -F. Robillard, A. Devos, I. Roch-Jeune, and P. A. Mante, “Collective acoustic modes in various two-dimensional crystals by ultrafast acoustics: Theory and experiment,” Phys. Rev. B 78(6), 064302 (2008).
[Crossref]

Djafari-Rouhani, B.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Doolin, C.

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

Dupont, S.

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Eftekhar, A. A.

Eich, M.

Eichenfield, M.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

El Boudouti, E. H.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

El Hassouani, Y.

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

El-Jallal, S.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Escalante, J. M.

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Fainstein, A.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

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

Fan, S.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551 (1999).
[Crossref]

Farmer, D. J.

Fink, Y.

G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[Crossref] [PubMed]

Fytas, G.

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

Gantzounis, G.

Gazalet, J.

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Gippius, N. A.

Girvin, S. M.

K. Børkje, A. Nunnenkamp, J. D. Tenfel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

Glezos, N.

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Gomis-Bresco, J.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Gomopoulos, N.

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

Gorishnyy, T.

T. Gorishnyy, M. Maldovan, C. Ullal, and E. L. Thomas, “Sound ideas,” Phys. World 18(12), 24–29 (2005).

Grahn, H. T.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34(6), 4129 (1986).
[Crossref]

Griol, A.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Gröblacher, S.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Groenen, J.

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

Gruson, Y.

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

Guldner, F.

Halevi, P.

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79(5), 053821 (2009).
[Crossref]

Hart, S. D.

G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[Crossref] [PubMed]

Hauer, B. D.

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

Hill, J. T.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Hommel, D.

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Hsiao, F. L.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Hsieh, C. Y.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Hsieh, H. Y.

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Hsu, J. C.

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

J. C. Hsu, C. H. Lin, Y. C. Ku, and T. R. Lin, “Photonic band gaps induced by submicron acoustic plate waves in dielectric slab waveguides,” Opt. Lett. 38(20), 4050–4053 (2013).
[Crossref] [PubMed]

Huynh, A.

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

Ippen, E. P.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551 (1999).
[Crossref]

Jakobs, S.

Joannopoulos, J. D.

G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[Crossref] [PubMed]

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551 (1999).
[Crossref]

Jusserand, B.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

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

Kastelik, J. C.

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Kent, A. J.

D. J. Farmer, A. V. Akimov, N. A. Gippius, J. Bailey, J. S. Sharp, and A. J. Kent, “High-frequency acousto-optic effects in Bragg reflectors,” Opt. Express 22(12), 15218–15231 (2014).
[Crossref] [PubMed]

P. M. Walker, J. S. Sharp, A. V. Akimov, and A. J. Kent, “Coherent elastic waves in a one-dimensional polymer hypersonic crystal,” Appl. Phys. Lett. 97(7), 073106 (2010).
[Crossref]

Khelif, A.

Kim, P. H.

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

Kipfstuhl, L.

Koh, C. Y.

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

Krause, A.

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Krishnamurthy, S.

S. Krishnamurthy and P. V. Santos, “High-contrast optical modulation by surface acoustic waves,” Appl. Phys. Lett. 83(13), 2548–2550 (2003).
[Crossref]

Kruse, C.

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Ku, Y. C.

Lanzillotti-Kimura, N. D.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

Larabi, H.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Laude, V.

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

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

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Lemaître, A.

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

Lévêque, G.

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Li, C.

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Li, J. P.

X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
[Crossref]

Lin, C. H.

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

J. C. Hsu, C. H. Lin, Y. C. Ku, and T. R. Lin, “Photonic band gaps induced by submicron acoustic plate waves in dielectric slab waveguides,” Opt. Lett. 38(20), 4050–4053 (2013).
[Crossref] [PubMed]

Lin, Q.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Lin, T. R.

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

J. C. Hsu, C. H. Lin, Y. C. Ku, and T. R. Lin, “Photonic band gaps induced by submicron acoustic plate waves in dielectric slab waveguides,” Opt. Lett. 38(20), 4050–4053 (2013).
[Crossref] [PubMed]

Lu, M.

X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
[Crossref]

Lu, Y.

X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
[Crossref]

Ma, H.

H. Ma, S. Qu, and Z. Xu, “Photonic crystals based on acousto-optic effects,” J. Appl. Phys. 103(10), 104904 (2008).
[Crossref]

Ma, T. X.

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, ”Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect,” J. Opt. 16(8), 085002 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

MacDonald, A. J. R.

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

Makhoute, A.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Maldovan, M.

M. Maldovan and E. L. Thomas, “Simultaneous complete elastic and electromagnetic band gaps in periodic structures,” Appl. Phys. B: Lasers and Optics 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]

T. Gorishnyy, M. Maldovan, C. Ullal, and E. L. Thomas, “Sound ideas,” Phys. World 18(12), 24–29 (2005).

Mante, P. A.

J. -F. Robillard, A. Devos, I. Roch-Jeune, and P. A. Mante, “Collective acoustic modes in various two-dimensional crystals by ultrafast acoustics: Theory and experiment,” Phys. Rev. B 78(6), 064302 (2008).
[Crossref]

Manzanares-Martinez, B.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Manzanares-Martinez, J.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Maris, H. J.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34(6), 4129 (1986).
[Crossref]

Mark, J. E.

J. E. Mark, Polymer Data Handbook (Oxford University, 2009).

Martinez, A.

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Martínez, A.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Maschke, D.

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

Matar, O. B.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Matsuda, O.

Mayer Alegre, T. P.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

Meenehan, S.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

Miard, A.

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

Moctezuma-Enriquez, D.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Modinos, A.

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, ”A layer-multiple-scattering method for phononic crystals and heterostructures of such,” Comput. Phys. Commun. 166(3), 197–240 (2005).
[Crossref]

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1), 189 (2000).
[Crossref]

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49 (1998).
[Crossref]

Mohammadi, S.

Navarro-Urrios, D.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Nunnenkamp, A.

K. Børkje, A. Nunnenkamp, J. D. Tenfel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

Ohmachi, Y.

Y. Ohmachi and N. Uchida, “Vitreous As2Se3; Investigation of acousto-optical properties and application to infrared modulator,” J. Appl. Phys. 43(4), 1709–1712 (1972).
[Crossref]

Oudich, M.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Painter, O.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Papanikolaou, N.

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
[Crossref]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96(23), 231917 (2010).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Pennec, Y.

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

V. Laude, J. C. Beugnot, S. Benchabane, Y. Pennec, B. Djafari-Rouhani, N. Papanikolaou, J. M. Escalante, and A. Martinez, “Simultaneous guidance of slow photons and slow acoustic phonons in silicon phoxonic crystal slabs,” Opt. Express 19(10), 9690–9698 (2011).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

Y. Pennec, B. Djafari-Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

Perrin, B.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

Petrov, A.

Pogreb, R.

E. Bormashenko, R. Pogreb, Z. Pogreb, and S. Sutovski, “Development of new near-infrared filters based on the sandwich polymer-chalcogenide glass-polymer composites,” Opt. Eng. 40(5), 661–662 (2001).
[Crossref]

Pogreb, Z.

E. Bormashenko, R. Pogreb, Z. Pogreb, and S. Sutovski, “Development of new near-infrared filters based on the sandwich polymer-chalcogenide glass-polymer composites,” Opt. Eng. 40(5), 661–662 (2001).
[Crossref]

Poinsotte, F.

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

Prunnila, M.

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

Psarobas, I.

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96(23), 231917 (2010).
[Crossref]

Psarobas, I. E.

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, ”A layer-multiple-scattering method for phononic crystals and heterostructures of such,” Comput. Phys. Commun. 166(3), 197–240 (2005).
[Crossref]

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Puerto, D.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Qian, X. S.

X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
[Crossref]

Qu, S.

H. Ma, S. Qu, and Z. Xu, “Photonic crystals based on acousto-optic effects,” J. Appl. Phys. 103(10), 104904 (2008).
[Crossref]

Ramp, H.

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

Riedrich-Möller, J.

Robillard, J. -F.

J. -F. Robillard, A. Devos, I. Roch-Jeune, and P. A. Mante, “Collective acoustic modes in various two-dimensional crystals by ultrafast acoustics: Theory and experiment,” Phys. Rev. B 78(6), 064302 (2008).
[Crossref]

Roch-Jeune, I.

J. -F. Robillard, A. Devos, I. Roch-Jeune, and P. A. Mante, “Collective acoustic modes in various two-dimensional crystals by ultrafast acoustics: Theory and experiment,” Phys. Rev. B 78(6), 064302 (2008).
[Crossref]

Rodriguez-Viveros, Y. J.

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

Rolland, Q.

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[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]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Sainidou, R.

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, ”A layer-multiple-scattering method for phononic crystals and heterostructures of such,” Comput. Phys. Commun. 166(3), 197–240 (2005).
[Crossref]

Santos, P. V.

S. Krishnamurthy and P. V. Santos, “High-contrast optical modulation by surface acoustic waves,” Appl. Phys. Lett. 83(13), 2548–2550 (2003).
[Crossref]

Sharp, J. S.

D. J. Farmer, A. V. Akimov, N. A. Gippius, J. Bailey, J. S. Sharp, and A. J. Kent, “High-frequency acousto-optic effects in Bragg reflectors,” Opt. Express 22(12), 15218–15231 (2014).
[Crossref] [PubMed]

P. M. Walker, J. S. Sharp, A. V. Akimov, and A. J. Kent, “Coherent elastic waves in a one-dimensional polymer hypersonic crystal,” Appl. Phys. Lett. 97(7), 073106 (2010).
[Crossref]

Sotomayor Torres, C. M.

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

Stefanou, N.

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

E. Almpanis, N. Papanikolaou, G. Gantzounis, and N. Stefanou, “Tuning the spontaneous light emission in phoxonic cavities,” J. Opt. Soc. Am. B 29(9), 2567–2574 (2012).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96(23), 231917 (2010).
[Crossref]

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, ”A layer-multiple-scattering method for phononic crystals and heterostructures of such,” Comput. Phys. Commun. 166(3), 197–240 (2005).
[Crossref]

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1), 189 (2000).
[Crossref]

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49 (1998).
[Crossref]

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

Su, X. X.

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, ”Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect,” J. Opt. 16(8), 085002 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

Sutovski, S.

E. Bormashenko, R. Pogreb, Z. Pogreb, and S. Sutovski, “Development of new near-infrared filters based on the sandwich polymer-chalcogenide glass-polymer composites,” Opt. Eng. 40(5), 661–662 (2001).
[Crossref]

Tauc, J.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34(6), 4129 (1986).
[Crossref]

Temelkuran, B.

G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
[Crossref]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[Crossref] [PubMed]

Tenfel, J. D.

K. Børkje, A. Nunnenkamp, J. D. Tenfel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

Thierry-Mieg, V.

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

Thomas, E. L.

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

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: Lasers and Optics 83(4), 595–600 (2006).
[Crossref]

T. Gorishnyy, M. Maldovan, C. Ullal, and E. L. Thomas, “Sound ideas,” Phys. World 18(12), 24–29 (2005).

Thomsen, C.

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34(6), 4129 (1986).
[Crossref]

Tremel, W.

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

Trigo, M.

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

Uchida, N.

Y. Ohmachi and N. Uchida, “Vitreous As2Se3; Investigation of acousto-optical properties and application to infrared modulator,” J. Appl. Phys. 43(4), 1709–1712 (1972).
[Crossref]

Ullal, C.

T. Gorishnyy, M. Maldovan, C. Ullal, and E. L. Thomas, “Sound ideas,” Phys. World 18(12), 24–29 (2005).

Ulliac, G.

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

Vasseur, J.

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

Vasseur, J. O.

Walker, P. M.

P. M. Walker, J. S. Sharp, A. V. Akimov, and A. J. Kent, “Coherent elastic waves in a one-dimensional polymer hypersonic crystal,” Appl. Phys. Lett. 97(7), 073106 (2010).
[Crossref]

Wang, Y. F.

Wang, Y. S.

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, ”Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect,” J. Opt. 16(8), 085002 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, Y. F. Wang, and X. X. Su, “Three-dimensional dielectric phoxonic crystals with network topology,” Opt. Express 21(3), 2727–2732 (2013).
[Crossref] [PubMed]

Winger, M.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Winn, J. N.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551 (1999).
[Crossref]

Wright, O. B.

Xu, Z.

H. Ma, S. Qu, and Z. Xu, “Photonic crystals based on acousto-optic effects,” J. Appl. Phys. 103(10), 104904 (2008).
[Crossref]

Yakovlev, D. R.

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Yannopapas, V.

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1), 189 (2000).
[Crossref]

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49 (1998).
[Crossref]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 2003).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 2003).

Zhang, C.

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, ”Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect,” J. Opt. 16(8), 085002 (2014).
[Crossref]

Zurita-Sánchez, J. R.

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79(5), 053821 (2009).
[Crossref]

Zwick, A.

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

Adv. Mater. (1)

G. Benoit, S. D. Hart, B. Temelkuran, J. D. Joannopoulos, and Y. Fink, “Static and dynamic properties of optical microcavities in photonic bandgap yarns,” Adv. Mater. 15(24), 2053–2056 (2003).
[Crossref]

AIP Advances (1)

Y. Pennec, B. Djafari-Rouhani, C. Li, J. M. Escalante, A. Martinez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Advances 1(4), 041901 (2011).
[Crossref]

Appl. Phys. B: Lasers and Optics (1)

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

Appl. Phys. Lett. (8)

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]

F. L. Hsiao, C. Y. Hsieh, H. Y. Hsieh, and C. C. Chiu, “High-efficiency acousto-optical interaction in phoxonic nanobeam waveguide,” Appl. Phys. Lett. 100(17), 171103 (2012).
[Crossref]

Q. Rolland, M. Oudich, S. El-Jallal, S. Dupont, Y. Pennec, J. Gazalet, J. C. Kastelik, G. Lévêque, and B. Djafari-Rouhani, “Acousto-optic couplings in two-dimensional phoxonic crystal cavities,” Appl. Phys. Lett. 101(6), 061109 (2012).
[Crossref]

S. Krishnamurthy and P. V. Santos, “High-contrast optical modulation by surface acoustic waves,” Appl. Phys. Lett. 83(13), 2548–2550 (2003).
[Crossref]

N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
[Crossref]

P. M. Walker, J. S. Sharp, A. V. Akimov, and A. J. Kent, “Coherent elastic waves in a one-dimensional polymer hypersonic crystal,” Appl. Phys. Lett. 97(7), 073106 (2010).
[Crossref]

J. Manzanares-Martinez, D. Moctezuma-Enriquez, Y. J. Rodriguez-Viveros, B. Manzanares-Martinez, and P. Castro-Garay, “Non-perpendicular hypersonic and optical stop-bands in porous silicon multilayers,” Appl. Phys. Lett. 101(26), 261902 (2012).
[Crossref]

N. Papanikolaou, I. Psarobas, and N. Stefanou, “Absolute spectral gaps for infrared light and hypersound in three-dimensional metallodielectric phoxonic crystals,” Appl. Phys. Lett. 96(23), 231917 (2010).
[Crossref]

Comput. Phys. Commun. (3)

N. Stefanou, V. Yannopapas, and A. Modinos, “Heterostructures of photonic crystals: frequency bands and transmission coefficients,” Comput. Phys. Commun. 113(1), 49 (1998).
[Crossref]

N. Stefanou, V. Yannopapas, and A. Modinos, “MULTEM2: A new version of the program for transmission and band-structure calculations of photonic crystals,” Comput. Phys. Commun. 132(1), 189 (2000).
[Crossref]

R. Sainidou, N. Stefanou, I. E. Psarobas, and A. Modinos, ”A layer-multiple-scattering method for phononic crystals and heterostructures of such,” Comput. Phys. Commun. 166(3), 197–240 (2005).
[Crossref]

J. Appl. Phys. (7)

Y. Ohmachi and N. Uchida, “Vitreous As2Se3; Investigation of acousto-optical properties and application to infrared modulator,” J. Appl. Phys. 43(4), 1709–1712 (1972).
[Crossref]

X. S. Qian, J. P. Li, M. Lu, Y. Lu, and Y. Chen, “Acousto-optic interaction in photonic crystals with defects,” J. Appl. Phys. 106(4), 043107 (2009).
[Crossref]

H. Ma, S. Qu, and Z. Xu, “Photonic crystals based on acousto-optic effects,” J. Appl. Phys. 103(10), 104904 (2008).
[Crossref]

T. R. Lin, C. H. Lin, and J. C. Hsu, “Enhanced acousto-optic interaction in two-dimensional phoxonic crystals with a line defect,” J. Appl. Phys. 113(5), 053508 (2013).
[Crossref]

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

D. Bria, M. B. Assouar, M. Oudich, Y. Pennec, J. Vasseur, and B. Djafari-Rouhani, “Opening of simultaneous photonic and phononic band gap in two-dimensional square lattice periodic structure,” J. Appl. Phys. 109(1), 014507 (2011).
[Crossref]

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

J. Opt. (1)

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, ”Simultaneous guiding of slow elastic and light waves in three-dimensional topology-type phoxonic crystals with a line defect,” J. Opt. 16(8), 085002 (2014).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. : Condens. Matter (1)

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, A. Makhoute, Q. Rolland, S. Dupont, and J. Gazalet, “Optomechanical interactions in two-dimensional Si and GaAs phoXonic cavities,” J. Phys. : Condens. Matter 26(1), 015005 (2014).

Microel. Eng. (1)

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microel. Eng. 90, 155–158 (2012).
[Crossref]

Nano Lett. (1)

N. Gomopoulos, D. Maschke, C. Y. Koh, E. L. Thomas, W. Tremel, H.-J. Butt, and G. Fytas, “One-dimensional hypersonic phononic crystals,” Nano Lett. 10(3), 980–984 (2010).
[Crossref] [PubMed]

Nat. Commun. (1)

J. Gomis-Bresco, D. Navarro-Urrios, M. Oudich, S. El-Jallal, A. Griol, D. Puerto, E. Chavez, Y. Pennec, B. Djafari-Rouhani, F. Alzina, A. Martínez, and C. M. Sotomayor Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Nature (4)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 (2002).
[Crossref] [PubMed]

Opt. Commun. (1)

T. X. Ma, Y. S. Wang, and C. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312, 68–72 (2014).
[Crossref]

Opt. Eng. (1)

E. Bormashenko, R. Pogreb, Z. Pogreb, and S. Sutovski, “Development of new near-infrared filters based on the sandwich polymer-chalcogenide glass-polymer composites,” Opt. Eng. 40(5), 661–662 (2001).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. A (2)

C. Doolin, B. D. Hauer, P. H. Kim, A. J. R. MacDonald, H. Ramp, and J. P. Davis, “Nonlinear optomechanics in the stationary regime,” Phys. Rev. A 89(5), 053838 (2014).
[Crossref]

J. R. Zurita-Sánchez, P. Halevi, and J. C. Cervantes-González, “Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function ε(t),” Phys. Rev. A 79(5), 053821 (2009).
[Crossref]

Phys. Rev. B (9)

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551 (1999).
[Crossref]

J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, “Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures,” Phys. Rev. B 77(4), 045420 (2008).
[Crossref]

I. E. Psarobas, N. Papanikolaou, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Enhanced acousto-optic interactions in a one-dimensional phoxonic cavity,” Phys. Rev. B 82(17), 174303 (2010).
[Crossref]

C. Thomsen, H. T. Grahn, H. J. Maris, and J. Tauc, “Surface generation and detection of phonons by picosecond light pulses,” Phys. Rev. B 34(6), 4129 (1986).
[Crossref]

J. -F. Robillard, A. Devos, I. Roch-Jeune, and P. A. Mante, “Collective acoustic modes in various two-dimensional crystals by ultrafast acoustics: Theory and experiment,” Phys. Rev. B 78(6), 064302 (2008).
[Crossref]

T. Berstermann, C. Brüggemann, M. Bombeck, A. V. Akimov, D. R. Yakovlev, C. Kruse, D. Hommel, and M. Bayer, “Optical bandpass switching by modulating a microcavity using ultrafast acoustics,” Phys. Rev. B 81(8), 085316 (2010).
[Crossref]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. B. Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari-Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
[Crossref]

S. El-Jallal, M. Oudich, Y. Pennec, B. Djafari-Rouhani, V. Laude, J. C. Beugnot, A. Martínez, J. M. Escalante, and A. Makhoute, “Analysis of optomechanical coupling in two-dimensional square lattice phoxonic crystal slab cavities,” Phys. Rev. B 88(20), 205410 (2013).
[Crossref]

M. Oudich, S. El-Jallal, Y. Pennec, B. Djafari-Rouhani, J. Gomis-Bresco, D. Navarro-Urrios, C. M. Sotomayor Torres, A. Martínez, and A. Makhoute, “Optomechanic interaction in a corrugated phoxonic nanobeam cavity,” Phys. Rev. B 89(24), 245122 (2014).
[Crossref]

Phys. Rev. Lett. (5)

K. Børkje, A. Nunnenkamp, J. D. Tenfel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
[Crossref] [PubMed]

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, “Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light,” Phys. Rev. Lett. 110(3), 037403 (2013).
[Crossref] [PubMed]

N. D. Lanzillotti-Kimura, A. Fainstein, A. Huynh, B. Perrin, B. Jusserand, A. Miard, and A. Lemaître, “Coherent generation of acoustic phonons in an optical microcavity,” Phys. Rev. Lett. 99(21), 217405 (2007).
[Crossref]

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

Phys. World (1)

T. Gorishnyy, M. Maldovan, C. Ullal, and E. L. Thomas, “Sound ideas,” Phys. World 18(12), 24–29 (2005).

Other (5)

A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley and Sons, 2003).

Y. Pennec, V. Laude, N. Papanikolaou, B. Djafari-Rouhani, M. Oudich, S. El-Jallal, J. C. Beugnot, J. M. Escalante, and A. Martínez, “Modeling light-sound interaction in nanoscale cavities and waveguides,” Nanophotonics (posted 30 September 2014, in press).

M. E. Boyle and R. F. Cozzens, “Acousto-optic and linear electro-optic properties of organic polymeric materials,” Naval Research LabWashington DC, No. NRL-MR-6454 (1989).

J. E. Mark, Polymer Data Handbook (Oxford University, 2009).

E. Almpanis, N. Papanikolaou, I. E. Psarobas, N. Stefanou, N. Glezos, B. Djafari-Rouhani, B. Bonello, V. Laude, and A. Martinez, “Acousto-optical engineering in polymeric multilayers,” XXVII Panhellenic Conference on Solid State Physics and Materials Science, Limassol, Cyprus, 18–21 Sep. 2011, proceedings pp. 17–18.

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 (6)

Fig. 1
Fig. 1 (a) Schematic view of the one-dimensional As2Se3/PES multilayer structure under consideration. (b) Associated optical reflectivity spectrum at normal incidence, without acoustic excitation. (c) Corresponding electric field amplitude profile, normalized to the input field level Ein, at the resonance frequency ω0a/c = 1.775 (thick line: Real part, thin line: Imaginary part).
Fig. 2
Fig. 2 (a) Acoustic reflectivity spectrum of the structure of Fig. 1(a) for a normally incident compressional acoustic wave. Displacement and strain field amplitude profiles in the multilayer stack, normalized to to the input displacement level uin, associated with the lower (at Ω1a/cl;SiO2 = 1.25) and higher (at Ω2a/cl;SiO2 = 2.31) resonant modes are depicted in diagrams (b), (c) and (d), (e) respectively. Real and imaginary parts of the fields are shown by thick and thin lines, respectively. Color stripes in the background of the field distribution diagrams depict the regions of As2Se3 and PES [see Fig. 1(a)].
Fig. 3
Fig. 3 (a) Oscillatory behavior of the optical resonance frequency [see Fig. 1(b)] under continuous excitation by a normally incident compressional acoustic wave [see Fig. 1(a)] at the resonance frequency Ω2a/cl;SiO2 = 2.31. The straight horizontal line shows the unperturbed optical resonance frequency, ω0. (b) Snapshots of the optical reflectivity at normal incidence, at which maximum frequency shift of the resonance, Δω, is obtained. The input displacement level in (a) and (b) is uin/a = 5 × 10−5. (c) Maximum frequency shift of the optical resonance as a function of the input acoustic displacement level. Solid line: Full treatment. Dashed line: First-order Born approximation.
Fig. 4
Fig. 4 Time variation of the optical reflection coefficient at the eigenfrequency of the cavity ω0a/c = 1.775 [see Fig. 1(b)] under the action of a normally incident compressional acoustic wave at the resonance frequency Ω2a/cl;SiO2 = 2.31 [see Fig. 2(a)] for uin/a = 2 × 10−5(a) and uin/a = 5 × 10−5(b). (c) Corresponding intensities of the elastically and inelastically reflected light beams as a function of the input acoustic intensity factor (uin/a)2. The difference between Stokes and anti-Stokes components is not discernible in the scale of the figure. The dashed lines in the diagrams show the results of the first-order Born approximation given by Eq. (10).
Fig. 5
Fig. 5 (a) Oscillatory behavior of the optical resonance frequency [see Fig. 1(b)] under continuous excitation by a normally incident compressional acoustic wave [see Fig. 1(a)] at the resonance frequency Ω1a/cl;SiO2 = 1.25. The straight horizontal line shows the unperturbed optical resonance frequency, ω0. (b) Snapshots of the optical reflectivity at normal incidence, at which maximum frequency shift of the resonance, Δω, is obtained. The input displacement level in (a) and (b) is uin/a = 3 × 10−4. (c) Maximum frequency shift of the optical resonance as a function of the input acoustic displacement level. A detail view demonstrating the quadratic behavior at low uin is shown in the inset.
Fig. 6
Fig. 6 (a) Time variation of the optical reflection coefficient at the eigenfrequency of the cavity ω0a/c = 1.775 [see Fig. 1(b)] under the action of a normally incident compressional acoustic wave at the resonance frequency Ω1a/cl;SiO2 = 1.25 [see Fig. 2(a)] with input displacement level uin/a = 3 × 10−4. (b) Corresponding intensities of the elastically and inelastically reflected light beams for the given input displacement.

Equations (12)

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

δ ε̿ B ( z , t ) = ε 2 ( z ) S ( z , t ) ( p 12 ( z ) 0 0 0 p 12 ( z ) 0 0 0 p 11 ( z ) ) ,
δ ε̿ ( r , t ) = δ ε I ( z , t ) + δ ε̿ B ( z , t ) .
γ Λ α γ ( r , t ) E γ ( r , t ) = 1 c 2 β δ ε α β ( r , t ) 2 t 2 E β ( r , t ) ,
Λ α γ ( r , t ) = [ × ( × ) ] α γ δ α γ ε ( r ) c 2 2 t 2 .
γ Λ α γ ( r , t ) G γ β 0 ( r , t ; r , t ) = δ α β δ ( r r ) δ ( t t ) ,
E ( r , t ) = E 0 ( r , t ) + 1 c 2 d 3 r d t G̿ 0 ( r , t ; r , t ) δ ε̿ ( r , t ) t 2 E 0 ( r , t ) + 1 c 4 d 3 r d t d 3 r d t G̿ 0 ( r , t ; r , t ) δ ε̿ ( r , t ) × t 2 G̿ 0 ( r , t ; r , t ) δ ε̿ ( r , t ) t 2 E 0 ( r , t ) + ,
E ( r , t ) = e [ e i ω t n = 0 , ± 1 , E n ( r ) e i n Ω t ] .
r ( t ) = r ( t + 2 π / Ω ) = n = 0 , ± 1 , r n e i n Ω t
< ( t ) > = < r ( t ) r * ( t ) > = Ω 2 π n , n r n r n 0 2 π / Ω e i ( n n ) Ω t d t = n | r n | 2 ,
r 1 ( 1 ) = i ω 4 c n h [ d z p 12 ( z ) ε 2 ( z ) u ( z ) z { E 0 ( z ) / E in } 2 + j ( ε j + 1 ε j ) u ( z j ) { E 0 ( z j ) / E in } 2 ] ,
( ω , t ) = | r 0 ( 0 ) ( ω ) + r 1 ( 1 ) ( ω ) exp ( i Ω t ) + r 1 ( 1 ) ( ω ) exp ( i Ω t ) | 2 | r 0 ( 0 ) ( ω ) | 2 + 2 e [ r 0 ( 0 ) * ( ω ) { r 1 ( 1 ) ( ω ) exp ( i Ω t ) + r 1 ( 1 ) ( ω ) exp ( i Ω t ) } ]
( ω , t ) = | r 0 ( 0 ) ( ω ) + r 0 ( 2 ) ( ω ) + r 2 ( 2 ) ( ω ) exp ( 2 i Ω t ) + r 2 ( 2 ) ( ω ) exp ( 2 i Ω t ) | 2 | r 0 ( 0 ) ( ω ) | 2 + 2 e [ r 0 ( 0 ) * ( ω ) { r 0 ( 2 ) ( ω ) + r 2 ( 2 ) ( ω ) exp ( 2 i Ω t ) + r 2 ( 2 ) ( ω ) exp ( 2 i Ω t ) } ] ,

Metrics