Abstract

We investigate the acousto-optic coupling rates between different acoustic resonance modes and a specified optical resonance mode in a one-dimensional phoxonic crystal fishbone nanobeam formed by periodically arranging semi-cylinders of air on both sides of a suspended silicon waveguide. The gradually tapered unit cells form optical and acoustic resonators. In acousto-optic coupling rate calculation, the acoustic fields and optical fields are obtained by steady state monochromatic analysis and eigen-mode computation, respectively. Results showed that the acoustic polarizations and symmetries of the acoustic resonance modes are dominant factors in the acousto-optic coupling efficiency, and appropriate selection of these parameters can prevent cancellation of acousto-optic interactions, thereby enhancing acousto-optic coupling rates. This study provides important insights that can be applied to acousto-optic device designs.

© 2017 Optical Society of America

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2016 (3)

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
[Crossref]

T. Yu, Z. Wang, W. Liu, T. Wang, N. Liu, and Q. Liao, “Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals,” Opt. Express 24(8), 7951–7959 (2016).
[Crossref] [PubMed]

2015 (1)

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

2014 (9)

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[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]

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 3(6), 413–440 (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]

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).
[Crossref] [PubMed]

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (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]

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
[Crossref] [PubMed]

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. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

2013 (7)

T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
[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]

T. W. Lu and P. T. Lee, “Photonic crystal nanofishbone nanocavity,” Opt. Lett. 38(16), 3129–3132 (2013).
[Crossref] [PubMed]

P. Seidler, K. Lister, U. Drechsler, J. Hofrichter, and T. Stöferle, “Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio,” Opt. Express 21(26), 32468–32483 (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]

R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
[Crossref] [PubMed]

2012 (8)

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

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

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]

J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
[Crossref] [PubMed]

2011 (6)

S. Y. Su, L. Tang, and T. Yoshie, “Optical surface Bloch modes of complete photonic bandgap materials as a basis of optical sensing,” Opt. Lett. 36(12), 2266–2268 (2011).
[Crossref] [PubMed]

S. P. Anderson and P. M. Fauchet, “Experimental demonstration of evanescent coupling and photon confinement in oxide-clad silicon microcavities,” Opt. Lett. 36(14), 2698–2700 (2011).
[Crossref] [PubMed]

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

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

J. Chan, T. P. 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]

2010 (9)

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (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]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, 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).
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D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (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]

T. W. Lu, Y. H. Hsiao, W. D. Ho, and P. T. Lee, “High-index sensitivity of surface mode in photonic crystal hetero-slab-edge microcavity,” Opt. Lett. 35(9), 1452–1454 (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. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
[Crossref] [PubMed]

2009 (7)

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[Crossref] [PubMed]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
[Crossref] [PubMed]

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

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

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

2008 (3)

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

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

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

2007 (1)

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

2006 (5)

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]

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

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

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[Crossref] [PubMed]

A. I. Rahachou and I. V. Zozoulenko, “Waveguiding properties of surface states in photonic crystals,” J. Opt. Soc. Am. B 23(8), 1679–1683 (2006).
[Crossref]

2003 (1)

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

2002 (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
[Crossref] [PubMed]

Adibi, A.

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]

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

Akjouj, A.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, 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]

Alegre, T. P.

J. Chan, T. P. 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]

Almpanis, E.

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. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

Amoudache, S.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

Anderson, S. P.

Andrews, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Aoubiza, B.

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

Aspelmeyer, M.

J. Chan, T. P. 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]

Becher, C.

Benchabane, S.

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 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. Martínez, “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]

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]

Beugnot, J. C.

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 3(6), 413–440 (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]

Bonello, B.

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. 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]

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[Crossref] [PubMed]

Bou Matar, O.

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, 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]

Bouwmeester, D.

D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
[Crossref]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007).
[Crossref] [PubMed]

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]

Callebaut, H.

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
[Crossref]

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]

Cappellaro, P.

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

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]

Chan, J.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref] [PubMed]

J. Chan, T. P. 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]

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
[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]

Charles, C.

C. Charles, B. Bonello, and F. Ganot, “Propagation of guided elastic waves in 2D phononic crystals,” Ultrasonics 44(Suppl 1), e1209–e1213 (2006).
[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. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
[Crossref] [PubMed]

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]

Cicak, K.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
[Crossref]

Clerk, A. A.

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
[Crossref]

Dadgar, A.

Deotare, P. B.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
[Crossref]

Deymier, P. A.

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

Distel, M.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Djafari Rouhani, B.

S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
[Crossref]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
[Crossref]

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

Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, 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. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Djafari-Rouhani, B.

Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (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).
[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 3(6), 413–440 (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. 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]

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,” Microelectron. Eng. 90, 155–158 (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]

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

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

Dong, C.

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
[Crossref]

Drechsler, U.

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).
[Crossref] [PubMed]

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

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
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J. Chan, T. P. 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).
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A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
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M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
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Seidler, P.

Shi, N. N.

Simmonds, R. W.

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
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D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
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K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
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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).
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K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
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N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
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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).
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Su, M.

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
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T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
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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).
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M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
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D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
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C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
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S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
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S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
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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. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
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T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
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T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
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I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
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M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
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M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
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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).
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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. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
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Y. Pennec, B. Djafari-Rouhani, H. Larabi, J. O. Vasseur, and A. C. Hladky-Hennion, “Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate,” Phys. Rev. B 78(10), 104105 (2008).
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J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, Y. Pennec, and A. C. Hladky-Hennion, “Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates,” Phys. Rev. B 77(8), 085415 (2008).
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D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
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C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
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Wang, Y. D.

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
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T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
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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).
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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).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066611 (2002).
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B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
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D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
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T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
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T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
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J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
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T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
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Yu, T.

Zhang, C.

T. X. Ma, Y. S. Wang, C. Zhang, and X. X. Su, “Theoretical research on a two-dimensional phoxonic crystal liquid sensor by utilizing surface optical and acoustic waves,” Sens. Actuators A Phys. 242, 123–131 (2016).
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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).
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K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
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R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
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AIP Adv. (1)

Y. Pennec, B. Djafari Rouhani, C. Li, J. M. Escalante, A. Martínez, S. Benchabane, V. Laude, and N. Papanikolaou, “Band gaps and cavity modes in dual phononic and photonic strip waveguides,” AIP Adv. 1(4), 041901 (2011).
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R. Lucklum, M. Zubtsov, and A. Oseev, “Phoxonic crystals--a new platform for chemical and biochemical sensors,” Anal. Bioanal. Chem. 405(20), 6497–6509 (2013).
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Ann. Phys. (1)

C. Dong, V. Fiore, M. C. Kuzyk, L. Tian, and H. Wang, “Optical wavelength conversion via optomechanical coupling in a silica resonator,” Ann. Phys. 527(1-2), 100–106 (2015).
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Appl. Phys. Lett. (8)

B. S. Williams, H. Callebaut, S. Kumar, Q. Hu, and J. L. Reno, “3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation,” Appl. Phys. Lett. 82(7), 1015–1017 (2003).
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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).
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M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
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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).
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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).
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T. T. Wu, Z. G. Huang, T. C. Tsai, and T. C. Wu, “Evidence of complete band gap and resonances in a plate with periodic stubbed surface,” Appl. Phys. Lett. 93(11), 111902 (2008).
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P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Lončar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94(12), 121106 (2009).
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T. W. Lu, W. C. Tsai, T. Y. Wu, and P. T. Lee, “Laser emissions from one-dimensional photonic crystal rings on silicon-dioxide,” Appl. Phys. Lett. 102(5), 051103 (2013).
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J. Appl. Phys. (6)

D. Goettler, M. Su, Z. Leseman, Y. Soliman, R. Olsson, and I. El-Kady, “Realizing the frequency quality factor product limit in silicon via compact phononic crystal resonators,” J. Appl. Phys. 108(8), 084505 (2010).
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S. Sadat-Saleh, S. Benchabane, F. I. Baida, M. P. Bernal, and V. Laude, “Tailoring simultaneous photonic and phononic band gaps,” J. Appl. Phys. 106(7), 074912 (2009).
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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).
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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]

S. Amoudache, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Simultaneous sensing of light and sound velocities of fluids in a two-dimensional phoXonic crystal with defects,” J. Appl. Phys. 115(13), 134503 (2014).
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S. Amoudache, R. Moiseyenko, Y. Pennec, B. Djafari Rouhani, A. Khater, R. Lucklum, and R. Tigrine, “Optical and acoustic sensing using Fano-like resonances in dual phononic and photonic crystal plate,” J. Appl. Phys. 119(11), 114502 (2016).
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J. Opt. Soc. Am. B (2)

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).
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Microelectron. Eng. (1)

N. Papanikolaou, I. E. Psarobas, N. Stefanou, B. Djafari-Rouhani, B. Bonello, and V. Laude, “Light modulation in phoxonic nanocavities,” Microelectron. Eng. 90, 155–158 (2012).
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Nanophotonics (1)

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 3(6), 413–440 (2014).
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Nat. Commun. (2)

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. Torres, “A one-dimensional optomechanical crystal with a complete phononic band gap,” Nat. Commun. 5, 4452 (2014).
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J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
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Nat. Photonics (2)

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
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D. A. Fuhrmann, S. M. Thon, H. Kim, D. Bouwmeester, P. M. Petroff, A. Wixforth, and H. J. Krenner, “Dynamic modulation of photonic crystal nanocavities using gigahertz acoustic phonons,” Nat. Photonics 5(10), 605–609 (2011).
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Nat. Phys. (1)

R. W. Andrews, R. W. Peterson, T. P. Purdy, K. Cicak, R. W. Simmonds, C. A. Regal, and K. W. Lehnert, “Bidirectional and efficient conversion between microwave and optical light,” Nat. Phys. 10(4), 321–326 (2014).
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Nature (3)

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009).
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J. Chan, T. P. 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).
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M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
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New J. Phys. (1)

Y. D. Wang and A. A. Clerk, “Using dark modes for high-fidelity optomechanical quantum state transfer,” New J. Phys. 14(10), 105010 (2012).
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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).
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Opt. Express (10)

M. Eichenfield, J. Chan, A. H. Safavi-Naeini, K. J. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17(22), 20078–20098 (2009).
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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).
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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. Martínez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
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A. H. Safavi-Naeini and O. Painter, “Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab,” Opt. Express 18(14), 14926–14943 (2010).
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J. Zheng, X. Sun, Y. Li, M. Poot, A. Dadgar, N. N. Shi, W. H. P. Pernice, H. X. Tang, and C. W. Wong, “Femtogram dispersive L3-nanobeam optomechanical cavities: design and experimental comparison,” Opt. Express 20(24), 26486–26498 (2012).
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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).
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P. Seidler, K. Lister, U. Drechsler, J. Hofrichter, and T. Stöferle, “Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio,” Opt. Express 21(26), 32468–32483 (2013).
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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).
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Q. Rolland, S. Dupont, J. Gazalet, J. C. Kastelik, Y. Pennec, B. Djafari-Rouhani, and V. Laude, “Simultaneous bandgaps in LiNbO3 phoxonic crystal slab,” Opt. Express 22(13), 16288–16297 (2014).
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T. Yu, Z. Wang, W. Liu, T. Wang, N. Liu, and Q. Liao, “Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals,” Opt. Express 24(8), 7951–7959 (2016).
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Opt. Lett. (4)

Phys. Rev. B (8)

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
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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).
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Y. El Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martínez, 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).
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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).
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J. C. Hsu and T. T. Wu, “Efficient formulation for band-structure calculations of two-dimensional phononic- crystal plates,” Phys. Rev. B 74(14), 144303 (2006).
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Figures (9)

Fig. 1
Fig. 1 Schematic of (a) 1D phoxonic crystal nanobeam cavity, (b) unit cell, (c) even symmetric cavity, and (d) odd symmetric cavity.
Fig. 2
Fig. 2 Simulation results for even symmetric cavity (blue) and a reference with no defective region (red): (a) optical transmission spectra, (b) acoustic transmission spectra, and (c) X-direction component of normalized electric field of optical resonance mode (OR1).
Fig. 3
Fig. 3 Simulation results for odd symmetric cavity (blue) and a reference with no defective region (red): (a) optical and transmission spectra, (b) acoustic transmission spectra, and (c) X-direction component of normalized electric field of optical resonance mode (OR2).
Fig. 4
Fig. 4 Simulation results for odd symmetric cavity (blue) and a reference with no defective region (red): (a) Optical photonic band structures of mirror. Blue dotted lines mark the frequencies of OR1 and OR2. Phononic band structure of mirror with corresponding acoustic resonance peaks (marked by black dotted lines) in (b) even symmetric structure and (c) odd symmetric structure.
Fig. 5
Fig. 5 AO coupling rates in even symmetric cavity between optical resonance mode OR1 mode and all acoustic resonance modes from 6.10 to 7.16 GHz.
Fig. 6
Fig. 6 Displacement fields of acoustic resonance modes ϕ1, κ, α, β, δ, γ, ϕ2, and η: black dashed lines mark the defect centers, and Γ and Φ indicate the reference planes of symmetry.
Fig. 7
Fig. 7 AO coupling rates in the odd symmetric cavity between optical resonance mode OR2 mode and all acoustic resonance modes from 6.10 to 7.16 GHz.
Fig. 8
Fig. 8 Displacement fields of acoustic resonance modes A, F, B, C, D, G, and E. Black dashed lines indicate defect centers. Γ and Φ indicate reference planes of symmetry.
Fig. 9
Fig. 9 Θacoustic, Θoptical, and g density plots on the odd symmetrical cavity surface, with individual unit cell contributions to the total g density, for acoustic resonance modes (a) A, (b) B, (c) E, (d) G, (e) C, and (f) F.

Tables (4)

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Table 1 Total AO coupling rates (in MHz) between optical resonance mode OR1 and phononic resonance modes in even symmetric cavity when both PE and MB effects are considered.

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Table 2 Total AO coupling rates (in MHz) between optical resonance mode OR2 and acoustic resonance modes in odd symmetric cavity when both PE and MB effects are considered.

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Table 3 AO interactions and Qacoustic for five phononic modes (α, β, γ, δ, and η) in even symmetric cavity phoxonic crystal nanobeams with different cavity designs.

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Table 4 AO interactions and Qacoustic for six phononic modes in odd symmetric cavity phoxonic crystal nanobeams with different cavity designs.

Equations (6)

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g PE = ω 0 2 E| ε α |E EDdV 2 m eff Ω m
g MB = ω 0 2 ( Q n ^ )( Δε E || 2 Δ ε 1 D 2 ) dS EDdV 2 m eff Ω m
g= g MB + g PE
gdensity= 1 4 ( Q n ^ )[ Δε | E || | 2 Δ( ε 1 ) ( D ) 2 ]
Θ acoustic =Q n ^
Θ optical =Δε | E || | 2 Δ( ε 1 ) | D | 2

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