Abstract

Acousto-optic (AO) coupling in a two-layer GaAs/Ag heterogeneous phoxonic crystal nanobeam cavity with plasmonic behavior is studied numerically. Because of the Ag metal layer, the cavity structure hybridizes photons and surface plasmons, squeezing the optical energy into small regions near the GaAs/Ag interface; the phononic cavity modes can be simultaneously tailored to highly match the photonic cavity modes at reduced regions in the cavity. Consequently, AO coupling is enhanced at near–infrared wavelengths. Boosting of the interface effect by the acoustic displacement field mainly contributes to the AO coupling enhancement. The simultaneous small photonic mode volume and high spatial matching of photonic and phononic cavity modes enhance the photonic resonance wavelength shift by one order of magnitude. This study enables applications of strong AO or photon–phonon interaction in subwavelength nano-structures.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  28. 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]
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    [Crossref] [PubMed]

2015 (1)

T.-R. Lin, C.-H. Lin, and J.-C. Hsu, “Strong optomechanical interaction in hybrid plasmonic-photonic crystal nanocavities with surface acoustic waves,” Sci. Rep. 5, 13782 (2015).
[Crossref]

2014 (2)

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (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]

2013 (4)

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]

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]

L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102(15), 153507 (2013).
[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]

2012 (3)

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

M. Davanço, J. Chan, A. H. Safavi-Naeini, O. Painter, and K. Srinivasan, “Slot-mode-coupled optomechanical crystals,” Opt. Express 20(22), 24394–24410 (2012).
[Crossref] [PubMed]

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, 061109 (2012).
[Crossref]

2011 (4)

J.-C. Hsu, “Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators,” J. Phys. D Appl. Phys. 44(5), 055401 (2011).
[Crossref]

Y. Pennec, B. D. 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]

G. Gantzounis, N. Papanikolaou, and N. Stefanou, “Nonlinear interactions between high-Q optical and acoustic modes in dielectric particles,” Phys. Rev. B 84(10), 104303 (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]

2010 (4)

N. Papanikolaou, I. E. 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]

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]

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 (4)

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

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

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

2008 (1)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

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 (2)

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006).
[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]

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]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Benchabane, S.

Y. Pennec, B. D. 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]

Beugnot, J. C.

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (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]

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.

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]

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]

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

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]

Chan, J.

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

M. Davanço, J. Chan, A. H. Safavi-Naeini, O. Painter, and K. Srinivasan, “Slot-mode-coupled optomechanical crystals,” Opt. Express 20(22), 24394–24410 (2012).
[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]

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

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Davanço, M.

Distel, M.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, P. 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.

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]

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, 061109 (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]

Dupont, S.

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, 061109 (2012).
[Crossref]

Eichenfield, M.

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

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

El Jallal, S.

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]

El-Jallal, S.

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, 061109 (2012).
[Crossref]

Escalante, J. M.

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]

Y. Pennec, B. D. 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]

Fan, L.

L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102(15), 153507 (2013).
[Crossref]

Fuhrmann, D. A.

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]

Gantzounis, G.

G. Gantzounis, N. Papanikolaou, and N. Stefanou, “Nonlinear interactions between high-Q optical and acoustic modes in dielectric particles,” Phys. Rev. B 84(10), 104303 (2011).
[Crossref]

Gauthier, D. J.

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]

Gazalet, J.

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, 061109 (2012).
[Crossref]

Grudinin, I. S.

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]

Hill, J. T.

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

Hsu, J.-C.

T.-R. Lin, C.-H. Lin, and J.-C. Hsu, “Strong optomechanical interaction in hybrid plasmonic-photonic crystal nanocavities with surface acoustic waves,” Sci. Rep. 5, 13782 (2015).
[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]

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, “Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators,” J. Phys. D Appl. Phys. 44(5), 055401 (2011).
[Crossref]

Hu, Q.

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]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

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, 061109 (2012).
[Crossref]

Kim, H.

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]

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

Köster, P. W.

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

Krenner, H. J.

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]

Ku, Y.-C.

Kumar, S.

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]

Kuramochi, E.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006).
[Crossref] [PubMed]

Laude, V.

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. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (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, B. D. 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]

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]

Lebrun, S.

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
[Crossref] [PubMed]

Lee, H.

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]

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, 061109 (2012).
[Crossref]

Li, C.

Y. Pennec, B. D. 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]

Lin, C.-H.

T.-R. Lin, C.-H. Lin, and J.-C. Hsu, “Strong optomechanical interaction in hybrid plasmonic-photonic crystal nanocavities with surface acoustic waves,” Sci. Rep. 5, 13782 (2015).
[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]

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]

Lin, T.-R.

T.-R. Lin, C.-H. Lin, and J.-C. Hsu, “Strong optomechanical interaction in hybrid plasmonic-photonic crystal nanocavities with surface acoustic waves,” Sci. Rep. 5, 13782 (2015).
[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]

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]

Ma, R.

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

Maillotte, H.

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
[Crossref] [PubMed]

Makhoute, A.

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 localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[Crossref]

Martínez, A.

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]

Y. Pennec, B. D. 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]

Meenehan, S.

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

Mitsugi, S.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006).
[Crossref] [PubMed]

Notomi, M.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006).
[Crossref] [PubMed]

Ntziachristos, V.

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

Oudich, M.

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]

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, 061109 (2012).
[Crossref]

Painter, O.

M. Davanço, J. Chan, A. H. Safavi-Naeini, O. Painter, and K. Srinivasan, “Slot-mode-coupled optomechanical crystals,” Opt. Express 20(22), 24394–24410 (2012).
[Crossref] [PubMed]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[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]

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]

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]

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

Papanikolaou, N.

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]

G. Gantzounis, N. Papanikolaou, and N. Stefanou, “Nonlinear interactions between high-Q optical and acoustic modes in dielectric particles,” Phys. Rev. B 84(10), 104303 (2011).
[Crossref]

Y. Pennec, B. D. 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]

N. Papanikolaou, I. E. 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]

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]

Pauliat, G.

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
[Crossref] [PubMed]

Pennec, Y.

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]

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, 061109 (2012).
[Crossref]

Y. Pennec, B. D. 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]

Perrimon, N.

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

Petroff, P. M.

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]

Psarobas, I. E.

N. Papanikolaou, I. E. 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]

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]

Razansky, D.

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

Reno, J. L.

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]

Rolland, Q.

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, 061109 (2012).
[Crossref]

Rouhani, B. D.

Y. Pennec, B. D. 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]

Safavi-Naeini, A. H.

Schuck, C.

L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102(15), 153507 (2013).
[Crossref]

Srinivasan, K.

Stefanou, N.

G. Gantzounis, N. Papanikolaou, and N. Stefanou, “Nonlinear interactions between high-Q optical and acoustic modes in dielectric particles,” Phys. Rev. B 84(10), 104303 (2011).
[Crossref]

N. Papanikolaou, I. E. 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]

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]

Sun, X.

L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102(15), 153507 (2013).
[Crossref]

Sylvestre, T.

J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, “Brillouin light scattering from surface acoustic waves in a subwavelength-diameter optical fibre,” Nat. Commun. 5, 5242 (2014).
[Crossref] [PubMed]

Tang, H. X.

L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102(15), 153507 (2013).
[Crossref]

Taniyama, H.

M. Notomi, H. Taniyama, S. Mitsugi, and E. Kuramochi, “Optomechanical wavelength and energy conversion in high-Q double-layer cavities of photonic crystal slabs,” Phys. Rev. Lett. 97(2), 023903 (2006).
[Crossref] [PubMed]

Thomas, E. L.

M. Maldovan and E. L. Thomas, “Simultaneous localization of photons and phonons in two-dimensional periodic structures,” Appl. Phys. Lett. 88(25), 251907 (2006).
[Crossref]

Thon, S. M.

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]

Vahala, K. J.

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]

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

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

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

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

Vinegoni, C.

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

Williams, B. S.

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]

Wixforth, A.

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]

Xiong, C.

L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102(15), 153507 (2013).
[Crossref]

Zhu, Z.

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]

AIP Adv. (1)

Y. Pennec, B. D. 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]

Appl. Phys. Lett. (6)

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]

N. Papanikolaou, I. E. 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]

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]

L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102(15), 153507 (2013).
[Crossref]

J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal cavity with acoustic radiation shield,” Appl. Phys. Lett. 101(8), 081115 (2012).
[Crossref]

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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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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of the GaAs/Ag phoxonic crystal nanobeam cavity and definition of the coordinates. (b) Geometry of the unit cell of the nanobeam outside the cavity region. The lattice constant a is 294 nm, beam width w is 294 nm, hole radius r0 is 100 nm, GaAs thickness hGaAs is 176 nm, and Ag thickness hAg is 75 nm. (c) Definition of the graded cavity obtained by varying the lattice constant and hole radii. The cavity consists of 15 varied lattice constants.
Fig. 2
Fig. 2 (a) Photonic band structure of the GaAs (all-dielectric) phoxonic crystal nanobeam with no Ag layer. Shaded region represents the inner region divided by the light line. A band gap exists from 317.2 to 327.1 THz. (b) Electric field intensity |Ey|2 distributions of the lower and upper band-edge modes at the Brillouin zone boundary. (c) Corresponding phononic band structure. A phononic band gap for all phononic eigenmodes appears from 5.35 to 5.94 GHz. (d) Total displacement field |ui| of the upper and lower phononic band-edge modes.
Fig. 3
Fig. 3 (a) |Ei| field distributions of the GaAs photonic cavity mode on the xz and yz planes. The cavity mode is confined by the graded cavity with a high quality, Q = 3500. The mode volume Vm is 2.37(λ/nGaAs)3. (b) The |ui| field distribution of the phononic cavity modes, which is concentrated in the cavity central region. (c) Modulation of the optical resonance wavelength λr by the phononic cavity mode as a function of the acoustic phase Ωt.
Fig. 4
Fig. 4 (a) Photonic band structure of the GaAs/Ag phoxonic crystal nanobeam. A photonic band gap appears from 182 to 198 THz. Three bands of waveguide modes appear around the band gap and are labeled as modes A, B, and C at the Brillouin zone edge. With the graded cavity, two cavity modes Ad1 and Ad2 exist in the band gap. (b) Electric field intensity |Ey|2 distributions of the lower and upper band-edge modes at the Brillouin zone boundary.
Fig. 5
Fig. 5 (a) Phononic band structure and defect bands of the GaAs/Ag phoxonic crystal nanobeam. Two phononic band gaps appear from 3.92 to 4.12 and 4.54 to 4.76 GHz. The lower and upper band-edge modes of the two band gaps are labeled as modes α, β, γ, and δ. (b) The |ui| field distributions of the four band-edge modes, which exhibit asymmetric distributions along the beam thickness.
Fig. 6
Fig. 6 (a) |Ei| field distributions of the GaAs/Ag photonic cavity modes Ad1 and Ad2 on the xz and yz planes, respectively. The two cavity modes are confined by the graded cavity with reduced mode volumes Vm = 0.0657(λ/nGaAs)3 and 0.11(λ/nGaAs)3. (b), (c) Illustration of the |ui| field distributions of several phononic cavity modes labeled in Fig. 5(a). They are classified into symmetric stretching (SSi) modes, asymmetric stretching (ASi) modes, and twisting (Ti) modes. The field distributions of the SS3 and SS2 modes are highly matched to those of the Ad1 and Ad2 modes, respectively.
Fig. 7
Fig. 7 AO modulation of optical resonance wavelength in the GaAs/Ag phoxonic crystal nanobeam cavity as a function of acoustic phase Ωt from 0 to π for different photonic–phononic mode pair combinations, taking into account the contributions of (a), (d) joint (bulk + interface) effect, (b), (e) bulk effect, and (c), (f) interface effect. The used phononic cavity modes, the AS1, SS2, and SS3 modes, are in or near the first phononic band gap. (a–c) Ad1 mode. (d–f) Ad2 mode.
Fig. 8
Fig. 8 AO modulation of optical resonance wavelength in the GaAs/Ag phoxonic crystal nanobeam cavity as a function of acoustic phase Ωt from 0 to π for different photonic–phononic mode pair combinations, taking into account the contributions of (a), (d) joint (bulk + interface) effect, (b), (e) bulk effect, and (c), (f) interface effect. The used phononic cavity modes, the SS5 and SS7 modes, are in the second phononic band gap. (a–c) Ad1 mode. (d–f) Ad2 mode.

Tables (2)

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Table 1 Material constants of GaAs and Ag used for the calculations

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Table 2 Properties of photonic resonant modes and AO coupling (displacement amplitude |Ui| = 2.97 nm).

Equations (11)

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u i (x,y,z,t)= U i (x,y,z)exp(iΩtiKz),i=x,y,z,
ρ 2 u i t 2 x j ( c ijkl u k x l )= F i ,i,j,k,l=x,y,z,
S ij = 1 2 ( u i x j + u j x i ) and T ij = c ijkl S kl .
Traction ( stress vector ) free: T jk m k =0;
Continuity of stress vector: T jk (GaAs) m k (GaAs) = T jk (Ag) m k (Ag) ;
Continuity of displacement vector: u j (GaAs) = u j (Ag) ;
Δ ( 1/ n 2 ) ij = p ijkl S kl ,
E i (x,y,z,t)= A i (x,y,z)exp(iωtikz),
b lm b mt e skt x s ( e ijk E j x i )= ( ω c ) 2 E l ,
Δ λ c = λ max λ min ,
V m = W( x,y,z )dxdydz max[ W( x,y,z ) ] ,whereW= 1 2 ( Re( d( ωε ) dω ) | E i | 2 +μ | H i | 2 ).

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