Abstract

We report the simultaneous existence of acoustic and optical asymmetric transmission by combining a periodic array of silicon rods in air with a periodic grating (grating-phoxonic crystals). Theoretically and numerically, we demonstrate that the grating-phoxonic crystals with a square lattice of silicon rods can exhibit simultaneous asymmetric propagation in the same reduced frequency range both for sound and light. The sound and light can transmit through the composite structure when incident from the grating interface but are completely reflected for the reverse direction incidence. Furthermore, when the silicon rods are tuned into a triangular lattice, reversed asymmetric transmissions are also achieved. Sound and light are blocked when incident from the grating interface while being fully able to pass through the composite structure for the reverse direction incidence. These two tunable dual acoustic and optical asymmetric transmissions show great potential for acoustic-optic devices by simultaneously manipulating sound and light.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
  26. M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
    [Crossref]
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    [Crossref] [PubMed]
  28. B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, “An acoustic rectifier,” Nat. Mater. 9(12), 989–992 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  35. X. F. Zhu, X. Y. Zou, B. Liang, and J. C. Cheng, “One-way mode transmission in one-dimensional phononic crystal plates,” J. Appl. Phys. 108(12), 124909 (2010).
    [Crossref]
  36. H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2016 (2)

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]

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
[Crossref] [PubMed]

2015 (3)

Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
[Crossref] [PubMed]

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

J. C. Hsu, T. Y. Lu, and T. R. Lin, “Acousto-optic coupling in phoxonic crystal nanobeam cavities with plasmonic behavior,” Opt. Express 23(20), 25814–25826 (2015).
[Crossref] [PubMed]

2014 (4)

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

T. X. Ma, Y. S. Wang, and C. Z. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312(4), 68–72 (2014).
[Crossref]

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]

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343(6170), 516–519 (2014).
[Crossref] [PubMed]

2013 (1)

J. J. Chen, X. Han, and G. Y. Li, “Asymmetric Lamb wave propagation in phononic crystal slabs with graded grating,” J. Appl. Phys. 113(18), 184506 (2013).
[Crossref]

2012 (1)

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3(11), 1196 (2012).
[Crossref] [PubMed]

2011 (4)

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

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]

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode,” Phys. Rev. Lett. 106(8), 084301 (2011).
[Crossref] [PubMed]

J. Xu, C. Cheng, M. Kang, J. Chen, Z. Zheng, Y. X. Fan, and H. T. Wang, “Unidirectional optical transmission in dual-metal gratings in the absence of anisotropic and nonlinear materials,” Opt. Lett. 36(10), 1905–1907 (2011).
[Crossref] [PubMed]

2010 (9)

C. Xue, H. Jiang, and H. Chen, “Highly efficient all-optical diode action based on light-tunneling heterostructures,” Opt. Express 18(7), 7479–7487 (2010).
[Crossref] [PubMed]

B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, “An acoustic rectifier,” Nat. Mater. 9(12), 989–992 (2010).
[Crossref] [PubMed]

B. Liang, X. Y. Zou, B. Yuan, and J. C. Cheng, “Frequency-dependence of the acoustic rectifying efficiency of an acoustic diode model,” Appl. Phys. Lett. 96(23), 233511 (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]

X. F. Zhu, X. Y. Zou, B. Liang, and J. C. Cheng, “One-way mode transmission in one-dimensional phononic crystal plates,” J. Appl. Phys. 108(12), 124909 (2010).
[Crossref]

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

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

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

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

2009 (5)

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]

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

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
[Crossref]

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic diode: rectification of acoustic energy flux in one-dimensional systems,” Phys. Rev. Lett. 103(10), 104301 (2009).
[Crossref] [PubMed]

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[Crossref] [PubMed]

2008 (2)

J. J. Chen, B. Bonello, and Z. L. Hou, “Plate-mode waves in phononic crystal thin slabs: mode conversion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036609 (2008).
[Crossref] [PubMed]

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

2007 (1)

H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
[Crossref]

2006 (2)

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

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

2005 (1)

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 037602 (2005).
[Crossref] [PubMed]

2002 (1)

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref] [PubMed]

1995 (1)

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

Adibi, A.

Akimov, A. V.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

Akjouj, A.

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

Alù, A.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343(6170), 516–519 (2014).
[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]

Bayer, M.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

Beauvillain, P.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
[Crossref]

Benchabane, S.

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

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

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

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]

Bloemer, M. J.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[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]

J. J. Chen, B. Bonello, and Z. L. Hou, “Plate-mode waves in phononic crystal thin slabs: mode conversion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036609 (2008).
[Crossref] [PubMed]

Bou Matar, O.

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

Bowden, C. M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

Brendel, C.

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

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]

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.

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Chen, J.

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Cheng, J. C.

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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. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
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N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96(13), 131103 (2010).
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B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, “An acoustic rectifier,” Nat. Mater. 9(12), 989–992 (2010).
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R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343(6170), 516–519 (2014).
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S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
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A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, “Two-dimensional phononic-photonic band gap optomechanical crystal cavity,” Phys. Rev. Lett. 112(15), 153603 (2014).
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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(11), 1196 (2012).
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J. J. Chen, B. Bonello, and Z. L. Hou, “Plate-mode waves in phononic crystal thin slabs: mode conversion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036609 (2008).
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Jiang, H.

Kang, M.

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A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
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Kastelik, J. C.

Khelif, A.

Kivshar, Y. S.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 037602 (2005).
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E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
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Y. E. I. Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
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Laude, V.

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]

Y. E. I. Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
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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. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

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

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

Li, G. Y.

J. J. Chen, X. Han, and G. Y. Li, “Asymmetric Lamb wave propagation in phononic crystal slabs with graded grating,” J. Appl. Phys. 113(18), 184506 (2013).
[Crossref]

Li, X. F.

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode,” Phys. Rev. Lett. 106(8), 084301 (2011).
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Liang, B.

B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, “An acoustic rectifier,” Nat. Mater. 9(12), 989–992 (2010).
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B. Liang, X. Y. Zou, B. Yuan, and J. C. Cheng, “Frequency-dependence of the acoustic rectifying efficiency of an acoustic diode model,” Appl. Phys. Lett. 96(23), 233511 (2010).
[Crossref]

X. F. Zhu, X. Y. Zou, B. Liang, and J. C. Cheng, “One-way mode transmission in one-dimensional phononic crystal plates,” J. Appl. Phys. 108(12), 124909 (2010).
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B. Liang, B. Yuan, and J. C. Cheng, “Acoustic diode: rectification of acoustic energy flux in one-dimensional systems,” Phys. Rev. Lett. 103(10), 104301 (2009).
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Lin, Q.

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

Liu, D. H.

H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
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Liu, N.

Liu, W.

Liu, X. P.

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
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Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
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M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
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Lu, M. H.

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
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Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
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X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode,” Phys. Rev. Lett. 106(8), 084301 (2011).
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Ma, T. X.

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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. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
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Y. E. I. Hassouani, C. Li, Y. Pennec, E. H. El Boudouti, H. Larabi, A. Akjouj, O. Bou Matar, V. Laude, N. Papanikolaou, A. Martinez, and B. Djafari Rouhani, “Dual phononic and photonic band gaps in a periodic array of pillars deposited on a thin plate,” Phys. Rev. B 82(15), 155405 (2010).
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A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472(7341), 69–73 (2011).
[Crossref] [PubMed]

Meenehan, S.

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

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E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref] [PubMed]

Mingaleev, S. F.

Mohammadi, S.

Ni, X.

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
[Crossref] [PubMed]

Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
[Crossref] [PubMed]

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode,” Phys. Rev. Lett. 106(8), 084301 (2011).
[Crossref] [PubMed]

Oudich, M.

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]

Ouyang, M.

H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
[Crossref]

Ozbay, E.

Painter, O.

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

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3(11), 1196 (2012).
[Crossref] [PubMed]

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

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

Papanikolaou, N.

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

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

Peano, V.

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

Pennec, Y.

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]

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

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

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

Pevtsov, A. B.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

Postava, K.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
[Crossref]

Psarobas, I. E.

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]

Rolland, Q.

Sadat-Saleh, S.

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

Safavi-Naeini, A. H.

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

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3(11), 1196 (2012).
[Crossref] [PubMed]

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

Scalora, M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

Schmidt, M.

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

Serebryannikov, A. E.

Shadrivov, I. V.

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 037602 (2005).
[Crossref] [PubMed]

Shen, Y.

H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
[Crossref]

Sieck, C. F.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343(6170), 516–519 (2014).
[Crossref] [PubMed]

Smigaj, W.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
[Crossref]

Sounas, D. L.

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343(6170), 516–519 (2014).
[Crossref] [PubMed]

Stefanou, N.

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. C.

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
[Crossref] [PubMed]

Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
[Crossref] [PubMed]

Tamura, S.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

Tanaka, Y.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

Thomas, E. L.

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

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

Tocci, M. D.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

Tu, J.

B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, “An acoustic rectifier,” Nat. Mater. 9(12), 989–992 (2010).
[Crossref] [PubMed]

Ulliac, G.

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

Vahala, K. J.

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

Vanwolleghem, M.

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
[Crossref]

Vasseur, J.

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

Vasseur, J. O.

Wang, H. T.

Wang, Q.

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
[Crossref] [PubMed]

Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
[Crossref] [PubMed]

Wang, T.

Wang, Y.

H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
[Crossref]

Wang, Y. S.

T. X. Ma, Y. S. Wang, and C. Z. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312(4), 68–72 (2014).
[Crossref]

Wang, Z.

Winger, M.

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

Xu, J.

Xu, Y. L.

Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
[Crossref] [PubMed]

Xue, C.

Yakovlev, D. R.

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

Yan, X. J.

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
[Crossref] [PubMed]

Yang, Y.

Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
[Crossref] [PubMed]

Yu, S. Y.

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
[Crossref] [PubMed]

Yu, T.

Yuan, B.

B. Liang, X. Y. Zou, B. Yuan, and J. C. Cheng, “Frequency-dependence of the acoustic rectifying efficiency of an acoustic diode model,” Appl. Phys. Lett. 96(23), 233511 (2010).
[Crossref]

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic diode: rectification of acoustic energy flux in one-dimensional systems,” Phys. Rev. Lett. 103(10), 104301 (2009).
[Crossref] [PubMed]

Zhang, C. Z.

T. X. Ma, Y. S. Wang, and C. Z. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312(4), 68–72 (2014).
[Crossref]

Zhang, D.

B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, “An acoustic rectifier,” Nat. Mater. 9(12), 989–992 (2010).
[Crossref] [PubMed]

Zheng, Z.

Zhou, J.

H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
[Crossref]

Zhu, X. F.

X. F. Zhu, X. Y. Zou, B. Liang, and J. C. Cheng, “One-way mode transmission in one-dimensional phononic crystal plates,” J. Appl. Phys. 108(12), 124909 (2010).
[Crossref]

Zou, X. Y.

X. F. Zhu, X. Y. Zou, B. Liang, and J. C. Cheng, “One-way mode transmission in one-dimensional phononic crystal plates,” J. Appl. Phys. 108(12), 124909 (2010).
[Crossref]

B. Liang, X. Y. Zou, B. Yuan, and J. C. Cheng, “Frequency-dependence of the acoustic rectifying efficiency of an acoustic diode model,” Appl. Phys. Lett. 96(23), 233511 (2010).
[Crossref]

Appl. Phys. B (1)

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

Appl. Phys. Lett. (4)

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]

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

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66(18), 2324–2326 (1995).
[Crossref]

B. Liang, X. Y. Zou, B. Yuan, and J. C. Cheng, “Frequency-dependence of the acoustic rectifying efficiency of an acoustic diode model,” Appl. Phys. Lett. 96(23), 233511 (2010).
[Crossref]

J. Appl. Phys. (4)

J. J. Chen, X. Han, and G. Y. Li, “Asymmetric Lamb wave propagation in phononic crystal slabs with graded grating,” J. Appl. Phys. 113(18), 184506 (2013).
[Crossref]

X. F. Zhu, X. Y. Zou, B. Liang, and J. C. Cheng, “One-way mode transmission in one-dimensional phononic crystal plates,” J. Appl. Phys. 108(12), 124909 (2010).
[Crossref]

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

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

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3(11), 1196 (2012).
[Crossref] [PubMed]

Nat. Mater. (2)

B. Liang, X. S. Guo, J. Tu, D. Zhang, and J. C. Cheng, “An acoustic rectifier,” Nat. Mater. 9(12), 989–992 (2010).
[Crossref] [PubMed]

S. Y. Yu, X. C. Sun, X. Ni, Q. Wang, X. J. Yan, C. He, X. P. Liu, L. Feng, M. H. Lu, and Y. F. Chen, “Surface phononic graphene,” Nat. Mater. 15(12), 1243–1247 (2016).
[Crossref] [PubMed]

Nature (3)

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

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[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]

Opt. Commun. (1)

T. X. Ma, Y. S. Wang, and C. Z. Zhang, “Investigation of dual photonic and phononic bandgaps in two-dimensional phoxonic crystals with veins,” Opt. Commun. 312(4), 68–72 (2014).
[Crossref]

Opt. Express (7)

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[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]

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]

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

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

C. Xue, H. Jiang, and H. Chen, “Highly efficient all-optical diode action based on light-tunneling heterostructures,” Opt. Express 18(7), 7479–7487 (2010).
[Crossref] [PubMed]

J. C. Hsu, T. Y. Lu, and T. R. Lin, “Acousto-optic coupling in phoxonic crystal nanobeam cavities with plasmonic behavior,” Opt. Express 23(20), 25814–25826 (2015).
[Crossref] [PubMed]

Opt. Lett. (1)

Optik (Stuttg.) (1)

H. Gao, M. Ouyang, Y. Wang, Y. Shen, J. Zhou, and D. H. Liu, “Analysis on diffraction properties of the transmission phase grating,” Optik (Stuttg.) 118(9), 452–456 (2007).
[Crossref]

Phys. Rev. B (3)

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

M. Vanwolleghem, X. Checoury, W. Śmigaj, B. Gralak, L. Magdenko, K. Postava, B. Dagens, P. Beauvillain, and J. M. Lourtioz, “Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals,” Phys. Rev. B 80(12), 121102 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Bistable diode action in left-handed periodic structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(33 Pt 2B), 037602 (2005).
[Crossref] [PubMed]

J. J. Chen, B. Bonello, and Z. L. Hou, “Plate-mode waves in phononic crystal thin slabs: mode conversion,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 036609 (2008).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

X. F. Li, X. Ni, L. Feng, M. H. Lu, C. He, and Y. F. Chen, “Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode,” Phys. Rev. Lett. 106(8), 084301 (2011).
[Crossref] [PubMed]

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic diode: rectification of acoustic energy flux in one-dimensional systems,” Phys. Rev. Lett. 103(10), 104301 (2009).
[Crossref] [PubMed]

A. V. Akimov, Y. Tanaka, A. B. Pevtsov, S. F. Kaplan, V. G. Golubev, S. Tamura, D. R. Yakovlev, and M. Bayer, “Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials,” Phys. Rev. Lett. 101(3), 033902 (2008).
[Crossref] [PubMed]

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

Phys. Rev. X (1)

V. Peano, C. Brendel, M. Schmidt, and F. Marquardt, “Topological phases of sound and light,” Phys. Rev. X 5(3), 031011 (2015).
[Crossref]

Sci. Rep. (1)

Q. Wang, Y. Yang, X. Ni, Y. L. Xu, X. C. Sun, Z. G. Chen, L. Feng, X. P. Liu, M. H. Lu, and Y. F. Chen, “Acoustic asymmetric transmission based on time-dependent dynamical scattering,” Sci. Rep. 5(1), 10880 (2015).
[Crossref] [PubMed]

Science (1)

R. Fleury, D. L. Sounas, C. F. Sieck, M. R. Haberman, and A. Alù, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator,” Science 343(6170), 516–519 (2014).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Schematic geometry of composite GPxCs structure: (a) a square lattice array of circular silicon rods combined with rectangular grating in air and (b) a triangular lattice array of circular silicon rods combined with rectangular grating in air.
Fig. 2
Fig. 2 (a) Calculated band structures of PnCs for a square lattice of silicon rods in air. (b) Calculated band structure of PtCs (TE polarized light) for a square lattice of silicon rods in air. And the transmission spectra of acoustic waves (c) and TE polarized light (d) in composite GPxCs structure for PI and NI, respectively.
Fig. 3
Fig. 3 Simulated acoustic pressure field intensity distributions at Ω = 0.428 for PI (a), NI (b), respectively. And simulated magnetic field intensity distributions of TE waves at Ω = 0.428 for PI (c), NI (d), respectively.
Fig. 4
Fig. 4 Calculated band structures of PnCs (a) and PtCs (b) for a triangular lattice of silicon rods in air. The transmission spectra of acoustic (c) and TE polarized light (d) for a triangular lattice of silicon rods in air under normal incidence (θ = 0°) and oblique incidence (θ = 15°), respectively.
Fig. 5
Fig. 5 The Geometric viewpoint of GPxCs for asymmetrical propagation, the indigo rectangles represent the 2D PxCs layers, the blue arrays are the periodic grating. (a) The waves (acoustic and TE) are mostly blocked for PI and (b) the waves (acoustic and TE polarized light) can pass through the whole composite structure for NI.
Fig. 6
Fig. 6 The transmission spectra of normal incident acoustic (a) and TE polarized light (b) for a triangular lattice of silicon rods combined with periodic grating in air under the PI and NI, respectively. The inset in Fig. 6(a) shows the acoustic transmission spectra of five degree oblique incidence. And the inset in Fig. 6(b) shows the optical transmission spectra of five degree oblique incidence. Simulated acoustic pressure field intensity distributions at Ω = 0.516 for PI (c), and NI (d), respectively. And simulated magnetic field intensity distributions of TE polarized light at Ω = 0.516 for PI (e), and NI (f), respectively.

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