Abstract

We report numerically large and complete photonic and phononic band gaps that simultaneously exist in eight-fold phoxonic quasicrystals (PhXQCs). PhXQCs can possess simultaneous photonic and phononic band gaps over a wide range of geometric parameters. Abundant localized modes can be achieved in defect-free PhXQCs for all photonic and phononic polarizations. These defect-free localized modes exhibit multiform spatial distributions and can confine simultaneously electromagnetic and elastic waves in a large area, thereby providing rich selectivity and enlarging the interaction space of optical and elastic waves. The simulated results based on finite element method show that quasiperiodic structures formed of both solid rods in air and holes in solid materials can simultaneously confine and tailor electromagnetic and elastic waves; these structures showed advantages over the periodic counterparts.

© 2016 Optical Society of America

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2016 (2)

F. X. Xu, Q. S. Zou, Q. C. Zhou, T. B. Wang, T. B. Yu, and N. H. Liu, “Self-imaging effect in photonic quasicrystal waveguides: application to 3 dB power splitter for terahertz waves,” Opt. Commun. 367, 108–111 (2016).
[Crossref]

Q. S. Zou, T. B. Yu, T. B. Wang, N. H. Liu, Q. H. Liao, and X. M. Xu, “Novel 1×N ultrasonic power splitters based on self-imaging effect of phononic crystal waveguide arrays,” J. Appl. Phys. 119(8), 084509 (2016).
[Crossref]

2015 (3)

Q. S. Zou, T. B. Yu, J. T. Liu, N. H. Liu, T. B. Wang, and Q. H. Liao, “Acoustic multimode interference and self-imaging phenomena realized in multimodal phononic crystal waveguides,” J. Phys. D Appl. Phys. 48(34), 345301 (2015).
[Crossref]

Z. Huang, K. Cui, Y. Li, X. Feng, F. Liu, W. Zhang, and Y. Huang, “Strong optomechanical coupling in nanobeam cavities based on hetero optomechanical crystals,” Sci. Rep. 5, 15964 (2015).

R. Leijssen and E. Verhagen, “Strong optomechanical interactions in a sliced photonic crystal nanobeam,” Sci. Rep. 5, 15974 (2015).

2014 (2)

T.-X. Ma, K. Zou, Y.-S. Wang, C. Zhang, and X. X. Su, “Acousto-optical interaction of surface acoustic and optical waves in a two-dimensional phoxonic crystal hetero-structure cavity,” Opt. Express 22(23), 28443–28451 (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]

T. B. Yu, S. Z. Li, N. H. Liu, T. B. Wang, Q. H. Liao, and X. M. Xu, “Highly efficient coupling between inner and surface fields in photonic crystal waveguides,” IEEE Photonics Technol. Lett. 25(15), 1496–1499 (2013).
[Crossref]

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87(16), 165116 (2013).
[Crossref]

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[Crossref]

2012 (3)

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]

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]

M. Zhang, W. Zhong, and X. Zhang, “Defect-free localized modes and coupled-resonator acoustic waveguides constructed in two-dimensional phononic quasicrystals,” J. Appl. Phys. 111(10), 104314 (2012).
[Crossref]

2009 (2)

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

2008 (1)

A. L. Chen, Y.-S. Wang, Y.-F. Guo, and Z.-D. Wang, “Band structures of Fibonacci phononic quasicrystals,” Solid State Commun. 145(3), 103–108 (2008).
[Crossref]

2007 (5)

F.-L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C.-C. Chen, and V. Laude, “Waveguiding inside the complete band gap of a phononic crystal slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(5), 056601 (2007).
[Crossref] [PubMed]

K. Mnaymneh and R. C. Gauthier, “Mode localization and band-gap formation in defect-free photonic quasicrystals,” Opt. Express 15(8), 5089–5099 (2007).
[Crossref] [PubMed]

W. Steurer and D. Sutter-Widmer, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
[Crossref]

D. Sutter-Widmer, S. Deloudi, and W. Steurer, “Prediction of Bragg-scattering-induced band gaps in phononic quasicrystals,” Phys. Rev. B 75(9), 094304 (2007).
[Crossref]

X. Zhang, “Universal non-near-field focus of acoustic waves through high-symmetry quasicrystals,” Phys. Rev. B 75(2), 024209 (2007).
[Crossref]

2006 (3)

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]

A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express 14(21), 10021–10027 (2006).
[Crossref] [PubMed]

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]

2005 (1)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

2003 (1)

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68(16), 165106 (2003).
[Crossref]

2000 (2)

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[Crossref] [PubMed]

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

1999 (1)

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75(13), 1848–1850 (1999).
[Crossref]

1998 (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998).
[Crossref]

1995 (1)

H. E. Bass, L. C. Sutherland, A. J. Zuckerwar, D. T. Blackstock, and D. M. Hester, “Atmospheric absorption of sound: Further developments,” J. Acoust. Soc. Am. 97(1), 680–683 (1995).
[Crossref]

1993 (1)

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[Crossref] [PubMed]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

Agrawal, A.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[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]

Ban, S.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75(13), 1848–1850 (1999).
[Crossref]

Bass, H. E.

H. E. Bass, L. C. Sutherland, A. J. Zuckerwar, D. T. Blackstock, and D. M. Hester, “Atmospheric absorption of sound: Further developments,” J. Acoust. Soc. Am. 97(1), 680–683 (1995).
[Crossref]

Baumberg, J. J.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Benchabane, 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]

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]

Beugnot, J.-C.

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

Blackstock, D. T.

H. E. Bass, L. C. Sutherland, A. J. Zuckerwar, D. T. Blackstock, and D. M. Hester, “Atmospheric absorption of sound: Further developments,” J. Acoust. Soc. Am. 97(1), 680–683 (1995).
[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]

Capolino, F.

Carmon, T.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

Chan, C. T.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[Crossref] [PubMed]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998).
[Crossref]

Chan, J.

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

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998).
[Crossref]

Charlton, M. D. B.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

Chen, A. L.

A. L. Chen, Y.-S. Wang, Y.-F. Guo, and Z.-D. Wang, “Band structures of Fibonacci phononic quasicrystals,” Solid State Commun. 145(3), 103–108 (2008).
[Crossref]

Chen, C.-C.

F.-L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C.-C. Chen, and V. Laude, “Waveguiding inside the complete band gap of a phononic crystal slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(5), 056601 (2007).
[Crossref] [PubMed]

Cheng, B.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68(16), 165106 (2003).
[Crossref]

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75(13), 1848–1850 (1999).
[Crossref]

Choujaa, A.

F.-L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C.-C. Chen, and V. Laude, “Waveguiding inside the complete band gap of a phononic crystal slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(5), 056601 (2007).
[Crossref] [PubMed]

Cui, K.

Z. Huang, K. Cui, Y. Li, X. Feng, F. Liu, W. Zhang, and Y. Huang, “Strong optomechanical coupling in nanobeam cavities based on hetero optomechanical crystals,” Sci. Rep. 5, 15964 (2015).

Dadgar, A.

Della Villa, A.

Deloudi, S.

D. Sutter-Widmer, S. Deloudi, and W. Steurer, “Prediction of Bragg-scattering-induced band gaps in phononic quasicrystals,” Phys. Rev. B 75(9), 094304 (2007).
[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]

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[Crossref] [PubMed]

Dobrzynski, L.

M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
[Crossref] [PubMed]

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).
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Eichenfield, M.

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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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).
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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).
[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]

Enoch, S.

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).
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Feng, X.

Z. Huang, K. Cui, Y. Li, X. Feng, F. Liu, W. Zhang, and Y. Huang, “Strong optomechanical coupling in nanobeam cavities based on hetero optomechanical crystals,” Sci. Rep. 5, 15964 (2015).

Florescu, M.

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87(16), 165116 (2013).
[Crossref]

Galdi, V.

Gauthier, R. C.

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).
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Guo, Y.-F.

A. L. Chen, Y.-S. Wang, Y.-F. Guo, and Z.-D. Wang, “Band structures of Fibonacci phononic quasicrystals,” Solid State Commun. 145(3), 103–108 (2008).
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M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
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H. E. Bass, L. C. Sutherland, A. J. Zuckerwar, D. T. Blackstock, and D. M. Hester, “Atmospheric absorption of sound: Further developments,” J. Acoust. Soc. Am. 97(1), 680–683 (1995).
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Hsiao, F.-L.

F.-L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C.-C. Chen, and V. Laude, “Waveguiding inside the complete band gap of a phononic crystal slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(5), 056601 (2007).
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Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68(16), 165106 (2003).
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Huang, Y.

Z. Huang, K. Cui, Y. Li, X. Feng, F. Liu, W. Zhang, and Y. Huang, “Strong optomechanical coupling in nanobeam cavities based on hetero optomechanical crystals,” Sci. Rep. 5, 15964 (2015).

Huang, Z.

Z. Huang, K. Cui, Y. Li, X. Feng, F. Liu, W. Zhang, and Y. Huang, “Strong optomechanical coupling in nanobeam cavities based on hetero optomechanical crystals,” Sci. Rep. 5, 15964 (2015).

Jin, C.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75(13), 1848–1850 (1999).
[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).
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Khelif, A.

F.-L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C.-C. Chen, and V. Laude, “Waveguiding inside the complete band gap of a phononic crystal slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(5), 056601 (2007).
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T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
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M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Phys. Rev. Lett. 71(13), 2022–2025 (1993).
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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]

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]

F.-L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C.-C. Chen, and V. Laude, “Waveguiding inside the complete band gap of a phononic crystal slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(5), 056601 (2007).
[Crossref] [PubMed]

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R. Leijssen and E. Verhagen, “Strong optomechanical interactions in a sliced photonic crystal nanobeam,” Sci. Rep. 5, 15974 (2015).

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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, 061109 (2012).
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Li, S. Z.

T. B. Yu, S. Z. Li, N. H. Liu, T. B. Wang, Q. H. Liao, and X. M. Xu, “Highly efficient coupling between inner and surface fields in photonic crystal waveguides,” IEEE Photonics Technol. Lett. 25(15), 1496–1499 (2013).
[Crossref]

Li, Y.

Z. Huang, K. Cui, Y. Li, X. Feng, F. Liu, W. Zhang, and Y. Huang, “Strong optomechanical coupling in nanobeam cavities based on hetero optomechanical crystals,” Sci. Rep. 5, 15964 (2015).

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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C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75(13), 1848–1850 (1999).
[Crossref]

Liao, Q. H.

Q. S. Zou, T. B. Yu, T. B. Wang, N. H. Liu, Q. H. Liao, and X. M. Xu, “Novel 1×N ultrasonic power splitters based on self-imaging effect of phononic crystal waveguide arrays,” J. Appl. Phys. 119(8), 084509 (2016).
[Crossref]

Q. S. Zou, T. B. Yu, J. T. Liu, N. H. Liu, T. B. Wang, and Q. H. Liao, “Acoustic multimode interference and self-imaging phenomena realized in multimodal phononic crystal waveguides,” J. Phys. D Appl. Phys. 48(34), 345301 (2015).
[Crossref]

T. B. Yu, S. Z. Li, N. H. Liu, T. B. Wang, Q. H. Liao, and X. M. Xu, “Highly efficient coupling between inner and surface fields in photonic crystal waveguides,” IEEE Photonics Technol. Lett. 25(15), 1496–1499 (2013).
[Crossref]

Liu, F.

Z. Huang, K. Cui, Y. Li, X. Feng, F. Liu, W. Zhang, and Y. Huang, “Strong optomechanical coupling in nanobeam cavities based on hetero optomechanical crystals,” Sci. Rep. 5, 15964 (2015).

Liu, J. T.

Q. S. Zou, T. B. Yu, J. T. Liu, N. H. Liu, T. B. Wang, and Q. H. Liao, “Acoustic multimode interference and self-imaging phenomena realized in multimodal phononic crystal waveguides,” J. Phys. D Appl. Phys. 48(34), 345301 (2015).
[Crossref]

Liu, N. H.

Q. S. Zou, T. B. Yu, T. B. Wang, N. H. Liu, Q. H. Liao, and X. M. Xu, “Novel 1×N ultrasonic power splitters based on self-imaging effect of phononic crystal waveguide arrays,” J. Appl. Phys. 119(8), 084509 (2016).
[Crossref]

F. X. Xu, Q. S. Zou, Q. C. Zhou, T. B. Wang, T. B. Yu, and N. H. Liu, “Self-imaging effect in photonic quasicrystal waveguides: application to 3 dB power splitter for terahertz waves,” Opt. Commun. 367, 108–111 (2016).
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Q. S. Zou, T. B. Yu, J. T. Liu, N. H. Liu, T. B. Wang, and Q. H. Liao, “Acoustic multimode interference and self-imaging phenomena realized in multimodal phononic crystal waveguides,” J. Phys. D Appl. Phys. 48(34), 345301 (2015).
[Crossref]

T. B. Yu, S. Z. Li, N. H. Liu, T. B. Wang, Q. H. Liao, and X. M. Xu, “Highly efficient coupling between inner and surface fields in photonic crystal waveguides,” IEEE Photonics Technol. Lett. 25(15), 1496–1499 (2013).
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Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
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Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80(5), 956–959 (1998).
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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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C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75(13), 1848–1850 (1999).
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Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
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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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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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Mnaymneh, K.

Moubchir, H.

F.-L. Hsiao, A. Khelif, H. Moubchir, A. Choujaa, C.-C. Chen, and V. Laude, “Waveguiding inside the complete band gap of a phononic crystal slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(5), 056601 (2007).
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Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
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G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
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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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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).
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Painter, O.

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.

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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Parker, G. J.

G. J. Parker, M. E. Zoorob, M. D. B. Charlton, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature 404(6779), 740–743 (2000).
[Crossref] [PubMed]

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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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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]

Pernice, W. H. P.

Pierro, V.

Poot, M.

Rokhsari, H.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

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]

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]

Sheng, P.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[Crossref] [PubMed]

Shi, N. N.

Steinhardt, P. J.

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87(16), 165116 (2013).
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W. Steurer and D. Sutter-Widmer, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
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D. Sutter-Widmer, S. Deloudi, and W. Steurer, “Prediction of Bragg-scattering-induced band gaps in phononic quasicrystals,” Phys. Rev. B 75(9), 094304 (2007).
[Crossref]

Su, X. X.

Sun, B.

C. Jin, B. Cheng, B. Man, Z. Li, D. Zhang, S. Ban, and B. Sun, “Band gap and wave guiding effect in a quasiperiodic photonic crystal,” Appl. Phys. Lett. 75(13), 1848–1850 (1999).
[Crossref]

Sun, X.

Sutherland, L. C.

H. E. Bass, L. C. Sutherland, A. J. Zuckerwar, D. T. Blackstock, and D. M. Hester, “Atmospheric absorption of sound: Further developments,” J. Acoust. Soc. Am. 97(1), 680–683 (1995).
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W. Steurer and D. Sutter-Widmer, “Photonic and phononic quasicrystals,” J. Phys. D Appl. Phys. 40(13), R229–R247 (2007).
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D. Sutter-Widmer, S. Deloudi, and W. Steurer, “Prediction of Bragg-scattering-induced band gaps in phononic quasicrystals,” Phys. Rev. B 75(9), 094304 (2007).
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Tang, H. X.

Tayeb, G.

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]

Torquato, S.

M. Florescu, P. J. Steinhardt, and S. Torquato, “Optical cavities and waveguides in hyperuniform disordered photonic solids,” Phys. Rev. B 87(16), 165116 (2013).
[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]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

Vardeny, Z. V.

Z. V. Vardeny, A. Nahata, and A. Agrawal, “Optics of photonic quasicrystals,” Nat. Photonics 7(3), 177–187 (2013).
[Crossref]

Verhagen, E.

R. Leijssen and E. Verhagen, “Strong optomechanical interactions in a sliced photonic crystal nanobeam,” Sci. Rep. 5, 15974 (2015).

Wang, T. B.

F. X. Xu, Q. S. Zou, Q. C. Zhou, T. B. Wang, T. B. Yu, and N. H. Liu, “Self-imaging effect in photonic quasicrystal waveguides: application to 3 dB power splitter for terahertz waves,” Opt. Commun. 367, 108–111 (2016).
[Crossref]

Q. S. Zou, T. B. Yu, T. B. Wang, N. H. Liu, Q. H. Liao, and X. M. Xu, “Novel 1×N ultrasonic power splitters based on self-imaging effect of phononic crystal waveguide arrays,” J. Appl. Phys. 119(8), 084509 (2016).
[Crossref]

Q. S. Zou, T. B. Yu, J. T. Liu, N. H. Liu, T. B. Wang, and Q. H. Liao, “Acoustic multimode interference and self-imaging phenomena realized in multimodal phononic crystal waveguides,” J. Phys. D Appl. Phys. 48(34), 345301 (2015).
[Crossref]

T. B. Yu, S. Z. Li, N. H. Liu, T. B. Wang, Q. H. Liao, and X. M. Xu, “Highly efficient coupling between inner and surface fields in photonic crystal waveguides,” IEEE Photonics Technol. Lett. 25(15), 1496–1499 (2013).
[Crossref]

Wang, Y.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68(16), 165106 (2003).
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Wang, Y.-S.

Wang, Z.-D.

A. L. Chen, Y.-S. Wang, Y.-F. Guo, and Z.-D. Wang, “Band structures of Fibonacci phononic quasicrystals,” Solid State Commun. 145(3), 103–108 (2008).
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Wong, C. W.

Xu, F. X.

F. X. Xu, Q. S. Zou, Q. C. Zhou, T. B. Wang, T. B. Yu, and N. H. Liu, “Self-imaging effect in photonic quasicrystal waveguides: application to 3 dB power splitter for terahertz waves,” Opt. Commun. 367, 108–111 (2016).
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Xu, X.

Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B 68(16), 165106 (2003).
[Crossref]

Xu, X. M.

Q. S. Zou, T. B. Yu, T. B. Wang, N. H. Liu, Q. H. Liao, and X. M. Xu, “Novel 1×N ultrasonic power splitters based on self-imaging effect of phononic crystal waveguide arrays,” J. Appl. Phys. 119(8), 084509 (2016).
[Crossref]

T. B. Yu, S. Z. Li, N. H. Liu, T. B. Wang, Q. H. Liao, and X. M. Xu, “Highly efficient coupling between inner and surface fields in photonic crystal waveguides,” IEEE Photonics Technol. Lett. 25(15), 1496–1499 (2013).
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T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

Yang, Z.

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, “Locally resonant sonic materials,” Science 289(5485), 1734–1736 (2000).
[Crossref] [PubMed]

Yu, T. B.

Q. S. Zou, T. B. Yu, T. B. Wang, N. H. Liu, Q. H. Liao, and X. M. Xu, “Novel 1×N ultrasonic power splitters based on self-imaging effect of phononic crystal waveguide arrays,” J. Appl. Phys. 119(8), 084509 (2016).
[Crossref]

F. X. Xu, Q. S. Zou, Q. C. Zhou, T. B. Wang, T. B. Yu, and N. H. Liu, “Self-imaging effect in photonic quasicrystal waveguides: application to 3 dB power splitter for terahertz waves,” Opt. Commun. 367, 108–111 (2016).
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F. X. Xu, Q. S. Zou, Q. C. Zhou, T. B. Wang, T. B. Yu, and N. H. Liu, “Self-imaging effect in photonic quasicrystal waveguides: application to 3 dB power splitter for terahertz waves,” Opt. Commun. 367, 108–111 (2016).
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IEEE Photonics Technol. Lett. (1)

T. B. Yu, S. Z. Li, N. H. Liu, T. B. Wang, Q. H. Liao, and X. M. Xu, “Highly efficient coupling between inner and surface fields in photonic crystal waveguides,” IEEE Photonics Technol. Lett. 25(15), 1496–1499 (2013).
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H. E. Bass, L. C. Sutherland, A. J. Zuckerwar, D. T. Blackstock, and D. M. Hester, “Atmospheric absorption of sound: Further developments,” J. Acoust. Soc. Am. 97(1), 680–683 (1995).
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Science (1)

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Figures (7)

Fig. 1
Fig. 1 8-fold phoxonic quasicrystals (PhXQCs) models: (a) silicon rods in air (PhXQCs I) and (b) air holes in silicon (PhXQCs II).
Fig. 2
Fig. 2 (a) The transmission spectra of transvers electric (TE) modes of PhXQCs I with the radius 0.375 a 0   of rods for six incidence angles, namely 0°, 4.5°, 9°, 13.5°, 18°, 22.5°. (b) Magnified view of the sharp peaks indicated by a dash rectangle within the second bands in (a).
Fig. 3
Fig. 3 Photonic and phononic band gaps in 8-fold PhXQCs. For PhXQCs I made of silicon rods in air, the following are shown: (a) normalized photonic frequencies ωa/2πc for TE photonic band gaps versus the dimensionless ratio r/ a 0 , where c is the light speed in air. (b) Normalized phononic frequencies ωa/2π c air versus r/ a 0 , where c air is the sound speed in air. For PhXQCs II made of air holes in silicon, the following are shown: (c) Normalized photonic frequencies ωa/2πc for TE and TM photonic band gaps versus r/ a 0 . (d) Normalized phononic frequencies ωa/2π c T,Si for out-of-plane and in-plane phononic band gaps versus r/ a 0 , where c T,Si is the transverse sound speed in silicon. r is the radius of the silicon rods or air holes.
Fig. 4
Fig. 4 The normalized photonic and phononic frequencies of localized modes versus the ratio r/ a 0 in defect-free (a) PhXQCs I, (b) PhXQCs II.
Fig. 5
Fig. 5 The field distribution of localized modes in defect-free PhXQCs I with a radius 0.375 a 0 : (a) electric field profile for the TE mode and (b) pressure field profile for the phononic mode.
Fig. 6
Fig. 6 The field distribution of localized modes in defect-free PhXQCs II with a radius 0.375 a 0 : (a) electric field profile for the third TE mode with highest frequencies, (b) magnetic field profile for the second TM mode with higher frequency, (c) magnetic field profile for the first TM mode and (d) displacement uz for the out-of-plane phononic mode.
Fig. 7
Fig. 7 The extended field distribution of the localized modes in defect-free PhXQCs II with a radius 0.375 a 0 : (a) electric field profile for the first TE modes with lower frequencies, (b) total displacement u= [ ( u x ) 2 + ( u y ) 2 ] for the in-plane phononic mode.

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