Abstract

A fully planar two-dimensional optomechanical crystal formed in a silicon microchip is used to create a structure devoid of phonons in the GHz frequency range. A nanoscale photonic crystal cavity is placed inside the phononic bandgap crystal in order to probe the properties of the localized acoustic modes. By studying the trends in mechanical damping, mode density, and optomechanical coupling strength of the acoustic resonances over an array of structures with varying geometric properties, clear evidence of a complete phononic bandgap is shown.

© 2011 Optical Society of America

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    [CrossRef]

2011 (1)

A. H. Safavi-Naeini and O. Painter, “Proposal for an Optomechanical Traveling Wave Phonon-Photon Translator,” N. J. Phys. 13, 013017 (2011).
[CrossRef]

2010 (5)

2009 (5)

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a twodimensional phononic crystal slab,” Appl. Phys. Lett. 94(5), 051906 (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. 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]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical Oscillation and Cooling Actuated by the Optical Gradient Force,” Phys. Rev. Lett. 103(10), 103601 (2009).
[CrossRef] [PubMed]

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

2008 (3)

G. S. Wiederhecker, A. Brenn, H. L. Fragnito, and P. S. J. Russell, “Coherent Control of Ultrahigh-Frequency Acoustic Resonances in Photonic Crystal Fibers,” Phys. Rev. Lett. 100(20), 203903 (2008).
[CrossRef] [PubMed]

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (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)

C. T. C. Nguyen, “MEMS technology for timing and frequency control,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54(2), 251–270 (2007).
[CrossRef] [PubMed]

2006 (3)

W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals,” Nat. Mater. 5(10), 830–836 (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]

A. Duwel, R. Candler, T. Kenny, and M. Varghese, “Engineering MEMS Resonators With Low Thermoelastic Damping,” J. Microelectromech. Syst. 15(6), 1437–1445 (2006).
[CrossRef]

2005 (3)

T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, “Hypersonic Phononic Crystals,” Phys. Rev. Lett. 94(11), 115501 (2005).
[CrossRef] [PubMed]

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76(6), 061101–061101 (2005).
[CrossRef]

2004 (2)

S. K. Estreicher, M. Sanati, D. West, and F. Ruymgaart, “Thermodynamics of impurities in semiconductors,” Phys. Rev. B 70(12), 125209 (2004).
[CrossRef]

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Focusing of Sound in a 3D Phononic Crystal,” Phys. Rev. Lett. 93(2), 024301 (2004).
[CrossRef] [PubMed]

2003 (1)

X. Zhang, R. Sooryakumar, and K. Bussmann, “Confinement and transverse standing acoustic resonances in free-standing membranes,” Phys. Rev. B 68, 115430 (2003).
[CrossRef]

2002 (1)

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Ultrasound Tunneling through 3D Phononic Crystals,” Phys. Rev. Lett. 88(10), 104301 (2002).
[CrossRef] [PubMed]

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]

R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro- and nanomechanical systems,” Phys. Rev. B 61(8), 5600 (2000).
[CrossRef]

1995 (1)

S. D. Lambade, G. G. Sahasrabudhe, and S. Rajagopalan, “Temperature dependence of acoustic attenuation in silicon,” Phys. Rev. B 51(22), 15,861 (1995).
[CrossRef]

1983 (1)

J. Philip and M. A. Breazeale, “Third-order elastic constants and Gr¨uneisen parameters of silicon and germanium between 3 and 300 K,” J. Appl. Phys. 54(2), 752 (1983).
[CrossRef]

1973 (1)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22(276), 276–278 (1973).
[CrossRef]

1961 (1)

T. O. Woodruff and H. Ehrenreich, “Absorption of Sound in Insulators,” Phys. Rev. 123(5), 1553 (1961).
[CrossRef]

1939 (1)

A. Akhieser, J. Phys. (Moscow) 1, 277 (1939).

1938 (1)

C. Zener, “Internal Friction in Solids II. General Theory of Thermoelastic Internal Friction,” Phys. Rev. 53(1), 90 (1938).
[CrossRef]

1937 (2)

C. Zener, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev. 52(3), 230 (1937).
[CrossRef]

L. Landau and G. Rumer, “Absorption of sound in solids,” Phys. Z. Sowjetunion 11, 18 (1937).

Adibi, A.

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

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a twodimensional phononic crystal slab,” Appl. Phys. Lett. 94(5), 051906 (2009).
[CrossRef]

Akahane, Y.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Akhieser, A.

A. Akhieser, J. Phys. (Moscow) 1, 277 (1939).

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]

Asano, T.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Bae, E.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

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]

Benchabane, S.

Breazeale, M. A.

J. Philip and M. A. Breazeale, “Third-order elastic constants and Gr¨uneisen parameters of silicon and germanium between 3 and 300 K,” J. Appl. Phys. 54(2), 752 (1983).
[CrossRef]

Brenn, A.

G. S. Wiederhecker, A. Brenn, H. L. Fragnito, and P. S. J. Russell, “Coherent Control of Ultrahigh-Frequency Acoustic Resonances in Photonic Crystal Fibers,” Phys. Rev. Lett. 100(20), 203903 (2008).
[CrossRef] [PubMed]

Bussmann, K.

X. Zhang, R. Sooryakumar, and K. Bussmann, “Confinement and transverse standing acoustic resonances in free-standing membranes,” Phys. Rev. B 68, 115430 (2003).
[CrossRef]

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photoniccrystal 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]

Candler, R.

A. Duwel, R. Candler, T. Kenny, and M. Varghese, “Engineering MEMS Resonators With Low Thermoelastic Damping,” J. Microelectromech. Syst. 15(6), 1437–1445 (2006).
[CrossRef]

Chan, C. T.

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Focusing of Sound in a 3D Phononic Crystal,” Phys. Rev. Lett. 93(2), 024301 (2004).
[CrossRef] [PubMed]

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Ultrasound Tunneling through 3D Phononic Crystals,” Phys. Rev. Lett. 88(10), 104301 (2002).
[CrossRef] [PubMed]

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]

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]

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 photoniccrystal optomechanical cavity,” Nature 459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Cheng, W.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals,” Nat. Mater. 5(10), 830–836 (2006).
[CrossRef] [PubMed]

Cowan, M. L.

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Focusing of Sound in a 3D Phononic Crystal,” Phys. Rev. Lett. 93(2), 024301 (2004).
[CrossRef] [PubMed]

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Ultrasound Tunneling through 3D Phononic Crystals,” Phys. Rev. Lett. 88(10), 104301 (2002).
[CrossRef] [PubMed]

Dais, C.

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (2010).
[CrossRef]

Duwel, A.

A. Duwel, R. Candler, T. Kenny, and M. Varghese, “Engineering MEMS Resonators With Low Thermoelastic Damping,” J. Microelectromech. Syst. 15(6), 1437–1445 (2006).
[CrossRef]

Eftekhar, A. A.

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

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a twodimensional phononic crystal slab,” Appl. Phys. Lett. 94(5), 051906 (2009).
[CrossRef]

Ehrenreich, H.

T. O. Woodruff and H. Ehrenreich, “Absorption of Sound in Insulators,” Phys. Rev. 123(5), 1553 (1961).
[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 photoniccrystal 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]

Ekinci, K. L.

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76(6), 061101–061101 (2005).
[CrossRef]

El Boudouti, E. H.

El Hassouani, Y.

Estreicher, S. K.

S. K. Estreicher, M. Sanati, D. West, and F. Ruymgaart, “Thermodynamics of impurities in semiconductors,” Phys. Rev. B 70(12), 125209 (2004).
[CrossRef]

Fragnito, H. L.

G. S. Wiederhecker, A. Brenn, H. L. Fragnito, and P. S. J. Russell, “Coherent Control of Ultrahigh-Frequency Acoustic Resonances in Photonic Crystal Fibers,” Phys. Rev. Lett. 100(20), 203903 (2008).
[CrossRef] [PubMed]

Fytas, G.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals,” Nat. Mater. 5(10), 830–836 (2006).
[CrossRef] [PubMed]

T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, “Hypersonic Phononic Crystals,” Phys. Rev. Lett. 94(11), 115501 (2005).
[CrossRef] [PubMed]

Gaofeng, J.

J. Gaofeng and S. Zhifei, “A new seismic isolation system and its feasibility study,” Earthq. Eng. Eng. Vib. 9(1), 75–82 (2010).
[CrossRef]

Golubev, V. G.

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]

Gomopoulos, N.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

Gorishnyy, T.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, “Hypersonic Phononic Crystals,” Phys. Rev. Lett. 94(11), 115501 (2005).
[CrossRef] [PubMed]

Grtzmacher, D.

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (2010).
[CrossRef]

Hiltner, A.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

Hunt, W. D.

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a twodimensional phononic crystal slab,” Appl. Phys. Lett. 94(5), 051906 (2009).
[CrossRef]

Ippen, E. P.

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22(276), 276–278 (1973).
[CrossRef]

Jiang, X.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical Oscillation and Cooling Actuated by the Optical Gradient Force,” Phys. Rev. Lett. 103(10), 103601 (2009).
[CrossRef] [PubMed]

Jonas, U.

W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals,” Nat. Mater. 5(10), 830–836 (2006).
[CrossRef] [PubMed]

Kaplan, S. F.

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]

Kenny, T.

A. Duwel, R. Candler, T. Kenny, and M. Varghese, “Engineering MEMS Resonators With Low Thermoelastic Damping,” J. Microelectromech. Syst. 15(6), 1437–1445 (2006).
[CrossRef]

Khelif, A.

Lambade, S. D.

S. D. Lambade, G. G. Sahasrabudhe, and S. Rajagopalan, “Temperature dependence of acoustic attenuation in silicon,” Phys. Rev. B 51(22), 15,861 (1995).
[CrossRef]

Landau, L.

L. Landau and G. Rumer, “Absorption of sound in solids,” Phys. Z. Sowjetunion 11, 18 (1937).

Laude, V.

Li, C.

Lifshitz, R.

R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro- and nanomechanical systems,” Phys. Rev. B 61(8), 5600 (2000).
[CrossRef]

Lin, Q.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical Oscillation and Cooling Actuated by the Optical Gradient Force,” Phys. Rev. Lett. 103(10), 103601 (2009).
[CrossRef] [PubMed]

Liu, Z.

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Focusing of Sound in a 3D Phononic Crystal,” Phys. Rev. Lett. 93(2), 024301 (2004).
[CrossRef] [PubMed]

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Ultrasound Tunneling through 3D Phononic Crystals,” Phys. Rev. Lett. 88(10), 104301 (2002).
[CrossRef] [PubMed]

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]

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]

T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, “Hypersonic Phononic Crystals,” Phys. Rev. Lett. 94(11), 115501 (2005).
[CrossRef] [PubMed]

Mao, Y.

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]

Martinez, A.

Mohammadi, S.

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]

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a twodimensional phononic crystal slab,” Appl. Phys. Lett. 94(5), 051906 (2009).
[CrossRef]

Nguyen, C. T. C.

C. T. C. Nguyen, “MEMS technology for timing and frequency control,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54(2), 251–270 (2007).
[CrossRef] [PubMed]

Noda, S.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Page, J. H.

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Focusing of Sound in a 3D Phononic Crystal,” Phys. Rev. Lett. 93(2), 024301 (2004).
[CrossRef] [PubMed]

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Ultrasound Tunneling through 3D Phononic Crystals,” Phys. Rev. Lett. 88(10), 104301 (2002).
[CrossRef] [PubMed]

Painter, O.

A. H. Safavi-Naeini and O. Painter, “Proposal for an Optomechanical Traveling Wave Phonon-Photon Translator,” N. J. Phys. 13, 013017 (2011).
[CrossRef]

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

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical Oscillation and Cooling Actuated by the Optical Gradient Force,” Phys. Rev. Lett. 103(10), 103601 (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]

Papanikolaou, N.

Pennec, Y.

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]

Philip, J.

J. Philip and M. A. Breazeale, “Third-order elastic constants and Gr¨uneisen parameters of silicon and germanium between 3 and 300 K,” J. Appl. Phys. 54(2), 752 (1983).
[CrossRef]

Rajagopalan, S.

S. D. Lambade, G. G. Sahasrabudhe, and S. Rajagopalan, “Temperature dependence of acoustic attenuation in silicon,” Phys. Rev. B 51(22), 15,861 (1995).
[CrossRef]

Rosenberg, J.

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical Oscillation and Cooling Actuated by the Optical Gradient Force,” Phys. Rev. Lett. 103(10), 103601 (2009).
[CrossRef] [PubMed]

Rouhani, B. D.

Roukes, M. L.

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76(6), 061101–061101 (2005).
[CrossRef]

R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro- and nanomechanical systems,” Phys. Rev. B 61(8), 5600 (2000).
[CrossRef]

Rumer, G.

L. Landau and G. Rumer, “Absorption of sound in solids,” Phys. Z. Sowjetunion 11, 18 (1937).

Russell, P. S. J.

G. S. Wiederhecker, A. Brenn, H. L. Fragnito, and P. S. J. Russell, “Coherent Control of Ultrahigh-Frequency Acoustic Resonances in Photonic Crystal Fibers,” Phys. Rev. Lett. 100(20), 203903 (2008).
[CrossRef] [PubMed]

Ruymgaart, F.

S. K. Estreicher, M. Sanati, D. West, and F. Ruymgaart, “Thermodynamics of impurities in semiconductors,” Phys. Rev. B 70(12), 125209 (2004).
[CrossRef]

Safavi-Naeini, A. H.

Sahasrabudhe, G. G.

S. D. Lambade, G. G. Sahasrabudhe, and S. Rajagopalan, “Temperature dependence of acoustic attenuation in silicon,” Phys. Rev. B 51(22), 15,861 (1995).
[CrossRef]

Sanati, M.

S. K. Estreicher, M. Sanati, D. West, and F. Ruymgaart, “Thermodynamics of impurities in semiconductors,” Phys. Rev. B 70(12), 125209 (2004).
[CrossRef]

Sheng, P.

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Focusing of Sound in a 3D Phononic Crystal,” Phys. Rev. Lett. 93(2), 024301 (2004).
[CrossRef] [PubMed]

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Ultrasound Tunneling through 3D Phononic Crystals,” Phys. Rev. Lett. 88(10), 104301 (2002).
[CrossRef] [PubMed]

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, J.

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (2010).
[CrossRef]

Song, B.

B. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Sooryakumar, R.

X. Zhang, R. Sooryakumar, and K. Bussmann, “Confinement and transverse standing acoustic resonances in free-standing membranes,” Phys. Rev. B 68, 115430 (2003).
[CrossRef]

Stefanou, N.

W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals,” Nat. Mater. 5(10), 830–836 (2006).
[CrossRef] [PubMed]

Stolen, R. H.

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22(276), 276–278 (1973).
[CrossRef]

Sun, C.

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (2010).
[CrossRef]

Sun, J.

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (2010).
[CrossRef]

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.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[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]

T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, “Hypersonic Phononic Crystals,” Phys. Rev. Lett. 94(11), 115501 (2005).
[CrossRef] [PubMed]

Ullal, C. K.

T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, and E. L. Thomas, “Hypersonic Phononic Crystals,” Phys. Rev. Lett. 94(11), 115501 (2005).
[CrossRef] [PubMed]

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]

Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical Oscillation and Cooling Actuated by the Optical Gradient Force,” Phys. Rev. Lett. 103(10), 103601 (2009).
[CrossRef] [PubMed]

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

Varghese, M.

A. Duwel, R. Candler, T. Kenny, and M. Varghese, “Engineering MEMS Resonators With Low Thermoelastic Damping,” J. Microelectromech. Syst. 15(6), 1437–1445 (2006).
[CrossRef]

Vasseur, J. O.

Walish, J.

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

Wang, J.

W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals,” Nat. Mater. 5(10), 830–836 (2006).
[CrossRef] [PubMed]

Wen, Y.

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (2010).
[CrossRef]

West, D.

S. K. Estreicher, M. Sanati, D. West, and F. Ruymgaart, “Thermodynamics of impurities in semiconductors,” Phys. Rev. B 70(12), 125209 (2004).
[CrossRef]

Wiederhecker, G. S.

G. S. Wiederhecker, A. Brenn, H. L. Fragnito, and P. S. J. Russell, “Coherent Control of Ultrahigh-Frequency Acoustic Resonances in Photonic Crystal Fibers,” Phys. Rev. Lett. 100(20), 203903 (2008).
[CrossRef] [PubMed]

Woodruff, T. O.

T. O. Woodruff and H. Ehrenreich, “Absorption of Sound in Insulators,” Phys. Rev. 123(5), 1553 (1961).
[CrossRef]

Wu, T.

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (2010).
[CrossRef]

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]

Yang, S.

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Focusing of Sound in a 3D Phononic Crystal,” Phys. Rev. Lett. 93(2), 024301 (2004).
[CrossRef] [PubMed]

S. Yang, J. H. Page, Z. Liu, M. L. Cowan, C. T. Chan, and P. Sheng, “Ultrasound Tunneling through 3D Phononic Crystals,” Phys. Rev. Lett. 88(10), 104301 (2002).
[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]

Zener, C.

C. Zener, “Internal Friction in Solids II. General Theory of Thermoelastic Internal Friction,” Phys. Rev. 53(1), 90 (1938).
[CrossRef]

C. Zener, “Internal Friction in Solids. I. Theory of Internal Friction in Reeds,” Phys. Rev. 52(3), 230 (1937).
[CrossRef]

Zhang, X.

X. Zhang, R. Sooryakumar, and K. Bussmann, “Confinement and transverse standing acoustic resonances in free-standing membranes,” Phys. Rev. B 68, 115430 (2003).
[CrossRef]

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]

Zhifei, S.

J. Gaofeng and S. Zhifei, “A new seismic isolation system and its feasibility study,” Earthq. Eng. Eng. Vib. 9(1), 75–82 (2010).
[CrossRef]

Zhu, Y. Y.

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]

Appl. Phys. Lett. (4)

S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, “High-Q micromechanical resonators in a twodimensional phononic crystal slab,” Appl. Phys. Lett. 94(5), 051906 (2009).
[CrossRef]

Y. Wen, J. Sun, C. Dais, D. Grtzmacher, T. Wu, J. Shi, and C. Sun, “Three-dimensional phononic nanocrystal composed of ordered quantum dots,” Appl. Phys. Lett. 96(12), 123113 (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]

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22(276), 276–278 (1973).
[CrossRef]

Earthq. Eng. Eng. Vib. (1)

J. Gaofeng and S. Zhifei, “A new seismic isolation system and its feasibility study,” Earthq. Eng. Eng. Vib. 9(1), 75–82 (2010).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

C. T. C. Nguyen, “MEMS technology for timing and frequency control,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54(2), 251–270 (2007).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

J. Philip and M. A. Breazeale, “Third-order elastic constants and Gr¨uneisen parameters of silicon and germanium between 3 and 300 K,” J. Appl. Phys. 54(2), 752 (1983).
[CrossRef]

J. Microelectromech. Syst. (1)

A. Duwel, R. Candler, T. Kenny, and M. Varghese, “Engineering MEMS Resonators With Low Thermoelastic Damping,” J. Microelectromech. Syst. 15(6), 1437–1445 (2006).
[CrossRef]

J. Phys. (Moscow) (1)

A. Akhieser, J. Phys. (Moscow) 1, 277 (1939).

N. J. Phys. (1)

A. H. Safavi-Naeini and O. Painter, “Proposal for an Optomechanical Traveling Wave Phonon-Photon Translator,” N. J. Phys. 13, 013017 (2011).
[CrossRef]

Nano Lett. (1)

W. Cheng, N. Gomopoulos, G. Fytas, T. Gorishnyy, J. Walish, E. L. Thomas, A. Hiltner, and E. Bae, “Phonon Dispersion and Nanomechanical Properties of Periodic 1D Multilayer Polymer Films,” Nano Lett. 8(5), 1423–1428 (2008).
[CrossRef] [PubMed]

Nat. Mater. (2)

W. Cheng, J. Wang, U. Jonas, G. Fytas, and N. Stefanou, “Observation and tuning of hypersonic bandgaps in colloidal crystals,” Nat. Mater. 5(10), 830–836 (2006).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Real space crystal lattice of the cross crystal with lattice constant a, cross length h, cross width w, and membrane thickness d. The bridge width is defined as b = a – h. (b) Reciprocal lattice of the first Brillouin zone for the cross crystal. (c) Phononic band diagram for the nominal cross structure with a = 1.265 μm, h = 1.220 μm, w = 340 nm. Dark blue lines represent the bands with even vector symmetry for reflections about the x – y plane, while the red lines are the flexural modes which have odd vector mirror symmetry about the x – y plane. (d) Tuning of the bandgap with bridge width, b. Light grey, dark grey, and white areas indicate regions of a symmetry-dependent (i.e., for modes of only one symmetry) bandgap, no bandgap, and full bandgap for all acoustic modes, respectively.

Fig. 2
Fig. 2

(a) Scanning electron micrograph (SEM) of one of the fabricated 2D-OMC structures. The photonic nanocavity region is shown in false green color. In (b), Zoom-in SEM image of the cross crystal phononic bandgap structure. (c) Zoom-in SEM image of the optical nanocavity within embedded in the phononic bandgap crystal. Darker (lighter) false colors represents larger (smaller) lattice constant in the optical cavity defect region. (d) FEM simulation of Ey electrical field for the optical cavity. (e) Typical measured transmission spectra for the optical nanocavity, showing a bare optical Q-factor of Qi = 1.5 × 106.

Fig. 3
Fig. 3

(a) Experimental setup for measuring the PSD. (b) Optical micrograph of the tapered fiber coupled to the device while performing experiments. (c) Optical spectra for two different positions of the taper relative to the device are shown.

Fig. 4
Fig. 4

(a) Optically transduced RF power spectral density of the thermal Brownian motion of S1 structures with b = 57 nm (top), b = 106 nm (middle), and b = 160 nm (bottom). The inferred region below the phononic bandgap is shaded grey (see main text). (b) Temperature dependence of the mechanical quality factor for the 1.4 GHz acoustic mode of the S1 structure with b = 57 nm.

Fig. 5
Fig. 5

(a) Plot of the 3D-FEM simulated in-plane localized acoustic modes of the S1 structure as a function of bridge width b. Each marker corresponds to a single acoustic mode, with the marker size proportional to the logarithm of the calculated acoustic radiation Q-factor. The light blue shaded markers correspond to acoustic bands which are optically dark. The shading corresponds to the same color coding of the phononic bandgaps as that used in Fig. 1(d). (b) Measured mode plot of the optically-transduced localized acoustic modes for an array of S1 structures with varying bridge width. The marker size of each resonance is related to the logarithm of the measured mechanical Q-factor. The inferred spectral region below the phononic bandgap is shaded grey. (c) and (d) FEM simulations of the displacement field amplitude (|Q(r)|) for the acoustic mode in the orange colored band around 1.35 GHz in (a). In (c) the mode is within the phononic band gap resulting in a radiation-limited Q M ( rad ) 10 9. In (d) the mode is on the edge of the bandgap and has a reduced Q M ( rad ) < 10 3. (e) Simulated (□) and measured (○) optomechanical coupling rate g for the orange (red) highlighted acoustic band in (a) ((b)). (f) Simulated (□) and measured (○) optomechanical coupling rate g for the series of acoustic modes of the S1 structure with b ∼ 100 nm (vertical dashed curves in (a) and (b))

Fig. 6
Fig. 6

(a) RF-power spectral density for three devices with different bridge widths, b. The gray shaded area refers to regions outside of the full bandgap while the orange shaded area are for frequencies within the bandgap. (b) results of full 3D-FEM simulations of phononic localized modes as a function of bridge width b. For each bridge-width a full 3D-FEM simulation with an absorbing perfect-matched-layer (PML) is performed. Each square corresponds to a single mode, with its size is proportional to the logarithm of the mechanical Q-factor. The gray shaded squares represent modes which are optically dark (g’s small enough to be lower than our detection noise floor). (c) Measurement (○) results of the localized mechanical modes for the a set of fabricated S2 samples. Each bridge size b was measured by careful analysis of scanning electron micrographs. The marker sizes are proportional to measured mechanical Q-factor.

Fig. 7
Fig. 7

(a) Comparison between the different sources of mechanical loss with the measured QM values versus temperature. The circles represent the measured values from the S1 samples; diamonds are computed QM from acoustic attenuation data from Ref. [34]; squares represent the simulated values for TED as explained on the text. The purple and green lines are the calculated QM due to Akheiser and Landau-Rumer phonon-phonon dissipation mechanism respectively. The insets show the measured RF PSD at 10 K and 300 K for extracting QM. (b) Thermo-mechanical 2D-FEM simulations for the mechanical mode at 1.4 GHz shown in Fig. 3 of the main text. The thermal profile is plotted at various times during the mechanical cycle.

Equations (1)

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α LR ( Ω ; T ) = π γ 2 Ω C v T 4 ρ c s 2 , and α AK ( Ω ; T ) = γ 2 Ω 2 C v T τ 3 ρ c s 2 ,

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