Abstract

Periodically structured materials can sustain both optical and mechanical excitations which are tailored by the geometry. Here we analyze the properties of dispersively coupled planar photonic and phononic crystals: optomechanical crystals. In particular, the properties of co-resonant optical and mechanical cavities in quasi-1D (patterned nanobeam) and quasi-2D (patterned membrane) geometries are studied. It is shown that the mechanical Q and optomechanical coupling in these structures can vary by many orders of magnitude with modest changes in geometry. An intuitive picture is developed based upon a perturbation theory for shifting material boundaries that allows the optomechanical properties to be designed and optimized. Several designs are presented with mechanical frequency ∼ 1-10 GHz, optical Q-factor Qo > 107, motional masses meff ≈ 100 femtograms, optomechanical coupling length LOM < 5 μm, and clampinig losses that are exponentially suppressed with increasing number of phononic crystal periods (radiation-limited mechanical Q-factor Qm > 107 for total device size less than 30 μm).

© 2009 Optical Society of America

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2009

M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, "Optomechanical Crystals," Nature, DOI:10.1038/nature08524 (2009).
[CrossRef]

I. Favero and K. Karrai, "Optomechanics of deformable optical cavities," Nature Physics 3(4), 201-205 (2009).

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, "Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators," Nat Phys 5(4), 276-280 (2009).
[CrossRef]

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]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, "Optical and mechanical design of a "zipper" photonic crystal optomechanical cavity," Opt. Express 17(5), 3802-3817 (2009).
[CrossRef]

2008

M. W. McCutcheon and M. Loncar, "Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal," Opt. Express 16(23), 136-145 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q Nanocavity with 1D Photonic Gap," Opt. Express 16(15), 905-102 (2008).

Y. Yi, "Geometric effects on thermoelastic damping in MEMS resonators," J. Sound Vibration 309(3-5), 588 -599 (2008).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321(5893), 1172-1176 (2008).
[CrossRef]

R. H. O. III, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, "Microfabricated VHF acoustic crystals and waveguides," Sensors Act. A: Physical 145-146, 87 - 93 (2008).

2007

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics," Opt. Express 15(25), 172-205 (2007).
[CrossRef]

T. Carmon and K. J. Vahala, "Optomechanical Modal Spectroscopy of Optoexcited Vibrations of a Micron-Scale on-Chip Sphere at Greater than 1 GHz," Phys. Rev. Lett. 98, 123901 (2007).

2006

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-Sensitivity Optical Monitoring of a Micromechanical Resonator with a Quantum-Limited Optomechanical Sensor," Phys. Rev. Lett. 97, 133601 (2006).
[CrossRef]

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef]

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444, 71-73 (2006).
[CrossRef]

D. Kleckner and D. Bouwmeester, "Sub-kelvin optical cooling of a micromechanical resonator," Nature 444, 75-78 (2006).
[CrossRef]

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, "Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction," Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, "Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance," Appl. Phys. Lett. 89, 171121 (2006).
[CrossRef]

M. Maldovan and E. Thomas, "Simultaneous complete elastic and electromagnetic band gaps in periodic structures," Appl. Phys. B 83(4), 595-600 (2006).
[CrossRef]

2005

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

C. Sauvan, P. Lalanne, and J. P. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef]

2003

O. Painter, K. Srinivasan, and P. E. Barclay, "A Wannier-like equation for photon states of locally perturbed photonic crystals," Phys. Rev. B 68, 035,214 (2003).

A. Duwel, J. Gorman, M. Weinstein, J. Borenstein, and P. Ward, "Experimental study of thermoelastic damping in MEMS gyros," Sensors Actuator. A 103(1-2), 70 - 75 (2003).
[CrossRef]

2002

W. Fon, K. C. Schwab, J. M. Worlock, and M. L. Roukes, "Phonon scattering mechanisms in suspended nanostructures from 4 to 40 K," Phys. Rev. B 66(4) (2002).
[CrossRef]

V. Braginsky and S. P. Vyachanin, "Low quantum noise tranquilizer for Fabry Perot interferometer," Phys. Lett. A 293(5-6), 228-234 (2002).
[CrossRef]

B. H. Houston, D. M. Photiadis, M. H. Marcus, J. A. Bucaro, X. Liu, and J. F. Vignola, "Thermoelastic loss in microscale oscillators," Appl. Phys. Lett. 80(7), 1300-1302 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65(6), 066611 (2002).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10(15), 670-684 (2002).

2001

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287(5-6), 331 - 338 (2001).
[CrossRef]

2000

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

1999

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1824 (1999).
[CrossRef]

M. Pinard and Y. Hadjar and A. Heidmann, "Effective mass in quantum effects of radiation pressure," Eur. Phys. J. D 7, 107-116 (1999).

I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. M¨uller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Phys. Rev. A 59(2), 1038-1044 (1999).
[CrossRef]

1998

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, "Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders," Phys. Rev. Lett. 80(24), 5325-5328 (1998).
[CrossRef]

W. M. Robertson and J . F. R . III, "Measurement of acoustic stop bands in two-dimensional periodic scattering arrays," J. Acoustical Soc. Am. 104(2), 694-699 (1998).
[CrossRef]

F. R. Montero de Espinosa, E. Jimenez, and M. Torres, "Ultrasonic Band Gap in a Periodic Two-Dimensional Composite," Phys. Rev. Lett. 80(6), 1208-1211 (1998).
[CrossRef]

1997

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, "Photonic-Bandgap microcavities in optical waveguides," Nature 390, 143-145 (1997).
[CrossRef]

1993

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]

1985

1983

A. Dorsel, J. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical Bistability and Mirror Confinement Induced by Radiation Pressure," Phys. Rev. Lett. 51, 1550-1553 (1983).
[CrossRef]

1940

T. A. Read, "The Internal Friction of Single Metal Crystals," Phys. Rev. 58(4) (1940).
[CrossRef]

1937

L. Landau and G. Rumer, "On the absorption of sound in solids," Phys. Zeit. Sowjet.  11(18), (1937).

Akahane, Y.

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

Arcizet, O.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444, 71-73 (2006).
[CrossRef]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-Sensitivity Optical Monitoring of a Micromechanical Resonator with a Quantum-Limited Optomechanical Sensor," Phys. Rev. Lett. 97, 133601 (2006).
[CrossRef]

Asano, T.

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

Aspelmeyer, M.

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O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-Sensitivity Optical Monitoring of a Micromechanical Resonator with a Quantum-Limited Optomechanical Sensor," Phys. Rev. Lett. 97, 133601 (2006).
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B. H. Houston, D. M. Photiadis, M. H. Marcus, J. A. Bucaro, X. Liu, and J. F. Vignola, "Thermoelastic loss in microscale oscillators," Appl. Phys. Lett. 80(7), 1300-1302 (2002).
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M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, "Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators," Nat Phys 5(4), 276-280 (2009).
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O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1824 (1999).
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O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1824 (1999).
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P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, "Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance," Appl. Phys. Lett. 89, 171121 (2006).
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B. H. Houston, D. M. Photiadis, M. H. Marcus, J. A. Bucaro, X. Liu, and J. F. Vignola, "Thermoelastic loss in microscale oscillators," Appl. Phys. Lett. 80(7), 1300-1302 (2002).
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P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, "Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance," Appl. Phys. Lett. 89, 171121 (2006).
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Pinard, L.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-Sensitivity Optical Monitoring of a Micromechanical Resonator with a Quantum-Limited Optomechanical Sensor," Phys. Rev. Lett. 97, 133601 (2006).
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O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-Sensitivity Optical Monitoring of a Micromechanical Resonator with a Quantum-Limited Optomechanical Sensor," Phys. Rev. Lett. 97, 133601 (2006).
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O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444, 71-73 (2006).
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W. M. Robertson and J . F. R . III, "Measurement of acoustic stop bands in two-dimensional periodic scattering arrays," J. Acoustical Soc. Am. 104(2), 694-699 (1998).
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P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, "Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance," Appl. Phys. Lett. 89, 171121 (2006).
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T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95(3), 033901 (2005).
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W. Fon, K. C. Schwab, J. M. Worlock, and M. L. Roukes, "Phonon scattering mechanisms in suspended nanostructures from 4 to 40 K," Phys. Rev. B 66(4) (2002).
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O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-Sensitivity Optical Monitoring of a Micromechanical Resonator with a Quantum-Limited Optomechanical Sensor," Phys. Rev. Lett. 97, 133601 (2006).
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J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, "Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders," Phys. Rev. Lett. 80(24), 5325-5328 (1998).
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M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, "Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators," Nat Phys 5(4), 276-280 (2009).
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Sanchez-Dehesa, J.

J. V. Sanchez-Perez, D. Caballero, R. Martinez-Sala, C. Rubio, J. Sanchez-Dehesa, F. Meseguer, J. Llinares, and F. Galvez, "Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders," Phys. Rev. Lett. 80(24), 5325-5328 (1998).
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T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95(3), 033901 (2005).
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O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1824 (1999).
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I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. M¨uller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Phys. Rev. A 59(2), 1038-1044 (1999).
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A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, "Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction," Phys. Rev. Lett. 97, 243905 (2006).
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S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
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W. Fon, K. C. Schwab, J. M. Worlock, and M. L. Roukes, "Phonon scattering mechanisms in suspended nanostructures from 4 to 40 K," Phys. Rev. B 66(4) (2002).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65(6), 066611 (2002).
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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, "Photonic-Bandgap microcavities in optical waveguides," Nature 390, 143-145 (1997).
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B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Materials 4, 207-210 (2005).
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O. Painter, K. Srinivasan, and P. E. Barclay, "A Wannier-like equation for photon states of locally perturbed photonic crystals," Phys. Rev. B 68, 035,214 (2003).

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10(15), 670-684 (2002).

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, "Photonic-Bandgap microcavities in optical waveguides," Nature 390, 143-145 (1997).
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I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. M¨uller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Phys. Rev. A 59(2), 1038-1044 (1999).
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V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287(5-6), 331 - 338 (2001).
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M. Notomi, E. Kuramochi, and H. Taniyama, "Ultrahigh-Q Nanocavity with 1D Photonic Gap," Opt. Express 16(15), 905-102 (2008).

Thoen, E. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, "Photonic-Bandgap microcavities in optical waveguides," Nature 390, 143-145 (1997).
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M. Maldovan and E. Thomas, "Simultaneous complete elastic and electromagnetic band gaps in periodic structures," Appl. Phys. B 83(4), 595-600 (2006).
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I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. M¨uller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Phys. Rev. A 59(2), 1038-1044 (1999).
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F. R. Montero de Espinosa, E. Jimenez, and M. Torres, "Ultrasonic Band Gap in a Periodic Two-Dimensional Composite," Phys. Rev. Lett. 80(6), 1208-1211 (1998).
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R. H. O. III, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, "Microfabricated VHF acoustic crystals and waveguides," Sensors Act. A: Physical 145-146, 87 - 93 (2008).

Vahala, K. J.

M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, "Optomechanical Crystals," Nature, DOI:10.1038/nature08524 (2009).
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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).
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T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321(5893), 1172-1176 (2008).
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T. Carmon and K. J. Vahala, "Optomechanical Modal Spectroscopy of Optoexcited Vibrations of a Micron-Scale on-Chip Sphere at Greater than 1 GHz," Phys. Rev. Lett. 98, 123901 (2007).

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics," Opt. Express 15(25), 172-205 (2007).
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A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, "Radiation Pressure Cooling of a Micromechanical Oscillator Using Dynamical Backaction," Phys. Rev. Lett. 97, 243905 (2006).
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T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95(3), 033901 (2005).
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Velha, P.

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, "Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance," Appl. Phys. Lett. 89, 171121 (2006).
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Vignes, E.

P. Meystre, E. M. Wright, J. D. McCullen, and E. Vignes, "Theory of radiation-pressure-driven interferometers," J. Opt. Soc. Am. B 2(11), 1830-1840 (1985).
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A. Dorsel, J. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical Bistability and Mirror Confinement Induced by Radiation Pressure," Phys. Rev. Lett. 51, 1550-1553 (1983).
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Vignola, J. F.

B. H. Houston, D. M. Photiadis, M. H. Marcus, J. A. Bucaro, X. Liu, and J. F. Vignola, "Thermoelastic loss in microscale oscillators," Appl. Phys. Lett. 80(7), 1300-1302 (2002).
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J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, "Photonic-Bandgap microcavities in optical waveguides," Nature 390, 143-145 (1997).
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V. Braginsky and S. P. Vyachanin, "Low quantum noise tranquilizer for Fabry Perot interferometer," Phys. Lett. A 293(5-6), 228-234 (2002).
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V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287(5-6), 331 - 338 (2001).
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A. Dorsel, J. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical Bistability and Mirror Confinement Induced by Radiation Pressure," Phys. Rev. Lett. 51, 1550-1553 (1983).
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S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65(6), 066611 (2002).
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Worlock, J. M.

W. Fon, K. C. Schwab, J. M. Worlock, and M. L. Roukes, "Phonon scattering mechanisms in suspended nanostructures from 4 to 40 K," Phys. Rev. B 66(4) (2002).
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Wright, E. M.

Yariv, A.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1824 (1999).
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Y. Yi, "Geometric effects on thermoelastic damping in MEMS resonators," J. Sound Vibration 309(3-5), 588 -599 (2008).
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Zeilinger, A.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef]

Appl. Phys. B

M. Maldovan and E. Thomas, "Simultaneous complete elastic and electromagnetic band gaps in periodic structures," Appl. Phys. B 83(4), 595-600 (2006).
[CrossRef]

Appl. Phys. Lett.

B. H. Houston, D. M. Photiadis, M. H. Marcus, J. A. Bucaro, X. Liu, and J. F. Vignola, "Thermoelastic loss in microscale oscillators," Appl. Phys. Lett. 80(7), 1300-1302 (2002).
[CrossRef]

P. Velha, J. C. Rodier, P. Lalanne, J. D. Hugonin, D. Peyrade, E. Picard, T. Charvolin, and E. Hadji, "Ultracompact silicon-on-insulator ridge-waveguide mirrors with high reflectance," Appl. Phys. Lett. 89, 171121 (2006).
[CrossRef]

Eur. Phys. J. D

M. Pinard and Y. Hadjar and A. Heidmann, "Effective mass in quantum effects of radiation pressure," Eur. Phys. J. D 7, 107-116 (1999).

J. Acoustical Soc. Am.

W. M. Robertson and J . F. R . III, "Measurement of acoustic stop bands in two-dimensional periodic scattering arrays," J. Acoustical Soc. Am. 104(2), 694-699 (1998).
[CrossRef]

J. Opt. Soc. Am. B

J. Sound Vibration

Y. Yi, "Geometric effects on thermoelastic damping in MEMS resonators," J. Sound Vibration 309(3-5), 588 -599 (2008).
[CrossRef]

Nat Phys

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, "Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators," Nat Phys 5(4), 276-280 (2009).
[CrossRef]

Nat. Materials

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

Nature

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MIT Photonic Bands (MPB) is a free software package for the solution of the electromagnetic eigenmodes of periodic structures. MPB has been developed at MIT, http://ab-initio.mit.edu/wiki/index.php/MPB.

COMSOL is a multiphysics software package for performing finite-element-method (FEM) simulations. See COMSOL AB, http://www.comsol.com/We use the COMSOL multiphysics software package to perform both optical and mechanical numerical simulations of the optomechanical crystal systems.

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