Abstract

We present here an optomechanical system fabricated with novel stress management techniques that allow us to suspend an ultrathin defect-free silicon photonic-crystal membrane above a Silicon-on-Insulator (SOI) substrate with a gap that is tunable to below 200 nm. Our devices are able to generate strong attractive and repulsive optical forces over a large surface area with simple in- and out- coupling and feature the strongest repulsive optomechanical coupling in any geometry to date (gOM/2? ? ?65 GHz/nm). The interplay between the optomechanical and photo-thermal-mechanical dynamics is explored, and the latter is used to achieve cooling and amplification of the mechanical mode, demonstrating that our platform is well-suited for potential applications in low-power mass, force, and refractive-index sensing as well as optomechanical accelerometry.

© 2013 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  44. H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Nonlinear micromechanical Casimir oscillator,” Phys. Rev. Lett. 87, 211801 (2001).
    [CrossRef] [PubMed]
  45. H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 293, 607–607 (2001).
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    [CrossRef]
  47. S. J. Rahi, A. W. Rodriguez, T. Emig, R. L. Jaffe, S. G. Johnson, and M. Kardar, “Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders,” Phys. Rev. A 77, 030101 (2008).
    [CrossRef]
  48. J. L. Yang, T. Ono, and M. Esashi, “Surface effects and high quality factors in ultrathin single-crystal silicon cantilevers,” Appl. Phys. Lett. 77, 3860–3862 (2000).
    [CrossRef]
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    [CrossRef]

2012 (6)

A. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat Photonics 6, 768–772 (2012).
[CrossRef]

J. Lee, B. Zhen, S. L. Chua, W. J. Qiu, J. D. Joannopoulos, M. Soljacic, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave Vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
[CrossRef] [PubMed]

E. Iwase, P. C. Hui, D. Woolf, A. W. Rodriguez, S. G. Johnson, F. Capasso, and M. Loncar, “Control of buckling in large micromembranes using engineered support structures” J. Micromech. Microeng. 22, 065028 (2012).
[CrossRef]

D. Blocher, A. T. Zehnder, R. H. Rand, and S. Mukerji, “Anchor deformations drive limit cycle oscillations in interferometrically transduced MEMS beams,” Finite. Elem. Anal. Des. 49, 52–57 (2012).
[CrossRef]

P. B. Deotare, I. Bulu, I. W. Frank, Q. M. Quan, Y. N. Zhang, R. Ilic, and M. Loncar, “All optical reconfiguration of optomechanical filters” Nat Commun 3, 846 (2012).
[CrossRef] [PubMed]

J. O. Grepstad, P. Kaspar, O. Solgaard, I. R. Johansen, and A. S. Sudbo, “Photonic-crystal membranes for optical detection of single nanoparticles, designed for biosensor application,” Opt. Express 20, 7954–7965 (2012).
[CrossRef] [PubMed]

2011 (8)

A. W. Rodriguez, F. Capasso, and S. G. Johnson, “The Casimir effect in microstructured geometries,” Nat. Photonics 5, 211–221 (2011).
[CrossRef]

J. L. Arlett, E. B. Myers, and M. L. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol 6, 203–215 (2011).
[CrossRef] [PubMed]

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the Quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[CrossRef] [PubMed]

H. Fu, C. D. Liu, Y. Liu, J. R. Chu, and G. Y. Cao, “Selective photothermal self-excitation of mechanical modes of a micro-cantilever for force microscopy,” Appl. Phys. Lett. 99, 173501 (2011).
[CrossRef]

Y. Y. Gong, A. Rundquist, A. Majumdar, and J. Vuckovic, “Low power resonant optical excitation of an optomechanical cavity,” Opt. Express 19, 1429–1440 (2011).
[CrossRef] [PubMed]

A. W. Rodriguez, F. Capasso, and S. G. Johnson, “Bonding, antibonding and tunable optical forces in asymmetric membranes,” Opt. Express 19, 2225–2241 (2011).
[CrossRef] [PubMed]

M. W. Pruessner, T. H. Stievater, J. B. Khurgin, and W. S. Rabinovich, “Integrated waveguide-DBR microcavity optomechanical system,” Opt. Express 19, 21904–21918 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (8)

Q. Lin, J. Rosenberg, X. S. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
[CrossRef] [PubMed]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
[CrossRef]

M. M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
[CrossRef]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

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

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 79, 033804 (2009).
[CrossRef]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–579 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3, 464–468 (2009).
[CrossRef]

2008 (4)

S. J. Rahi, A. W. Rodriguez, T. Emig, R. L. Jaffe, S. G. Johnson, and M. Kardar, “Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders,” Phys. Rev. A 77, 030101 (2008).
[CrossRef]

X. L. Feng, C. J. White, A. Hajimiri, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 3, 342–346 (2008).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

K. J. Vahala, “Back-action limit of linewidth in an optomechanical oscillator,” Phys Rev A 78, 023832 (2008).
[CrossRef]

2007 (3)

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15, 17172–17205 (2007).
[CrossRef] [PubMed]

B. R. Ilic, S. Krylov, M. Kondratovich, and H. G. Craighead, “Optically actuated nanoelectromechanical oscillators,” IEEE J. Sel. Top. Quantum Electron. 13, 392–399 (2007).
[CrossRef]

P. S. Waggoner and H. G. Craighead, “Micro- and nanomechanical sensors for environmental, chemical, and biological detection,” Lab Chip 7, 1238–1255 (2007).
[CrossRef] [PubMed]

2006 (6)

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[CrossRef]

T. P. Burg, A. R. Mirza, N. Milovic, C. H. Tsau, G. A. Popescu, J. S. Foster, and S. R. Manalis, “Vacuum-packaged suspended microchannel resonant mass sensor for biomolecular detection,” J. Microelectromech S 15, 1466–1476 (2006).
[CrossRef]

Y. T. Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6, 583–586 (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, 71–74 (2006).
[CrossRef] [PubMed]

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]

T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator,” Opt. Express 14, 817–831 (2006).
[CrossRef] [PubMed]

2005 (2)

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators,” Opt. Express 13, 8286–8295 (2005).
[CrossRef] [PubMed]

M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Opt. Lett. 30, 3042–3044 (2005).
[CrossRef] [PubMed]

2004 (1)

C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432, 1002–1005 (2004).
[CrossRef] [PubMed]

2003 (1)

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett. 82, 2697–2699 (2003).
[CrossRef]

2002 (1)

S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

2001 (2)

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Nonlinear micromechanical Casimir oscillator,” Phys. Rev. Lett. 87, 211801 (2001).
[CrossRef] [PubMed]

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 293, 607–607 (2001).

2000 (1)

J. L. Yang, T. Ono, and M. Esashi, “Surface effects and high quality factors in ultrathin single-crystal silicon cantilevers,” Appl. Phys. Lett. 77, 3860–3862 (2000).
[CrossRef]

1998 (1)

E. R. I. Abraham and E. A. Cornell, “Teflon feedthrough for coupling optical fibers into ultrahigh vacuum systems,” Appl. Optics 37, 1762–1763 (1998).
[CrossRef]

1989 (1)

D. Rugar, H. J. Mamin, and P. Guethner, “Improved Fiber-Optic Interferometer for Atomic Force Microscopy,” Appl. Phys. Lett. 55, 2588–2590 (1989).
[CrossRef]

Abraham, E. R. I.

E. R. I. Abraham and E. A. Cornell, “Teflon feedthrough for coupling optical fibers into ultrahigh vacuum systems,” Appl. Optics 37, 1762–1763 (1998).
[CrossRef]

Aksyuk, V. A.

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 293, 607–607 (2001).

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Nonlinear micromechanical Casimir oscillator,” Phys. Rev. Lett. 87, 211801 (2001).
[CrossRef] [PubMed]

Alegre, T. P. M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[CrossRef] [PubMed]

Anetsberger, G.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
[CrossRef]

Arcizet, O.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the Quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
[CrossRef]

O. Arcizet, P.F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[CrossRef] [PubMed]

Arlett, J. L.

J. L. Arlett, E. B. Myers, and M. L. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol 6, 203–215 (2011).
[CrossRef] [PubMed]

Aspelmeyer, M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[CrossRef] [PubMed]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 79, 033804 (2009).
[CrossRef]

Baehr-Jones, T.

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

Bishop, D. J.

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Nonlinear micromechanical Casimir oscillator,” Phys. Rev. Lett. 87, 211801 (2001).
[CrossRef] [PubMed]

H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, and F. Capasso, “Quantum mechanical actuation of microelectromechanical systems by the Casimir force,” Science 293, 607–607 (2001).

Blasius, T. D.

A. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat Photonics 6, 768–772 (2012).
[CrossRef]

Blocher, D.

D. Blocher, A. T. Zehnder, R. H. Rand, and S. Mukerji, “Anchor deformations drive limit cycle oscillations in interferometrically transduced MEMS beams,” Finite. Elem. Anal. Des. 49, 52–57 (2012).
[CrossRef]

Borselli, M.

T. J. Johnson, M. Borselli, and O. Painter, “Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator,” Opt. Express 14, 817–831 (2006).
[CrossRef] [PubMed]

M. Borselli, T. J. Johnson, and O. Painter, “Measuring the role of surface chemistry in silicon microphotonics,” Appl. Phys. Lett. 88, 131114 (2006).
[CrossRef]

Briant, T.

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T. P. Burg, A. R. Mirza, N. Milovic, C. H. Tsau, G. A. Popescu, J. S. Foster, and S. R. Manalis, “Vacuum-packaged suspended microchannel resonant mass sensor for biomolecular detection,” J. Microelectromech S 15, 1466–1476 (2006).
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D. Blocher, A. T. Zehnder, R. H. Rand, and S. Mukerji, “Anchor deformations drive limit cycle oscillations in interferometrically transduced MEMS beams,” Finite. Elem. Anal. Des. 49, 52–57 (2012).
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M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–579 (2009).
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M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3, 464–468 (2009).
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M. M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
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M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
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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, 71–74 (2006).
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Q. Lin, J. Rosenberg, X. S. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
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J. L. Arlett, E. B. Myers, and M. L. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol 6, 203–215 (2011).
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X. L. Feng, C. J. White, A. Hajimiri, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 3, 342–346 (2008).
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R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the Quantum ground state,” Phys. Rev. A 83, 063835 (2011).
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J. Lee, B. Zhen, S. L. Chua, W. J. Qiu, J. D. Joannopoulos, M. Soljacic, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave Vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
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J. O. Grepstad, P. Kaspar, O. Solgaard, I. R. Johansen, and A. S. Sudbo, “Photonic-crystal membranes for optical detection of single nanoparticles, designed for biosensor application,” Opt. Express 20, 7954–7965 (2012).
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J. Lee, B. Zhen, S. L. Chua, W. J. Qiu, J. D. Joannopoulos, M. Soljacic, and O. Shapira, “Observation and differentiation of unique high-Q optical resonances near zero wave Vector in macroscopic photonic crystal slabs,” Phys. Rev. Lett. 109, 067401 (2012).
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M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3, 464–468 (2009).
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M. M. Li, W. H. P. Pernice, and H. X. Tang, “Reactive cavity optical force on microdisk-coupled nanomechanical beam waveguides,” Phys. Rev. Lett. 103, 223901 (2009).
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M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
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C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 79, 033804 (2009).
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T. P. Burg, A. R. Mirza, N. Milovic, C. H. Tsau, G. A. Popescu, J. S. Foster, and S. R. Manalis, “Vacuum-packaged suspended microchannel resonant mass sensor for biomolecular detection,” J. Microelectromech S 15, 1466–1476 (2006).
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G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
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Q. Lin, J. Rosenberg, X. S. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 103601 (2009).
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M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–579 (2009).
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C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 79, 033804 (2009).
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G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
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R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the Quantum ground state,” Phys. Rev. A 83, 063835 (2011).
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X. L. Feng, C. J. White, A. Hajimiri, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 3, 342–346 (2008).
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A. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat Photonics 6, 768–772 (2012).
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M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
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Y. T. Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6, 583–586 (2006).
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J. L. Yang, T. Ono, and M. Esashi, “Surface effects and high quality factors in ultrathin single-crystal silicon cantilevers,” Appl. Phys. Lett. 77, 3860–3862 (2000).
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D. Blocher, A. T. Zehnder, R. H. Rand, and S. Mukerji, “Anchor deformations drive limit cycle oscillations in interferometrically transduced MEMS beams,” Finite. Elem. Anal. Des. 49, 52–57 (2012).
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Y. T. Y. T. Yang, C. Callegari, X. L. Feng, K. L. Ekinci, and M. L. Roukes, “Zeptogram-scale nanomechanical mass sensing,” Nano Lett. 6, 583–586 (2006).
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P. B. Deotare, I. Bulu, I. W. Frank, Q. M. Quan, Y. N. Zhang, R. Ilic, and M. Loncar, “All optical reconfiguration of optomechanical filters” Nat Commun 3, 846 (2012).
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Nat Photonics (1)

A. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat Photonics 6, 768–772 (2012).
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Nat. Nanotechnol (1)

J. L. Arlett, E. B. Myers, and M. L. Roukes, “Comparative advantages of mechanical biosensors,” Nat. Nanotechnol 6, 203–215 (2011).
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Nat. Nanotechnol. (1)

X. L. Feng, C. J. White, A. Hajimiri, and M. L. Roukes, “A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator,” Nat. Nanotechnol. 3, 342–346 (2008).
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Nat. Photonics (2)

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3, 464–468 (2009).
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A. W. Rodriguez, F. Capasso, and S. G. Johnson, “The Casimir effect in microstructured geometries,” Nat. Photonics 5, 211–221 (2011).
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G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5, 909–914 (2009).
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Nature (7)

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462, 633–636 (2009).
[CrossRef] [PubMed]

M. Li, W. H. P. Pernice, C. Xiong, T. Baehr-Jones, M. Hochberg, and H. X. Tang, “Harnessing optical forces in integrated photonic circuits,” Nature 456, 480–484 (2008).
[CrossRef] [PubMed]

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–579 (2009).
[CrossRef] [PubMed]

C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432, 1002–1005 (2004).
[CrossRef] [PubMed]

O. Arcizet, P.F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444, 71–74 (2006).
[CrossRef] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
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Opt. Express (2)

M. L. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators,” Opt. Express 13, 8286–8295 (2005).
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Opt. Express (6)

Opt. Lett. (1)

Phys Rev A (1)

K. J. Vahala, “Back-action limit of linewidth in an optomechanical oscillator,” Phys Rev A 78, 023832 (2008).
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Phys. Rev. A (1)

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 79, 033804 (2009).
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Phys. Rev. A (2)

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Other (3)

Near-field thermal heat-transfer will modify ?t by a small amount, though we ignore this small effect in our analysis here for simplicity.

H.A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

The expresion for the force is only strictly true when the (complex) wavevector is constant under translation, though it can still be used when the change in optical Q is small over the distance ds.

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