Abstract

Cavity opto-mechanics exploits optical forces acting on mechanical structures. Many opto-mechanics demonstrations either require extensive alignment of optical components for probing and measurement, which limits the number of opto-mechanical devices on-chip; or the approaches limit the ability to control the opto-mechanical parameters independently. In this work, we propose an opto-mechanical architecture incorporating a waveguide-DBR microcavity coupled to an in-plane micro-bridge resonator, enabling large-scale integration on-chip with the ability to individually tune the optical and mechanical designs. We experimentally characterize our device and demonstrate mechanical resonance damping and amplification, including the onset of coherent oscillations. The resulting collapse of the resonance linewidth implies a strong increase in effective mechanical quality-factor, which is of interest for high-resolution sensing.

© 2011 OSA

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    [CrossRef] [PubMed]
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  6. J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
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  7. C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004).
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    [CrossRef]
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    [CrossRef]
  37. M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002).
    [CrossRef]
  38. C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995).
    [CrossRef]
  39. M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557 .
    [CrossRef] [PubMed]
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    [CrossRef]

2011

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011).
[CrossRef] [PubMed]

2010

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

2009

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (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]

G. A. Cranch, G. M. H. Flockhart, and C. K. Kirkendall, “High-resolution distributed-feedback fiber laser dc magnetometer based on the Lorentzian force,” Meas. Sci. Technol. 20(3), 034023 (2009).
[CrossRef]

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009).
[CrossRef]

F. Marquardt and S. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

2008

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[CrossRef] [PubMed]

M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “In-plane microelectromechanical resonator with integrated Fabry–Pérot cavity,” Appl. Phys. Lett. 92(8), 081101 (2008).
[CrossRef]

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, “Optical self cooling of a deformable Fabry-Perot cavity in the classical limit,” Phys. Rev. B 78(3), 035309 (2008).
[CrossRef]

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

2007

T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007).
[CrossRef]

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557 .
[CrossRef] [PubMed]

2006

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[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(7115), 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(24), 243905 (2006).
[CrossRef] [PubMed]

2005

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]

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

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-14-5293 .
[PubMed]

2004

C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004).
[CrossRef] [PubMed]

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

N. V. Lavrik, M. J. Sepaniak, and P. G. Datskos, “Cantilever transducers as a platform for chemical and biological sensors,” Rev. Sci. Instrum. 75(7), 2229–2253 (2004).
[CrossRef]

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

2002

M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002).
[CrossRef]

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

2001

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

1996

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996).
[CrossRef]

1995

C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995).
[CrossRef]

1992

F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry,” J. Vac. Sci. Technol. B 10(1), 19–26 (1992).
[CrossRef]

1982

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

Aksyuk, V.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011).
[CrossRef] [PubMed]

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(7115), 71–74 (2006).
[CrossRef] [PubMed]

Arndt, F.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996).
[CrossRef]

Aspelmeyer, M.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

Baets, R.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Baker, C.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

Baker, M. S.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

Bao, M.

M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002).
[CrossRef]

Bass, R.

T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007).
[CrossRef]

Bäuerle, D.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Blaser, F.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Blom, F. R.

F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry,” J. Vac. Sci. Technol. B 10(1), 19–26 (1992).
[CrossRef]

Bogart, G. R.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

Böhm, H. R.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Boos, J. B.

T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007).
[CrossRef]

Bouwstra, S.

F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry,” J. Vac. Sci. Technol. B 10(1), 19–26 (1992).
[CrossRef]

Briant, T.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006).
[CrossRef] [PubMed]

Bucaro, J. A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[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]

Carmon, T.

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] [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]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-14-5293 .
[PubMed]

Carr, D. W.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[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]

Chen, L.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Clews, P. J.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

Cohadon, P.-F.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006).
[CrossRef] [PubMed]

Cole, G. D.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

Cole, J.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

Craighead, H. G.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Cranch, G. A.

G. A. Cranch, G. M. H. Flockhart, and C. K. Kirkendall, “High-resolution distributed-feedback fiber laser dc magnetometer based on the Lorentzian force,” Meas. Sci. Technol. 20(3), 034023 (2009).
[CrossRef]

Czaplewski, D.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Dandridge, A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

Datskos, P. G.

N. V. Lavrik, M. J. Sepaniak, and P. G. Datskos, “Cantilever transducers as a platform for chemical and biological sensors,” Rev. Sci. Instrum. 75(7), 2229–2253 (2004).
[CrossRef]

Davanço, M.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011).
[CrossRef] [PubMed]

De Vlaminck, I.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Del’Haye, P.

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(24), 243905 (2006).
[CrossRef] [PubMed]

Ding, L.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

Ducci, S.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

Ebel, J. L.

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

Eichenfield, M.

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 (2005).
[CrossRef]

Elwenspoek, M.

C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995).
[CrossRef]

F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry,” J. Vac. Sci. Technol. B 10(1), 19–26 (1992).
[CrossRef]

Favero, I.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009).
[CrossRef]

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, “Optical self cooling of a deformable Fabry-Perot cavity in the classical limit,” Phys. Rev. B 78(3), 035309 (2008).
[CrossRef]

Ferraro, M. S.

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557 .
[CrossRef] [PubMed]

Fischer, U.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996).
[CrossRef]

Flockhart, G. M. H.

G. A. Cranch, G. M. H. Flockhart, and C. K. Kirkendall, “High-resolution distributed-feedback fiber laser dc magnetometer based on the Lorentzian force,” Meas. Sci. Technol. 20(3), 034023 (2009).
[CrossRef]

Fluitman, J. H.

C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995).
[CrossRef]

Fluitman, J. H. J.

F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry,” J. Vac. Sci. Technol. B 10(1), 19–26 (1992).
[CrossRef]

Giallorenzi, T. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

Gigan, S.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Girvin, S.

F. Marquardt and S. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

Goetz, P. G.

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

Gondarenko, A.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Gröblacher, S.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

Gui, C.

C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995).
[CrossRef]

Hauser, H.

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

Heidmann, A.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006).
[CrossRef] [PubMed]

Hertzberg, J. B.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Hochberg, M.

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

Ilic, B.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Jachimowicz, A.

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

Karrai, K.

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009).
[CrossRef]

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, “Optical self cooling of a deformable Fabry-Perot cavity in the classical limit,” Phys. Rev. B 78(3), 035309 (2008).
[CrossRef]

C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004).
[CrossRef] [PubMed]

Keplinger, F.

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[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(24), 243905 (2006).
[CrossRef] [PubMed]

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] [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]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-14-5293 .
[PubMed]

Kirkendall, C. K.

G. A. Cranch, G. M. H. Flockhart, and C. K. Kirkendall, “High-resolution distributed-feedback fiber laser dc magnetometer based on the Lorentzian force,” Meas. Sci. Technol. 20(3), 034023 (2009).
[CrossRef]

Kohl, F.

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

Krishnamoorthy, U.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

Kropp, J.-R.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996).
[CrossRef]

Krylov, S.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

Kvasnica, S.

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

Lagae, L.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Langer, G.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Lavrik, N. V.

N. V. Lavrik, M. J. Sepaniak, and P. G. Datskos, “Cantilever transducers as a platform for chemical and biological sensors,” Rev. Sci. Instrum. 75(7), 2229–2253 (2004).
[CrossRef]

Legtenberg, R.

C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995).
[CrossRef]

Lemaitre, A.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

Leo, G.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

Li, M.

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

Lipson, M.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Maes, B.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Mahon, R.

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

Marquardt, F.

F. Marquardt and S. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

McGee, D. J.

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

McGill, R. A.

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

Metzger, C.

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, “Optical self cooling of a deformable Fabry-Perot cavity in the classical limit,” Phys. Rev. B 78(3), 035309 (2008).
[CrossRef]

Metzger, C. H.

C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004).
[CrossRef] [PubMed]

Miao, H.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011).
[CrossRef] [PubMed]

Neuzil, P.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

Newman, H. S.

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

Nooshi, N.

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(24), 243905 (2006).
[CrossRef] [PubMed]

Ober, C.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

Olkhovets, A.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Olsson, R. H.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

Ortlieb, A.

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, “Optical self cooling of a deformable Fabry-Perot cavity in the classical limit,” Phys. Rev. B 78(3), 035309 (2008).
[CrossRef]

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]

Papanicolaou, N. A.

T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007).
[CrossRef]

Parpia, J. M.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Paternostro, M.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Pernice, W. H. P.

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

Petermann, K.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996).
[CrossRef]

Pinard, M.

O. Arcizet, P.-F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006).
[CrossRef] [PubMed]

Priest, R.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

Pruessner, M. W.

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “In-plane microelectromechanical resonator with integrated Fabry–Pérot cavity,” Appl. Phys. Lett. 92(8), 081101 (2008).
[CrossRef]

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557 .
[CrossRef] [PubMed]

Rabinovich, W. S.

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “In-plane microelectromechanical resonator with integrated Fabry–Pérot cavity,” Appl. Phys. Lett. 92(8), 081101 (2008).
[CrossRef]

T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007).
[CrossRef]

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557 .
[CrossRef] [PubMed]

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

Rakher, M. T.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011).
[CrossRef] [PubMed]

Rashleigh, S.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

Roels, J.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Rokhsari, H.

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] [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]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-14-5293 .
[PubMed]

Roukes, M. L.

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

Scherer, A.

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] [PubMed]

Schliesser, A.

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(24), 243905 (2006).
[CrossRef] [PubMed]

Schwab, K. C.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Sekaric, L.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Senaratne, W.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

Senellart, P.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[CrossRef] [PubMed]

Sepaniak, M. J.

N. V. Lavrik, M. J. Sepaniak, and P. G. Datskos, “Cantilever transducers as a platform for chemical and biological sensors,” Rev. Sci. Instrum. 75(7), 2229–2253 (2004).
[CrossRef]

Sigel, G. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

Srinivasan, K.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011).
[CrossRef] [PubMed]

Stepnowski, J. L.

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

Steurer, J.

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

Stievater, T. H.

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “In-plane microelectromechanical resonator with integrated Fabry–Pérot cavity,” Appl. Phys. Lett. 92(8), 081101 (2008).
[CrossRef]

T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007).
[CrossRef]

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, and W. S. Rabinovich, “Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities,” Opt. Express 15(12), 7557–7563 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557 .
[CrossRef] [PubMed]

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

Sun, Y.

M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002).
[CrossRef]

Swiler, T. P.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

Turner, S.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[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. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[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(24), 243905 (2006).
[CrossRef] [PubMed]

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] [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]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express 13(14), 5293–5301 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-14-5293 .
[PubMed]

Van Thourhout, D.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Vanner, M. R.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

Wiederhecker, G. S.

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (2009).
[CrossRef] [PubMed]

Xiong, C.

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

Yang, H.

M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002).
[CrossRef]

Yang, L.

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]

Yin, H.

M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002).
[CrossRef]

Zalalutdinov, M.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Zehnder, A.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

Zeilinger, A.

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[CrossRef] [PubMed]

Zinke, T.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996).
[CrossRef]

Appl. Phys. Lett.

M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “In-plane microelectromechanical resonator with integrated Fabry–Pérot cavity,” Appl. Phys. Lett. 92(8), 081101 (2008).
[CrossRef]

T. H. Stievater, W. S. Rabinovich, N. A. Papanicolaou, R. Bass, and J. B. Boos, “Measured limits of detection based on thermal-mechanical frequency noise in micromechanical sensors,” Appl. Phys. Lett. 90(5), 051114 (2007).
[CrossRef]

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, “Autoparametric optical drive for micromechanical oscillators,” Appl. Phys. Lett. 79(5), 695–697 (2001).
[CrossRef]

T. H. Stievater, W. S. Rabinovich, H. S. Newman, R. Mahon, P. G. Goetz, J. L. Ebel, and D. J. McGee, “Measurement of thermal-mechanical noise in microelectromechanical systems,” Appl. Phys. Lett. 81(10), 1779–1781 (2002).
[CrossRef]

IEEE J. Quantum Electron.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. Cole, S. Rashleigh, and R. Priest, “Optical fiber sensor technology,” IEEE J. Quantum Electron. 18(4), 626–665 (1982).
[CrossRef]

IEEE Photon. Technol. Lett.

U. Fischer, T. Zinke, J.-R. Kropp, F. Arndt, and K. Petermann, “0.1 dB/cm waveguide losses in single-mode SOI rib waveguides,” IEEE Photon. Technol. Lett. 8(5), 647–648 (1996).
[CrossRef]

J. Appl. Phys.

B. Ilic, H. G. Craighead, S. Krylov, W. Senaratne, C. Ober, and P. Neuzil, “Attogram detection using nanoelectromechanical oscillators,” J. Appl. Phys. 95(7), 3694–3703 (2004).
[CrossRef]

J. Micromech. Microeng.

M. Bao, H. Yang, H. Yin, and Y. Sun, “Energy transfer model for squeeze-film air damping in low vacuum,” J. Micromech. Microeng. 12(3), 341–346 (2002).
[CrossRef]

C. Gui, R. Legtenberg, M. Elwenspoek, and J. H. Fluitman, “Q-factor dependence of one-port encapsulated polysilicon resonator on reactive sealing pressure,” J. Micromech. Microeng. 5(2), 183–185 (1995).
[CrossRef]

J. Vac. Sci. Technol. B

F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry,” J. Vac. Sci. Technol. B 10(1), 19–26 (1992).
[CrossRef]

Lab Chip

M. W. Pruessner, T. H. Stievater, M. S. Ferraro, W. S. Rabinovich, J. L. Stepnowski, and R. A. McGill, “Waveguide micro-opto-electro-mechanical resonant chemical sensors,” Lab Chip 10(6), 762–768 (2010).
[CrossRef] [PubMed]

Meas. Sci. Technol.

G. A. Cranch, G. M. H. Flockhart, and C. K. Kirkendall, “High-resolution distributed-feedback fiber laser dc magnetometer based on the Lorentzian force,” Meas. Sci. Technol. 20(3), 034023 (2009).
[CrossRef]

Nano Lett.

K. Srinivasan, H. Miao, M. T. Rakher, M. Davanço, and V. Aksyuk, “Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator,” Nano Lett. 11(2), 791–797 (2011).
[CrossRef] [PubMed]

Nat. Nanotechnol.

J. Roels, I. De Vlaminck, L. Lagae, B. Maes, D. Van Thourhout, and R. Baets, “Tunable optical forces between nanophotonic waveguides,” Nat. Nanotechnol. 4(8), 510–513 (2009).
[CrossRef] [PubMed]

Nat. Photonics

I. Favero and K. Karrai, “Optomechanics of deformable optical cavities,” Nat. Photonics 3(4), 201–205 (2009).
[CrossRef]

M. Li, W. H. P. Pernice, and H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves,” Nat. Photonics 3(8), 464–468 (2009).
[CrossRef]

Nat. Phys.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold microoptomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5(7), 485–488 (2009).
[CrossRef]

Nature

G. S. Wiederhecker, L. Chen, A. Gondarenko, and M. Lipson, “Controlling photonic structures using optical forces,” Nature 462(7273), 633–636 (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]

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(7221), 480–484 (2008).
[CrossRef] [PubMed]

C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004).
[CrossRef] [PubMed]

S. Gigan, H. R. Böhm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
[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(7115), 71–74 (2006).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, “Optical self cooling of a deformable Fabry-Perot cavity in the classical limit,” Phys. Rev. B 78(3), 035309 (2008).
[CrossRef]

Phys. Rev. Lett.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “High frequency GaAs nano-optomechanical disk resonator,” Phys. Rev. Lett. 105(26), 263903 (2010).
[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]

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(24), 243905 (2006).
[CrossRef] [PubMed]

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] [PubMed]

Physics

F. Marquardt and S. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

Rev. Sci. Instrum.

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

N. V. Lavrik, M. J. Sepaniak, and P. G. Datskos, “Cantilever transducers as a platform for chemical and biological sensors,” Rev. Sci. Instrum. 75(7), 2229–2253 (2004).
[CrossRef]

Science

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[CrossRef] [PubMed]

Sens. Actuators A Phys.

U. Krishnamoorthy, R. H. Olsson, G. R. Bogart, M. S. Baker, D. W. Carr, T. P. Swiler, and P. J. Clews, “In-plane MEMS-based nano-g accelerometer with sub-wavelength optical resonant sensor,” Sens. Actuators A Phys. 145–146, 283–290 (2008).
[CrossRef]

F. Keplinger, S. Kvasnica, A. Jachimowicz, F. Kohl, J. Steurer, and H. Hauser, “Lorentz force based magnetic field sensor with optical readout,” Sens. Actuators A Phys. 110(1-3), 112–118 (2004).
[CrossRef]

Other

D. F. Edwards, Handbook of Optical Constants of Solids (Academic Press, 1985), Chapter: Silicon (Si), p. 547.

http://www.ioffe.ru/SVA/NSM/Semicond/Si/mechanic.html (accessed on November 23, 2010).

M. W. Pruessner, J. B. Khurgin, T. H. Stievater, and W. S. Rabinovich, “an optically pumped phonon laser in a silicon micromechanical oscillator,” Conf. on Lasers and Electro-Optics (CLEO), May 1–6, 2011, Baltimore, MD. Technical Digest (CD) (Optical Society of America, 2011), paper QWI3. http://www.opticsinfobase.org/abstract.cfm?URI=QELS-2011-QWI3 .

P. Yeh, Optical Waves in Layered Media, B.E. Saleh, ed., (Wiley, 1998), Chapter 5.

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Figures (9)

Fig. 1
Fig. 1

Integrated waveguide-DBR microcavity opto-mechanical system. (a) Schematic showing optical waveguide, Fabry-Perot cavity consisting of one fixed and a second movable distributed Bragg reflector (DBR), a suspended micro-mechanical bridge resonator with spring constant KSpring, air gaps surrounding the movable DBR, and direction of optical forces (F-pt: photothermal pressure, F-rp: radiation pressure); the in-plane vibration of the movable DBR mirror modulates the Fabry-Perot cavity transmittance (out-of-plane beam motion can generally not be read out). (b) Fabricated silicon-on-insulator coupled opto-mechanical cavity with waveguide Fabry-Perot (red) and silicon microbridge mechanical resonator (green).

Fig. 2
Fig. 2

Transfer matrix calculation of cavity optical field. (a) Cross-section of DBR mirrors and optical cavity showing calculated electric field squared profile on-resonance. (b) Calculated power flow, where Popt. is the incident power on the input DBR, Pcav. is the cavity power, and PDBR. is the power in the Nth- silicon slab of the DBR. The βN-factors indicate the power in each DBR region relative to Pcav. The absorbed power in each silicon region N is found from the difference between the power flow into region N and the flow out of that region, summed for both forward and backward power flows.

Fig. 3
Fig. 3

Optical manipulation of a micro-mechanical spring. (a) Finite-element method simulation of radiation and photothermal pressure and resulting beam bending; the simulated images clearly show the opposing beam bending. (b) Calculated optical force modification of effective micro-mechanical spring constant (normalized by Keff) as a function of laser detuning for Popt = 370 μW. Radiation pressure and photothermal forces have opposite effect on Kopt. The solid lines in (b) are for the Fabry-Perot cavity only; the dashed lines include the effect of spurious cavities formed between the high reflectivity DBR mirrors and the cleaved waveguide facets at the sample input/output (see Fig. 4b inset).

Fig. 4
Fig. 4

(a) Experimental setup. (b) Measured optical spectrum; inset: detail of resonance near λ0 = 1593.75 nm and Lorentzian fit; the high frequency oscillations (0.2-0.3 nm spacing) are due to reflections from the cleaved end-facets of the input/output waveguides. (c) Measured mechanical resonance for the fundamental in-plane resonance mode (M = 0) for red and blue detuned laser (Δλ =+0.38 nm [λ = 1594.13 nm] and Δλ=−0.34 nm [1593.41 nm], respectively, both at Popt = 590 μW with effective QM ranging from 4.3×103 to >1×105; insets: detail of mechanical resonance for red (ν=101,139 Hz) and blue detuning (ν = 101,176 Hz) with Lorentzian fit. The displacement amplitude is ΔzRMS≈4.0 nm in (c) (red curve, Δλ=+0.38 nm).

Fig. 5
Fig. 5

Optical tuning of resonant frequency and damping. (a) Measured resonant frequency shift (ν-ν0) vs. detuning and theoretical shift. (b) Measured mechanical resonance width (Γ) vs. cavity detuning and theoretical linewidth. All measurements were performed at Popt = 370 μW. Frequency tuning is dominated by radiation pressure, while the linewidth Γ is determined entirely by photothermal forces. The vertical lines at Δλ = −0.34 nm and + 0.38 nm (Δλ = −0.33 nm and + 0.34 nm) indicate the detuning for power dependent measurements (theory) in Fig. 6a, 6b, and 6c. The model includes the effect of the sample input/output waveguide facets. The scattering in Fig. 5b for Δλ<0 results from the reduced oscillation amplitude due to opto-mechanical damping for blue-detuned wavelengths. The damped oscillations result in a lower signal-to-noise ratio and noisier Γ data for Δλ<0.

Fig. 6
Fig. 6

Laser power dependent tuning of micro-mechanical resonators (M = 0). (a) Measured and theoretical resonance shift vs. Popt for red- (Δλ=+0.38 nm) and blue- (Δλ = −0.34 nm) detuned laser. (b) Measured and theoretical mechanical resonance linewidth (Γ) for red- and blue-detuning; the vertical lines in (a,b) correspond to the power used in the detuning measurements in Fig. 5a and 5b. The shaded area indicates the measurement 1 Hz resolution limit of the electronic spectrum analyzer. (c) Extracted vibration power for red-detuning showing clear onset of coherent oscillations and sharp increase in amplitude as Γ goes to zero; inset: resonance spectra showing linewidth narrowing for increasing laser power. (d) Vibration power for device 2 with a similar mechanical design, but a higher finesse resulting in lower Pth; inset: resonance spectra at powers below and above threshold. For (c,d) the lines are linear fits to the pre-threshold and post-threshold data, respectively. The resonance frequency for device 1 in (c) is ν0≈101,150 Hz; for device 2 in (d) it is ν0≈101,560 Hz.

Fig. A2
Fig. A2

(a) Illustration of localized DBR heating due to absorption. The asymmetric heat load implies a thermal expansion such that the beam bends in a direction that shortens the cavity length. (b) Calculated temperature change at the heated DBR vs. time following a 1 μW heat impulse at t = 0. The DBR moves towards the optical cavity in response to this heat load.

Fig. A3
Fig. A3

Simulation and measurement of mechanical resonance modes. (a) Finite-element-method simulation of first four in-plane mechanical resonances; modes M = 1 (254.0 kHz) and M = 4 (718.0 kHz) are out-of-plane resonances (not shown). (b) Measured mechanical resonance modes M = 0 (101 kHz) and M = 3 (605 kHz) under vacuum (P<50 mTorr) and ambient conditions (atmosphere); inset: measured pressure dependent mechanical Q-factor for the M = 0 mode showing an inverse pressure relationship (QMechanical = 1/pressure0.96) over the range 20 mTorr – 2 Torr. The wavelength was λ = 1593.350 nm in (b) and λ = 1593.845 nm (inset).

Fig. A4
Fig. A4

(a) Measured Fabry-Perot optical spectrum for device 2 in Fig. 6d. The inset shows a detail of the resonance peak at λ0 = 1600.78 nm with Lorentzian fit to obtain δλ = 0.32 nm, FSR = 120 nm, Qopt = 5,000 and finesse f = 380. (b) Measured linewidth narrowing and collapse for device 2. The shaded area indicates the 1 Hz measurement resolution of our electronic spectrum analyzer, implying that measurements below 1 Hz can be interpreted as Γ → 0.

Tables (4)

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Table A1 Transfer matrix input parameters.

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Table A2 Transfer matrix output parameters.

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Table A3 Input material parameters for Comsol [35]

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Table A4 Output values from Comsol thermal-mechanical model.

Equations (5)

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F 0 rp [ 2( β 1 β 7 )/c ]( K eff / K p ) P opt,
F 0 pt K eff ( dz / d P abs ) P abs = K eff ( dz / d P abs )[ 2( β 2 β 6 ) α Si d Si ] P opt ,
K opt = F 0 ( f T cav π )( 16 β 1 f 2 Δλ λ 0 FSR ( ( 2Δλ / δλ ) 2 +1 ) 2 ),
ν 2 = ν 0 2 [ 1+ 1 K eff Force(N) K opt(N) 1 ( 2π ν 0 τ opt(N) ) 2 +1 ],
Γ= Γ 0 [ 1 Q M K eff Force(N) K opt(N) 2π ν 0 τ opt(N) ( 2π ν 0 τ opt(N) ) 2 +1 ],

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