Abstract

Mass sensing based on mechanical oscillation frequency shift in micro/nano scale mechanical oscillators is a well-known and widely used technique. Piezo-electric, electronic excitation/detection and free-space optical detection are the most common techniques used for monitoring the minute frequency shifts induced by added mass. The advent of optomechanical oscillator (OMO), enabled by strong interaction between circulating optical power and mechanical deformation in high quality factor optical microresonators, has created new possibilities for excitation and interrogation of micro/nanomechanical resonators. In particular, radiation pressure driven optomechanical oscillators (OMOs) are excellent candidates for mass detection/measurement due to their simplicity, sensitivity and all-optical operation. In an OMO, a high quality factor optical mode simultaneously serves as an efficient actuator and a sensitive probe for precise monitoring of the mechanical eigen-frequencies of the cavity structure. Here, we show the narrow linewidth of optomechanical oscillation combined with harmonic optical modulation generated by nonlinear optical transfer function, can result in sub-pg mass sensitivity in large silica microtoroid OMOs. Moreover by carefully studying the impact of mechanical mode selection, device dimensions, mass position and noise mechanisms we explore the performance limits of OMO both as a mass detector and a high resolution mass measurement system. Our analysis shows that femtogram level resolution is within reach even with relatively large OMOs.

© 2013 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  30. S. Dohn, R. Sandberg, W. Svendsen, and A. Boisen, “Enhanced functionality of cantilever based mass sensors using higher modes,” Appl. Phys. Lett.86(23), 233501 (2005).
    [CrossRef]
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    [CrossRef]
  32. T. W. Hansch and B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun.35(3), 441–444 (1980).
    [CrossRef]
  33. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
    [CrossRef]
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    [CrossRef] [PubMed]
  35. K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
    [CrossRef] [PubMed]
  36. B. Ilic, Y. Yang, and H. G. Craighead, “Virus detection using nanoelectromechanical devices,” Appl. Phys. Lett.85(13), 2604–2606 (2004).
    [CrossRef]
  37. R. Sandberg, K. Molhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng.15(12), 2249–2253 (2005).
    [CrossRef]
  38. N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng.20(4), 045023 (2010).
    [CrossRef]

2013 (4)

J. Tamayo, P. M. Kosaka, J. J. Ruz, A. San Paulo, and M. Calleja, “Biosensors based on nanomechanical systems,” Chem. Soc. Rev.42(3), 1287–1311 (2013).
[CrossRef] [PubMed]

F. Liu and M. Hossein-Zadeh, “Mass Sensing with Optomechanical Oscillation,” IEEE Sensors13(1), 146–147 (2013).
[CrossRef]

F. Liu and M. Hossein-Zadeh, “On the spectrum of the radiation-pressure-driven optomechanical oscillator and its application in sensing,” Opt. Commun.294, 338–343 (2013).
[CrossRef]

G. Bahl, K.-H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat Commun4, 1994 (2013).
[CrossRef] [PubMed]

2012 (2)

2011 (5)

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

A. Cagliani and Z. J. Davis, “Ultrasensitive bulk disk microresonator-based sensor for distributed mass sensing,” J. Micromech. Microeng.21(045016), 1–6 (2011).

S. Tallur, S. Sridaran, and S. A. Bhave, “A monolithic radiation-pressure driven, low phase noise silicon nitride opto-mechanical oscillator,” Opt. Express19(24), 24522–24529 (2011).
[CrossRef] [PubMed]

A. Boisen, S. Dohn, S. S. Keller, S. Schmid, and M. Tenje, “Cantilever-like micromechanical sensors,” Rep. Prog. Phys.74(036101), 1–30 (2011).

M. W. Pruessner, T. H. Stievater, J. B. Khurgin, and W. S. Rabinovich, “Integrated waveguide-DBR microcavity opto-mechanical system,” Opt. Express19(22), 21904–21918 (2011).
[CrossRef] [PubMed]

2010 (4)

M. Li, W. H. P. Pernice, and H. X. Tang, “Ultra-high-frequency nano-optomechanical resonators in slot waveguide ring cavities,” Appl. Phys. Lett.97(18), 183110 (2010).

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 Chip10(6), 762–768 (2010).
[CrossRef] [PubMed]

M. Hossein-Zadeh and K. J. Vahala, “Optomechanical Oscillator on a Silicon Chip”, Invited Paper, J Sel. Top. Quantum Electron. Special Issue on Silicon Photonics16(1), 276–287 (2010).

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng.20(4), 045023 (2010).
[CrossRef]

2009 (1)

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459(7246), 550–555 (2009).
[CrossRef] [PubMed]

2008 (2)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods5(7), 591–596 (2008).
[CrossRef] [PubMed]

A. Schliesser, G. Anetsberger, R. Riviere, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys.10(9), 095015 (2008).
[CrossRef]

2007 (4)

S. Dohn, W. Svendsen, A. Boisen, and O. Hansen, “Mass and position determination of attached particles on cantilever based mass sensors,” Rev. Sci. Instrum.78(10), 103303 (2007).
[CrossRef] [PubMed]

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol.2(2), 114–120 (2007).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity Opto-Mechanics,” Opt. Express15(25), 17172–17205 (2007).
[CrossRef] [PubMed]

P. S. Waggoner and H. G. Craighead, “Micro- and nanomechanical sensors for environmental, chemical, and biological detection,” Lab Chip7(10), 1238–1255 (2007).
[CrossRef] [PubMed]

2006 (4)

Y. Lee, G. Lim, and W. Moon, “A self-excited micro cantilever biosensor actuated by PZT using the mass micro balancing technique,” Sens. Actuators A Phys.130-131, 105–110 (2006).
[CrossRef]

H. Rokhsari, M. Hossein-Zadeh, A. Hajimiri, and K. J. Vahala, “Brownian noise in radiation-pressure-driven micromechanical oscillators,” Appl. Phys. Lett.89(6), 261109 (2006).

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74(2), 023813 (2006).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and Experimental Study of Radiation Pressure-Induced Mechanical Oscillations (Parametric Instability) in Optical Microcavities,” IEEE J. Sel. Top. Quantum Electron.12(1), 96–107 (2006).

2005 (3)

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

S. Dohn, R. Sandberg, W. Svendsen, and A. Boisen, “Enhanced functionality of cantilever based mass sensors using higher modes,” Appl. Phys. Lett.86(23), 233501 (2005).
[CrossRef]

R. Sandberg, K. Molhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng.15(12), 2249–2253 (2005).
[CrossRef]

2004 (2)

B. Ilic, Y. Yang, and H. G. Craighead, “Virus detection using nanoelectromechanical devices,” Appl. Phys. Lett.85(13), 2604–2606 (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]

2003 (2)

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett.82(16), 2697–2699 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

2002 (2)

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

J. W. Yi, W. Y. Shih, and W.-H. Shih, “Effect of length, width, and mode on the mass detection sensitivity of piezoelectric unimorph cantilevers,” J. Appl. Phys.91(3), 1680–1686 (2002).
[CrossRef]

1997 (1)

S. Seel, R. Storz, G. Ruoso, J. Mlynek, and S. Schiller, “Cryogenic Optical Resonators: A New Tool for Laser Frequency Stabilization at the 1 Hz Level,” Phys. Rev. Lett.78(25), 4741–4744 (1997).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

1980 (1)

T. W. Hansch and B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun.35(3), 441–444 (1980).
[CrossRef]

Alves, C. H. F.

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

Anetsberger, G.

A. Schliesser, G. Anetsberger, R. Riviere, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys.10(9), 095015 (2008).
[CrossRef]

Arcamone, J.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng.20(4), 045023 (2010).
[CrossRef]

Arcizet, O.

A. Schliesser, G. Anetsberger, R. Riviere, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys.10(9), 095015 (2008).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods5(7), 591–596 (2008).
[CrossRef] [PubMed]

Bahl, G.

G. Bahl, K.-H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat Commun4, 1994 (2013).
[CrossRef] [PubMed]

Bhave, S. A.

Boisen, A.

A. Boisen, S. Dohn, S. S. Keller, S. Schmid, and M. Tenje, “Cantilever-like micromechanical sensors,” Rep. Prog. Phys.74(036101), 1–30 (2011).

S. Dohn, W. Svendsen, A. Boisen, and O. Hansen, “Mass and position determination of attached particles on cantilever based mass sensors,” Rev. Sci. Instrum.78(10), 103303 (2007).
[CrossRef] [PubMed]

S. Dohn, R. Sandberg, W. Svendsen, and A. Boisen, “Enhanced functionality of cantilever based mass sensors using higher modes,” Appl. Phys. Lett.86(23), 233501 (2005).
[CrossRef]

R. Sandberg, K. Molhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng.15(12), 2249–2253 (2005).
[CrossRef]

Bowen, W. P.

Cagliani, A.

A. Cagliani and Z. J. Davis, “Ultrasensitive bulk disk microresonator-based sensor for distributed mass sensing,” J. Micromech. Microeng.21(045016), 1–6 (2011).

Calleja, M.

J. Tamayo, P. M. Kosaka, J. J. Ruz, A. San Paulo, and M. Calleja, “Biosensors based on nanomechanical systems,” Chem. Soc. Rev.42(3), 1287–1311 (2013).
[CrossRef] [PubMed]

Camacho, R.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Cannata, J. M.

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

Carmon, T.

G. Bahl, K.-H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat Commun4, 1994 (2013).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and Experimental Study of Radiation Pressure-Induced Mechanical Oscillations (Parametric Instability) in Optical Microcavities,” IEEE J. Sel. Top. Quantum Electron.12(1), 96–107 (2006).

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Chen, W. H.

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

Couillaud, B.

T. W. Hansch and B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun.35(3), 441–444 (1980).
[CrossRef]

Craighead, H. G.

P. S. Waggoner and H. G. Craighead, “Micro- and nanomechanical sensors for environmental, chemical, and biological detection,” Lab Chip7(10), 1238–1255 (2007).
[CrossRef] [PubMed]

B. Ilic, Y. Yang, and H. G. Craighead, “Virus detection using nanoelectromechanical devices,” Appl. Phys. Lett.85(13), 2604–2606 (2004).
[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]

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett.82(16), 2697–2699 (2003).
[CrossRef]

Davis, Z. J.

A. Cagliani and Z. J. Davis, “Ultrasensitive bulk disk microresonator-based sensor for distributed mass sensing,” J. Micromech. Microeng.21(045016), 1–6 (2011).

Dohn, S.

A. Boisen, S. Dohn, S. S. Keller, S. Schmid, and M. Tenje, “Cantilever-like micromechanical sensors,” Rep. Prog. Phys.74(036101), 1–30 (2011).

S. Dohn, W. Svendsen, A. Boisen, and O. Hansen, “Mass and position determination of attached particles on cantilever based mass sensors,” Rev. Sci. Instrum.78(10), 103303 (2007).
[CrossRef] [PubMed]

S. Dohn, R. Sandberg, W. Svendsen, and A. Boisen, “Enhanced functionality of cantilever based mass sensors using higher modes,” Appl. Phys. Lett.86(23), 233501 (2005).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

Eichenfield, M.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Fan, X.

G. Bahl, K.-H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat Commun4, 1994 (2013).
[CrossRef] [PubMed]

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 Chip10(6), 762–768 (2010).
[CrossRef] [PubMed]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

Hajimiri, A.

H. Rokhsari, M. Hossein-Zadeh, A. Hajimiri, and K. J. Vahala, “Brownian noise in radiation-pressure-driven micromechanical oscillators,” Appl. Phys. Lett.89(6), 261109 (2006).

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74(2), 023813 (2006).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

Hansch, T. W.

T. W. Hansch and B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun.35(3), 441–444 (1980).
[CrossRef]

Hansen, O.

S. Dohn, W. Svendsen, A. Boisen, and O. Hansen, “Mass and position determination of attached particles on cantilever based mass sensors,” Rev. Sci. Instrum.78(10), 103303 (2007).
[CrossRef] [PubMed]

Hentz, S.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng.20(4), 045023 (2010).
[CrossRef]

Hossein-Zadeh, M.

F. Liu and M. Hossein-Zadeh, “Mass Sensing with Optomechanical Oscillation,” IEEE Sensors13(1), 146–147 (2013).
[CrossRef]

F. Liu and M. Hossein-Zadeh, “On the spectrum of the radiation-pressure-driven optomechanical oscillator and its application in sensing,” Opt. Commun.294, 338–343 (2013).
[CrossRef]

M. Hossein-Zadeh and K. J. Vahala, “Optomechanical Oscillator on a Silicon Chip”, Invited Paper, J Sel. Top. Quantum Electron. Special Issue on Silicon Photonics16(1), 276–287 (2010).

H. Rokhsari, M. Hossein-Zadeh, A. Hajimiri, and K. J. Vahala, “Brownian noise in radiation-pressure-driven micromechanical oscillators,” Appl. Phys. Lett.89(6), 261109 (2006).

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74(2), 023813 (2006).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

Ilic, B.

B. Ilic, Y. Yang, and H. G. Craighead, “Virus detection using nanoelectromechanical devices,” Appl. Phys. Lett.85(13), 2604–2606 (2004).
[CrossRef]

Jiang, W. C.

Kacem, N.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng.20(4), 045023 (2010).
[CrossRef]

Keller, S. S.

A. Boisen, S. Dohn, S. S. Keller, S. Schmid, and M. Tenje, “Cantilever-like micromechanical sensors,” Rep. Prog. Phys.74(036101), 1–30 (2011).

Khurgin, J. B.

Kim, K.-H.

G. Bahl, K.-H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat Commun4, 1994 (2013).
[CrossRef] [PubMed]

Kippenberg, T. J.

A. Schliesser, G. Anetsberger, R. Riviere, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys.10(9), 095015 (2008).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity Opto-Mechanics,” Opt. Express15(25), 17172–17205 (2007).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and Experimental Study of Radiation Pressure-Induced Mechanical Oscillations (Parametric Instability) in Optical Microcavities,” IEEE J. Sel. Top. Quantum Electron.12(1), 96–107 (2006).

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Knittel, J.

Kosaka, P. M.

J. Tamayo, P. M. Kosaka, J. J. Ruz, A. San Paulo, and M. Calleja, “Biosensors based on nanomechanical systems,” Chem. Soc. Rev.42(3), 1287–1311 (2013).
[CrossRef] [PubMed]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

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]

N. V. Lavrik and P. G. Datskos, “Femtogram mass detection using photothermally actuated nanomechanical resonators,” Appl. Phys. Lett.82(16), 2697–2699 (2003).
[CrossRef]

Lee, K. H.

Lee, W.

G. Bahl, K.-H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat Commun4, 1994 (2013).
[CrossRef] [PubMed]

Lee, Y.

Y. Lee, G. Lim, and W. Moon, “A self-excited micro cantilever biosensor actuated by PZT using the mass micro balancing technique,” Sens. Actuators A Phys.130-131, 105–110 (2006).
[CrossRef]

Li, M.

M. Li, W. H. P. Pernice, and H. X. Tang, “Ultra-high-frequency nano-optomechanical resonators in slot waveguide ring cavities,” Appl. Phys. Lett.97(18), 183110 (2010).

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol.2(2), 114–120 (2007).
[CrossRef] [PubMed]

Li, X. X.

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

Lim, G.

Y. Lee, G. Lim, and W. Moon, “A self-excited micro cantilever biosensor actuated by PZT using the mass micro balancing technique,” Sens. Actuators A Phys.130-131, 105–110 (2006).
[CrossRef]

Lin, Q.

Liu, F.

F. Liu and M. Hossein-Zadeh, “On the spectrum of the radiation-pressure-driven optomechanical oscillator and its application in sensing,” Opt. Commun.294, 338–343 (2013).
[CrossRef]

F. Liu and M. Hossein-Zadeh, “Mass Sensing with Optomechanical Oscillation,” IEEE Sensors13(1), 146–147 (2013).
[CrossRef]

Liu, J.

G. Bahl, K.-H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat Commun4, 1994 (2013).
[CrossRef] [PubMed]

Lu, X. Y.

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 Chip10(6), 762–768 (2010).
[CrossRef] [PubMed]

McRae, T. G.

Meyer, R. J.

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

Mlynek, J.

S. Seel, R. Storz, G. Ruoso, J. Mlynek, and S. Schiller, “Cryogenic Optical Resonators: A New Tool for Laser Frequency Stabilization at the 1 Hz Level,” Phys. Rev. Lett.78(25), 4741–4744 (1997).
[CrossRef]

Molhave, K.

R. Sandberg, K. Molhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng.15(12), 2249–2253 (2005).
[CrossRef]

Moon, W.

Y. Lee, G. Lim, and W. Moon, “A self-excited micro cantilever biosensor actuated by PZT using the mass micro balancing technique,” Sens. Actuators A Phys.130-131, 105–110 (2006).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

Painter, O.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459(7246), 550–555 (2009).
[CrossRef] [PubMed]

Perez-Murano, F.

N. Kacem, J. Arcamone, F. Perez-Murano, and S. Hentz, “Dynamic range enhancement of nonlinear nanomechanical resonant cantilevers for highly sensitive NEMS gas/mass sensor applications,” J. Micromech. Microeng.20(4), 045023 (2010).
[CrossRef]

Pernice, W. H. P.

M. Li, W. H. P. Pernice, and H. X. Tang, “Ultra-high-frequency nano-optomechanical resonators in slot waveguide ring cavities,” Appl. Phys. Lett.97(18), 183110 (2010).

Pruessner, M. W.

M. W. Pruessner, T. H. Stievater, J. B. Khurgin, and W. S. Rabinovich, “Integrated waveguide-DBR microcavity opto-mechanical system,” Opt. Express19(22), 21904–21918 (2011).
[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 Chip10(6), 762–768 (2010).
[CrossRef] [PubMed]

Rabinovich, W. S.

M. W. Pruessner, T. H. Stievater, J. B. Khurgin, and W. S. Rabinovich, “Integrated waveguide-DBR microcavity opto-mechanical system,” Opt. Express19(22), 21904–21918 (2011).
[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 Chip10(6), 762–768 (2010).
[CrossRef] [PubMed]

Ritter, T. A.

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

Riviere, R.

A. Schliesser, G. Anetsberger, R. Riviere, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys.10(9), 095015 (2008).
[CrossRef]

Rokhsari, H.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74(2), 023813 (2006).
[CrossRef]

H. Rokhsari, M. Hossein-Zadeh, A. Hajimiri, and K. J. Vahala, “Brownian noise in radiation-pressure-driven micromechanical oscillators,” Appl. Phys. Lett.89(6), 261109 (2006).

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and Experimental Study of Radiation Pressure-Induced Mechanical Oscillations (Parametric Instability) in Optical Microcavities,” IEEE J. Sel. Top. Quantum Electron.12(1), 96–107 (2006).

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

Roukes, M. L.

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol.2(2), 114–120 (2007).
[CrossRef] [PubMed]

Ruoso, G.

S. Seel, R. Storz, G. Ruoso, J. Mlynek, and S. Schiller, “Cryogenic Optical Resonators: A New Tool for Laser Frequency Stabilization at the 1 Hz Level,” Phys. Rev. Lett.78(25), 4741–4744 (1997).
[CrossRef]

Ruz, J. J.

J. Tamayo, P. M. Kosaka, J. J. Ruz, A. San Paulo, and M. Calleja, “Biosensors based on nanomechanical systems,” Chem. Soc. Rev.42(3), 1287–1311 (2013).
[CrossRef] [PubMed]

San Paulo, A.

J. Tamayo, P. M. Kosaka, J. J. Ruz, A. San Paulo, and M. Calleja, “Biosensors based on nanomechanical systems,” Chem. Soc. Rev.42(3), 1287–1311 (2013).
[CrossRef] [PubMed]

Sandberg, R.

S. Dohn, R. Sandberg, W. Svendsen, and A. Boisen, “Enhanced functionality of cantilever based mass sensors using higher modes,” Appl. Phys. Lett.86(23), 233501 (2005).
[CrossRef]

R. Sandberg, K. Molhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng.15(12), 2249–2253 (2005).
[CrossRef]

Schiller, S.

S. Seel, R. Storz, G. Ruoso, J. Mlynek, and S. Schiller, “Cryogenic Optical Resonators: A New Tool for Laser Frequency Stabilization at the 1 Hz Level,” Phys. Rev. Lett.78(25), 4741–4744 (1997).
[CrossRef]

Schliesser, A.

A. Schliesser, G. Anetsberger, R. Riviere, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New J. Phys.10(9), 095015 (2008).
[CrossRef]

Schmid, S.

A. Boisen, S. Dohn, S. S. Keller, S. Schmid, and M. Tenje, “Cantilever-like micromechanical sensors,” Rep. Prog. Phys.74(036101), 1–30 (2011).

Seel, S.

S. Seel, R. Storz, G. Ruoso, J. Mlynek, and S. Schiller, “Cryogenic Optical Resonators: A New Tool for Laser Frequency Stabilization at the 1 Hz Level,” Phys. Rev. Lett.78(25), 4741–4744 (1997).
[CrossRef]

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]

Shih, W. Y.

J. W. Yi, W. Y. Shih, and W.-H. Shih, “Effect of length, width, and mode on the mass detection sensitivity of piezoelectric unimorph cantilevers,” J. Appl. Phys.91(3), 1680–1686 (2002).
[CrossRef]

Shih, W.-H.

J. W. Yi, W. Y. Shih, and W.-H. Shih, “Effect of length, width, and mode on the mass detection sensitivity of piezoelectric unimorph cantilevers,” J. Appl. Phys.91(3), 1680–1686 (2002).
[CrossRef]

Shung, K. K.

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

Snook, K. A.

K. A. Snook, J. Z. Zhao, C. H. F. Alves, J. M. Cannata, W. H. Chen, R. J. Meyer, T. A. Ritter, and K. K. Shung, “Design, fabrication, and evaluation of high frequency, single-element transducers incorporating different materials,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control49(2), 169–176 (2002).
[CrossRef] [PubMed]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Sridaran, S.

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 Chip10(6), 762–768 (2010).
[CrossRef] [PubMed]

Stievater, T. H.

M. W. Pruessner, T. H. Stievater, J. B. Khurgin, and W. S. Rabinovich, “Integrated waveguide-DBR microcavity opto-mechanical system,” Opt. Express19(22), 21904–21918 (2011).
[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 Chip10(6), 762–768 (2010).
[CrossRef] [PubMed]

Storz, R.

S. Seel, R. Storz, G. Ruoso, J. Mlynek, and S. Schiller, “Cryogenic Optical Resonators: A New Tool for Laser Frequency Stabilization at the 1 Hz Level,” Phys. Rev. Lett.78(25), 4741–4744 (1997).
[CrossRef]

Svendsen, W.

S. Dohn, W. Svendsen, A. Boisen, and O. Hansen, “Mass and position determination of attached particles on cantilever based mass sensors,” Rev. Sci. Instrum.78(10), 103303 (2007).
[CrossRef] [PubMed]

S. Dohn, R. Sandberg, W. Svendsen, and A. Boisen, “Enhanced functionality of cantilever based mass sensors using higher modes,” Appl. Phys. Lett.86(23), 233501 (2005).
[CrossRef]

R. Sandberg, K. Molhave, A. Boisen, and W. Svendsen, “Effect of gold coating on the Q-factor of a resonant cantilever,” J. Micromech. Microeng.15(12), 2249–2253 (2005).
[CrossRef]

Szorkovszky, A.

Tallur, S.

Tamayo, J.

J. Tamayo, P. M. Kosaka, J. J. Ruz, A. San Paulo, and M. Calleja, “Biosensors based on nanomechanical systems,” Chem. Soc. Rev.42(3), 1287–1311 (2013).
[CrossRef] [PubMed]

Tang, H. X.

M. Li, W. H. P. Pernice, and H. X. Tang, “Ultra-high-frequency nano-optomechanical resonators in slot waveguide ring cavities,” Appl. Phys. Lett.97(18), 183110 (2010).

M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol.2(2), 114–120 (2007).
[CrossRef] [PubMed]

Tao, Y. H.

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

Taylor, M. A.

Tenje, M.

A. Boisen, S. Dohn, S. S. Keller, S. Schmid, and M. Tenje, “Cantilever-like micromechanical sensors,” Rep. Prog. Phys.74(036101), 1–30 (2011).

Vahala, K. J.

M. Hossein-Zadeh and K. J. Vahala, “Optomechanical Oscillator on a Silicon Chip”, Invited Paper, J Sel. Top. Quantum Electron. Special Issue on Silicon Photonics16(1), 276–287 (2010).

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459(7246), 550–555 (2009).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity Opto-Mechanics,” Opt. Express15(25), 17172–17205 (2007).
[CrossRef] [PubMed]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74(2), 023813 (2006).
[CrossRef]

H. Rokhsari, M. Hossein-Zadeh, A. Hajimiri, and K. J. Vahala, “Brownian noise in radiation-pressure-driven micromechanical oscillators,” Appl. Phys. Lett.89(6), 261109 (2006).

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Theoretical and Experimental Study of Radiation Pressure-Induced Mechanical Oscillations (Parametric Instability) in Optical Microcavities,” IEEE J. Sel. Top. Quantum Electron.12(1), 96–107 (2006).

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express13(14), 5293–5301 (2005).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods5(7), 591–596 (2008).
[CrossRef] [PubMed]

Waggoner, P. S.

P. S. Waggoner and H. G. Craighead, “Micro- and nanomechanical sensors for environmental, chemical, and biological detection,” Lab Chip7(10), 1238–1255 (2007).
[CrossRef] [PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser Phase and Frequency Stabilization Using an Optical-Resonator,” Appl. Phys. B31(2), 97–105 (1983).
[CrossRef]

Wei, C. Z.

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

Xiong, B.

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

Xu, P. C.

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

Xu, T. G.

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

Yang, Y.

B. Ilic, Y. Yang, and H. G. Craighead, “Virus detection using nanoelectromechanical devices,” Appl. Phys. Lett.85(13), 2604–2606 (2004).
[CrossRef]

Yi, J. W.

J. W. Yi, W. Y. Shih, and W.-H. Shih, “Effect of length, width, and mode on the mass detection sensitivity of piezoelectric unimorph cantilevers,” J. Appl. Phys.91(3), 1680–1686 (2002).
[CrossRef]

Yu, H. T.

Y. H. Tao, X. X. Li, T. G. Xu, H. T. Yu, P. C. Xu, B. Xiong, and C. Z. Wei, “Resonant cantilever sensors operated in a high-Q in-plane mode for real-time bio/chemical detection in liquids,” Sens. Actuators B Chem.157(2), 606–614 (2011).
[CrossRef]

Zhang, J. D.

Zhao, J. Z.

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Chem. Soc. Rev. (1)

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IEEE J. Sel. Top. Quantum Electron. (1)

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IEEE Sensors (1)

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

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J. Appl. Phys. (1)

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Figures (7)

Fig. 1
Fig. 1

(a) Experimental arrangement used for mass measurement using microtoroid optomechanical oscillator. (b) SEM image of one of the silica microtoroids used in this study. D = 131 µm, Dp = 5.2 µm and d = 7.8 µm. Inset: a polyethylene microbead landed on the toroidal region of the resonator. (c) Schematic diagram showing the cross–section of a microtoroid, mechanical deformation of the silica membrane (associated with the 3rd mechanical mode), and the trajectory of the circulating WG optical mode (red line).

Fig. 2
Fig. 2

(a) Measured RF spectrum (RBW = 30 Hz) of the OMO optical output power in the absence of the microbeads. For this OMO D = 131 µm, Dp = 5.2 µm and d = 7.8 µm and fOMO = 8.505 MHz. Here: Q0 = 6.8 × 107, Qtot = 6.72 × 106,(Qtot is the loaded optical-Q), Qmech = 1300, Pth = 553.7µW, Pin = 2.4Pth and ΔλN = 0.56 (ΔλN = Δλ/δλ, where δλ = λres/Qtot). (b) Measured RF spectrum of the OMO in the vicinity of the fundamental frequency as microbeads are added sequentially (2 through 5). (c) Images of the distribution of microbeads on the microtoroid OMO. (d) SEM image of the microtoroid OMO and the microbeads distributed on it (the distribution corresponds to c-5). (e) FEM modeling of the mechanical deformation of the corresponding mechanical mode; the contours show the total displacements. (f) Measured RF spectrum (RBW = 30 Hz) of the OMO in the vicinity of the fifth harmonic frequency as microbeads are added sequentially (1 through 5). (g) Measured frequency shift of the fundamental oscillation ΔfOMO and its 5th harmonic Δ(5fOMO) plotted against the loaded mass. The dashed red line depicts the calculated results using numerical modeling. The inset is a close-up view for Δm< 5 pg.

Fig. 3
Fig. 3

(a) Top view images of the distribution of microbeads on the second microtoroid OMO. For this OMO D = 133 µm, DP = 11.25 µm, d = 7.24 µm and fOMO = 24.88 MHz, (b) Frequency shift of the fundamental oscillation ΔfOMO and its 5th harmonic Δ(5fOMO) plotted against the loaded mass. The dashed line depicts the calculated results using numerical modeling. The inset shows FEM modeling of the mechanical deformation of the corresponding mechanical mode. (c) and (d) are the measured RF spectrum ((RBW = 30 Hz)) of the OMO in the vicinity of the fundamental frequency (c) and its fifth harmonic (d) as microbeads are added sequentially (1 through 4). Here: Q0 = 3.6 × 106, Qtot = 2.3 × 106(Qtot is the loaded optical-Q), Qmech = 1466, ΔλN = 0.58 (ΔλN = Δλ/δλ, where δλ = λres/Qtot), Pth = 212 µW, and Pin = 3.67 Pth.

Fig. 4
Fig. 4

(a) FEM simulation of mechanical modes of a silica microtoroid. (a) Deformation of four eigen mechanical modes of a silica microtoroid with a pillar diameter Dp = 11.2 µm major diameter D = 133 µm, and minor diameter d = 7.4 µm. f0 is the eigen frequency of the corresponding mode. (b) η plotted against radial position of mass (θ = 0) for the four modes shown in part (a) using the FEM and Energy method. Compared to other modes, the η for the first mode is so small that appears as a straight line on the x-axis.

Fig. 5
Fig. 5

(a) Calculated maximum sensitivity ηmax plotted against D/DP for two different values of D and three eigen modes. (b) Sensitive area (As) for detecting 1 pg mass plotted against D for three eigen modes (assuming ΔfOMO-min = 40 Hz). Inset: Optimized microtoroid diameter Dopt plotted against the values of added mass.

Fig. 6
Fig. 6

Calculated Λ plotted against D/DP for two different values of D and the four eigen modes.

Fig. 7
Fig. 7

(a) Δmmin plotted against normalized detuning ΔνN for the fifth harmonic (n = 5) of the mechanical modes of the microtoroid in Fig. 2 (D = 131 µm, DP = 5.2 µm). The mass is located at the position of maximum sensitivity (ηmax = ηi(rmm)) for each mode. Here Q0 = 6.8 × 107, Qmech = 1300, Qtot/Q0 = 0.1 and Pin = 2 Pth. We have assumed RIN<90dB, δ(Δν0) is 500 Hz and ignored δ(Qtot/Q0) and δfI. (b) Δmmin plotted against the order of harmonic frequency used for the measurement (n) for two cases: δfI = 0 dashed lines) and δfI = 30 Hz (solid lines). The insets show the membrane deformation for the 2nd and 4th modes. The mass is located at the position of maximum sensitivity (ηmax = ηi(rmm)) for each mode shown as red zones in the insets. ΔλN is fixed at 0.28 that is the optimal detuning according to part-a. Other parameters are the same as the ones in part-a. (c) Δmmin plotted against the D/Dp based on the fifth harmonic shift, for D = 103 µm (dashed lines) and 133 µm (solid lines). Here all parameters are chosen according to the actual experiment. ΔλN = 0.56, Q0 = 6.8 × 107, Qmech~1400, and Pin~2 Pth. Qtot/Q0 = 0.1. Uncertainty of Qtot/Q0 and detuning δ (Δλ) are 1% and 400 KHz, respectively. Pin = 2Pth, δfI = 30 Hz.

Equations (7)

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Δ f OMO f OMO Δ E Δm 2 E total = π 2 f OMO 3 Δm(r,θ) U 2 (r,θ) E total
Δ f OMO π 2 f OMO 3 ρ(r,θ)Δa U 2 (r,θ) E total
Λ= π 2 f OMO 3 E total A ρ(r,θ) U 2 (r,θ) da
Δ m min = Δ f OMOmin η max
Δ f OMOmin =δ f L +δ(Δ f P )+δ f I
Δ f OMOmin (n) =δ f L +n×δ(Δ f P )+δ f I
Δ m min δ f L +δ f I n× η max + δ f P η max

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