Abstract

We present a laser amplitude modulation technique to actively stabilize the critical coupling of a microresonator by controlling the evanescent coupling gap from an optical fiber taper. It is a form of nulled lock-in detection, which decouples laser intensity fluctuations from the critical coupling measurement. We achieved a stabilization bandwidth of ∼ 20 Hz, with up to 5 orders of magnitude displacement noise suppression at 10 mHz, and an inferred gap stability of better than a picometer/√Hz.

© 2012 OSA

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  1. K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
    [CrossRef] [PubMed]
  2. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321, 1172–1176 (2008).
    [CrossRef] [PubMed]
  3. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett.93, 083904 (2004).
    [CrossRef] [PubMed]
  4. H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, “Radiation-pressure-driven micro-mechanical oscillator,” Opt. Express13, 5293–5301 (2005).
    [CrossRef] [PubMed]
  5. J. Knittel, T. G. McRae, K. H. Lee, and W. P. Bowen, “Interferometric detection of mode splitting for whispering gallery mode biosensors,” Appl. Phys. Lett.97, 123704 (2010).
    [CrossRef]
  6. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express, 124742–4750, (2004).
    [CrossRef] [PubMed]
  7. H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85, 3029–3031 (2004).
    [CrossRef]
  8. H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett.30, 427–429 (2005).
    [CrossRef] [PubMed]
  9. 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, 96–107 (2006).
    [CrossRef]
  10. M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74, 023813 (2006).
    [CrossRef]
  11. M. Hossein-Zadeh and K. J. Vahala, “An optomechanical oscillator on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.16, 276–287 (2010).
    [CrossRef]
  12. J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett.99, 243109 (2011).
    [CrossRef]
  13. T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
    [CrossRef]
  14. K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
    [CrossRef] [PubMed]
  15. C. Junge, S. Nickel, D. O’Shea, and A. Rauschenbeutel, “Bottle microresonator with actively stabilized evanescent coupling,” Opt. Lett.36, 3488–3490 (2011).
    [CrossRef] [PubMed]
  16. 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, 97–105 (1983).
    [CrossRef]
  17. E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys.69, 79–87 (2001).
    [CrossRef]
  18. P. R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors, 1st ed. (World Scientific, Singapore, 1994).
    [CrossRef]
  19. J. H. Chow, I. C. M. Littler, D. S. Rabeling, D. E. McClelland, and M. B. Gray, “Using active resonator impedance matching for shot-noise limited, cavity enhanced amplitude modulated laser absorption spectroscopy,” Opt. Express16, 7726–7738 (2008).
    [CrossRef] [PubMed]
  20. D.S. Rabeling, J.H. Chow, M.B. Gray, and D.E. McClelland, “Experimental demonstration of impedance match locking and control of coupled resonators,” Opt. Express18, 9314–9323 (2011).
    [CrossRef]
  21. J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett.24, 847–849 (1999).
    [CrossRef]
  22. A. Yariv, “Critical coupling and its control in optical wave-guide-ring resonator systems,” IEEE Photon. Technol. Lett.14483–485 (2002).
    [CrossRef]

2011

2010

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
[CrossRef]

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
[CrossRef] [PubMed]

J. Knittel, T. G. McRae, K. H. Lee, and W. P. Bowen, “Interferometric detection of mode splitting for whispering gallery mode biosensors,” Appl. Phys. Lett.97, 123704 (2010).
[CrossRef]

M. Hossein-Zadeh and K. J. Vahala, “An optomechanical oscillator on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.16, 276–287 (2010).
[CrossRef]

2008

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, 96–107 (2006).
[CrossRef]

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

2005

2004

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett.93, 083904 (2004).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85, 3029–3031 (2004).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express, 124742–4750, (2004).
[CrossRef] [PubMed]

2003

K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
[CrossRef] [PubMed]

2002

A. Yariv, “Critical coupling and its control in optical wave-guide-ring resonator systems,” IEEE Photon. Technol. Lett.14483–485 (2002).
[CrossRef]

2001

E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys.69, 79–87 (2001).
[CrossRef]

1999

1983

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, 97–105 (1983).
[CrossRef]

Black, E. D.

E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys.69, 79–87 (2001).
[CrossRef]

Bowen, W. P.

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett.99, 243109 (2011).
[CrossRef]

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
[CrossRef] [PubMed]

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
[CrossRef]

J. Knittel, T. G. McRae, K. H. Lee, and W. P. Bowen, “Interferometric detection of mode splitting for whispering gallery mode biosensors,” Appl. Phys. Lett.97, 123704 (2010).
[CrossRef]

Boyd, R. W.

Carmon, T.

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, 96–107 (2006).
[CrossRef]

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

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express, 124742–4750, (2004).
[CrossRef] [PubMed]

Chow, J. H.

Chow, J.H.

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, 97–105 (1983).
[CrossRef]

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, 97–105 (1983).
[CrossRef]

Gray, M. B.

Gray, M.B.

Hajimiri, A.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74, 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, 97–105 (1983).
[CrossRef]

Harris, G. I.

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
[CrossRef]

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
[CrossRef] [PubMed]

Heebner, J. E.

Hossein-Zadeh, M.

M. Hossein-Zadeh and K. J. Vahala, “An optomechanical oscillator on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.16, 276–287 (2010).
[CrossRef]

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74, 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, 97–105 (1983).
[CrossRef]

Junge, C.

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321, 1172–1176 (2008).
[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, 96–107 (2006).
[CrossRef]

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

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett.93, 083904 (2004).
[CrossRef] [PubMed]

Knittel, J.

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett.99, 243109 (2011).
[CrossRef]

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
[CrossRef] [PubMed]

J. Knittel, T. G. McRae, K. H. Lee, and W. P. Bowen, “Interferometric detection of mode splitting for whispering gallery mode biosensors,” Appl. Phys. Lett.97, 123704 (2010).
[CrossRef]

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
[CrossRef]

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, 97–105 (1983).
[CrossRef]

Lee, K. H.

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
[CrossRef]

J. Knittel, T. G. McRae, K. H. Lee, and W. P. Bowen, “Interferometric detection of mode splitting for whispering gallery mode biosensors,” Appl. Phys. Lett.97, 123704 (2010).
[CrossRef]

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
[CrossRef] [PubMed]

Littler, I. C. M.

McClelland, D. E.

McClelland, D.E.

McRae, T. G.

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
[CrossRef]

J. Knittel, T. G. McRae, K. H. Lee, and W. P. Bowen, “Interferometric detection of mode splitting for whispering gallery mode biosensors,” Appl. Phys. Lett.97, 123704 (2010).
[CrossRef]

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
[CrossRef] [PubMed]

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, 97–105 (1983).
[CrossRef]

Nickel, S.

O’Shea, D.

Rabeling, D. S.

Rabeling, D.S.

Rauschenbeutel, A.

Rokhsari, H.

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, “Characterization of a radiation-pressure-driven micromechanical oscillator,” Phys. Rev. A74, 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, 96–107 (2006).
[CrossRef]

H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett.30, 427–429 (2005).
[CrossRef] [PubMed]

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

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85, 3029–3031 (2004).
[CrossRef]

Saulson, P. R.

P. R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors, 1st ed. (World Scientific, Singapore, 1994).
[CrossRef]

Spillane, S. M.

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85, 3029–3031 (2004).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett.93, 083904 (2004).
[CrossRef] [PubMed]

Swaim, J. D.

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett.99, 243109 (2011).
[CrossRef]

Vahala, K. J.

M. Hossein-Zadeh and K. J. Vahala, “An optomechanical oscillator on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.16, 276–287 (2010).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321, 1172–1176 (2008).
[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, 96–107 (2006).
[CrossRef]

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

H. Rokhsari and K. J. Vahala, “Observation of Kerr nonlinearity in microcavities at room temperature,” Opt. Lett.30, 427–429 (2005).
[CrossRef] [PubMed]

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

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett.93, 083904 (2004).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85, 3029–3031 (2004).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express, 124742–4750, (2004).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
[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, 97–105 (1983).
[CrossRef]

Yang, L.

Yariv, A.

A. Yariv, “Critical coupling and its control in optical wave-guide-ring resonator systems,” IEEE Photon. Technol. Lett.14483–485 (2002).
[CrossRef]

Am. J. Phys.

E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys.69, 79–87 (2001).
[CrossRef]

Appl. Phys. B

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, 97–105 (1983).
[CrossRef]

Appl. Phys. Lett.

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett.99, 243109 (2011).
[CrossRef]

J. Knittel, T. G. McRae, K. H. Lee, and W. P. Bowen, “Interferometric detection of mode splitting for whispering gallery mode biosensors,” Appl. Phys. Lett.97, 123704 (2010).
[CrossRef]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett.85, 3029–3031 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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, 96–107 (2006).
[CrossRef]

M. Hossein-Zadeh and K. J. Vahala, “An optomechanical oscillator on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.16, 276–287 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Yariv, “Critical coupling and its control in optical wave-guide-ring resonator systems,” IEEE Photon. Technol. Lett.14483–485 (2002).
[CrossRef]

Nature

K. J. Vahala, “Optical microcavities,” Nature424, 839–846 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

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

T. G. McRae, K. H. Lee, G. I. Harris, J. Knittel, and W. P. Bowen, “Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction,” Phys. Rev. A82, 023825 (2010).
[CrossRef]

Phys. Rev. Lett.

K. H. Lee, T. G. McRae, G. I. Harris, J. Knittel, and W. P. Bowen, “Cooling and control of a cavity optoelectromechanical system,” Phys. Rev. Lett.104, 123604 (2010).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett.93, 083904 (2004).
[CrossRef] [PubMed]

Science

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science321, 1172–1176 (2008).
[CrossRef] [PubMed]

Other

P. R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors, 1st ed. (World Scientific, Singapore, 1994).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Top view microscope image of the microtoroid cavity used in our experiment, with a fiber taper for evanescent coupling. Ein is the input optical field, Ecirc is the circulating field, while Eout the output field from the optical system.

Fig. 2
Fig. 2

Experimental schematic for critical coupling control of a microtoroid cavity, showing two control loops: 1) The Pound-Drever-Hall locking using PM modulation; and 2) the critical coupling feedback using AM modulation.

Fig. 3
Fig. 3

The system behavior when the evanescent gap was varied while the PDH frequency locking was active: (a) the input voltage to the translation stage amplifier, which linearly varied the evanescent gap; (b) the output power from the microtoroid; (c) the demodulated critical coupling error signal. The PZT varied the coupling gap by 0.4 μm peak-to-peak.

Fig. 4
Fig. 4

The time series of the microtoroid output power during the lock acquisition process. The gap was injected with an 18 Hz dither, and was initially free-running with no feedback control. The first integrator of the locking servo was turned on at 8.5 seconds, and the second was engaged at 10.8 seconds.

Fig. 5
Fig. 5

The spectra of the critical coupling error signal calibrated for equivalent evanescent gap displacement for (a) when coupling stabilisation was not active; and (b) closed-loop performance of the critical coupling control.

Fig. 6
Fig. 6

The long term transmitted power over two hours, as a percentage fraction of total input power.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E out E in = a t 1 t a ,
E out = A e i ω 0 t [ a t 1 t a + β 2 e + i ω m t + β 2 e i ω m t ] .
S A 2 a t 1 t a .
S Q A 2 ( a t ) ,

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