Abstract

The measurement of dispersion and its control have become important considerations in nonlinear devices based on microcavities. A sideband technique is applied here to accurately measure dispersion in a microcavity resulting from both geometrical and material contributions. Moreover, by combining the method with finite element simulations, we show that mapping of spectral lines to their corresponding transverse mode families is possible. The method is applicable for high-Q, micro-cavities having microwave rate free spectral range and has a relative precision of 5.5 × 10−6 for a 2 mm disk cavity with FSR of 32.9382 GHz and Q of 150 milllion.

© 2012 OSA

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    [CrossRef] [PubMed]
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  3. V. S. Ilchenko and A. B. Matkso, “Optical resonators with whispering-gallery modes-Part II: Applications,” IEEE J. Quantum Electron.12, 15–32 (2006).
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  5. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: Back-action at the mesoscale,” Science321, 1172–1176 (2008).
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    [CrossRef] [PubMed]
  10. H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
    [CrossRef]
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    [CrossRef]
  23. A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express16, 4130–4144 (2008).
    [CrossRef] [PubMed]
  24. R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  27. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a Fiber-Taper-Coupled Microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
  29. O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, (CRC Press, 2009), Ch. 11.
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2012 (3)

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express20, 20170–20180, (2012).
[CrossRef] [PubMed]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

2011 (3)

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science322, 555–559 (2011).
[CrossRef]

S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A84, 053833 (2011).
[CrossRef]

2010 (1)

2009 (3)

I. Grudinin, A. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett.102, 043902 (2009).
[CrossRef] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3, 529–533 (2009).
[CrossRef]

2008 (3)

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express16, 4130–4144 (2008).
[CrossRef] [PubMed]

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

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

2007 (1)

M. Oxborrow, “Traceable 2-d finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech.55, 1209–1218 (2007).
[CrossRef]

2006 (4)

A. Schliesser, C. Gohle, T. Udem, and T. W. Hansch, “Complete characterization of a broadband high-finesse cavity using an optical frequency comb,” Opt. Express14, 5975–5983 (2006).
[CrossRef] [PubMed]

A. B. Matkso and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-Part I: Basics,” IEEE J. Quantum Electron.12, 3–14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matkso, “Optical resonators with whispering-gallery modes-Part II: Applications,” IEEE J. Quantum Electron.12, 15–32 (2006).
[CrossRef]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A70, 051804(R) (2004).
[CrossRef]

2003 (3)

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

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

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a Fiber-Taper-Coupled Microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

2000 (1)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

1998 (1)

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

1988 (1)

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
[CrossRef] [PubMed]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Arcizet, O.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3, 529–533 (2009).
[CrossRef]

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, (CRC Press, 2009), Ch. 11.

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, 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, 591–596 (2008).
[CrossRef] [PubMed]

Bowen, W. P.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Brewer, R. G.

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
[CrossRef] [PubMed]

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

Carmon, T.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

Chen, T.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express20, 20170–20180, (2012).
[CrossRef] [PubMed]

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

J. Li, H. Lee, T. Chen, O. Painter, and K. Vahala, “Chip-based Brillouin lasers as spectral purifiers for photonic systems,” arXiv:1201.4212 (2011).

Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Del’Haye, P.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3, 529–533 (2009).
[CrossRef]

DelHaye, P.

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, (CRC Press, 2009), Ch. 11.

DeVoe, R. G.

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
[CrossRef] [PubMed]

Diddams, S. A.

S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A84, 053833 (2011).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science322, 555–559 (2011).
[CrossRef]

Fabre, C.

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
[CrossRef] [PubMed]

Flagan, R. C.

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

Fraser, S. E.

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

Gohle, C.

Gorodetsky, M.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

Gorodetsky, M. L.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3, 529–533 (2009).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Grudinin, I.

I. Grudinin, A. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett.102, 043902 (2009).
[CrossRef] [PubMed]

Hansch, T. W.

Hartinger, K.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

Herchak, S.

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

Herr, T.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

Hoffnagle, J.

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
[CrossRef] [PubMed]

Holzwarth, R.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science322, 555–559 (2011).
[CrossRef]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3, 529–533 (2009).
[CrossRef]

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, (CRC Press, 2009), Ch. 11.

Ilchenko, V. S.

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett.35, 2822–2824 (2010).
[CrossRef] [PubMed]

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express16, 4130–4144 (2008).
[CrossRef] [PubMed]

A. B. Matkso and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-Part I: Basics,” IEEE J. Quantum Electron.12, 3–14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matkso, “Optical resonators with whispering-gallery modes-Part II: Applications,” IEEE J. Quantum Electron.12, 15–32 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A70, 051804(R) (2004).
[CrossRef]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett.23247–249 (1998).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Jeon, S.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

Jones, R. J.

Jungmann, K.

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
[CrossRef] [PubMed]

Kim, J.

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett.23247–249 (1998).
[CrossRef]

Kippenberg, T. J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science322, 555–559 (2011).
[CrossRef]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3, 529–533 (2009).
[CrossRef]

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

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

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

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a Fiber-Taper-Coupled Microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, (CRC Press, 2009), Ch. 11.

Lalezari, R.

Lee, H.

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express20, 20170–20180, (2012).
[CrossRef] [PubMed]

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

J. Li, H. Lee, T. Chen, O. Painter, and K. Vahala, “Chip-based Brillouin lasers as spectral purifiers for photonic systems,” arXiv:1201.4212 (2011).

Li, J.

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express20, 20170–20180, (2012).
[CrossRef] [PubMed]

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

J. Li, H. Lee, T. Chen, O. Painter, and K. Vahala, “Chip-based Brillouin lasers as spectral purifiers for photonic systems,” arXiv:1201.4212 (2011).

Liang, W.

Lu, T.

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

Mabuchi, H.

Maleki, L.

Matkso, A. B.

V. S. Ilchenko and A. B. Matkso, “Optical resonators with whispering-gallery modes-Part II: Applications,” IEEE J. Quantum Electron.12, 15–32 (2006).
[CrossRef]

A. B. Matkso and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-Part I: Basics,” IEEE J. Quantum Electron.12, 3–14 (2006).
[CrossRef]

Matsko, A.

I. Grudinin, A. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett.102, 043902 (2009).
[CrossRef] [PubMed]

Matsko, A. B.

Moll, K. D.

Oxborrow, M.

M. Oxborrow, “Traceable 2-d finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech.55, 1209–1218 (2007).
[CrossRef]

Painter, O.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

J. Li, H. Lee, T. Chen, O. Painter, and K. Vahala, “Chip-based Brillouin lasers as spectral purifiers for photonic systems,” arXiv:1201.4212 (2011).

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a Fiber-Taper-Coupled Microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

Papp, S. B.

S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A84, 053833 (2011).
[CrossRef]

Parkins, A. S.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

Rubiola, E.

Savchenkov, A. A.

Schliesser, A.

A. Schliesser, C. Gohle, T. Udem, and T. W. Hansch, “Complete characterization of a broadband high-finesse cavity using an optical frequency comb,” Opt. Express14, 5975–5983 (2006).
[CrossRef] [PubMed]

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, (CRC Press, 2009), Ch. 11.

Seidel, D.

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, 925–928 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a Fiber-Taper-Coupled Microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

Streed, E. W.

Thorpe, M. J.

Tomes, M.

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

Udem, T.

Vahala, K.

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

J. Li, H. Lee, T. Chen, O. Painter, and K. Vahala, “Chip-based Brillouin lasers as spectral purifiers for photonic systems,” arXiv:1201.4212 (2011).

Vahala, K. J.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express20, 20170–20180, (2012).
[CrossRef] [PubMed]

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

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

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

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

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a Fiber-Taper-Coupled Microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

Vernooy, D. W.

Vollmer, F.

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

Wang, C. Y.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

Wilcut, E.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Yang, K.

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

Ye, J.

IEEE J. Quantum Electron. (2)

A. B. Matkso and V. S. Ilchenko, “Optical resonators with whispering-gallery modes-Part I: Basics,” IEEE J. Quantum Electron.12, 3–14 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matkso, “Optical resonators with whispering-gallery modes-Part II: Applications,” IEEE J. Quantum Electron.12, 15–32 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

M. Oxborrow, “Traceable 2-d finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech.55, 1209–1218 (2007).
[CrossRef]

Nat. Methods (1)

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

Nat. Photon. (2)

H. Lee, T. Chen, J. Li, K. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photon.6, 369–373 (2012).
[CrossRef]

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photon.6, 480–487 (2012).
[CrossRef]

Nat. Photonics (1)

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics3, 529–533 (2009).
[CrossRef]

Nature (3)

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

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

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature443, 671–674 (2006).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A137, 393–397 (1989).
[CrossRef]

Phys. Rev. A (3)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A70, 051804(R) (2004).
[CrossRef]

S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A84, 053833 (2011).
[CrossRef]

R. G. DeVoe, C. Fabre, K. Jungmann, J. Hoffnagle, and R. G. Brewer, “Precision optical-frequency-difference measurements,” Phys. Rev. A37, 1802–1805 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to silica-microsphere whispering gallery mode system,” Phys. Rev. Lett.85, 74–77 (2000).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a Fiber-Taper-Coupled Microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003).
[CrossRef] [PubMed]

I. Grudinin, A. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett.102, 043902 (2009).
[CrossRef] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett.102, 113601 (2009).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

T. Lu, H. Lee, T. Chen, S. Herchak, J. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U.S.A.108, 5976–5979 (2011).
[CrossRef] [PubMed]

Science (2)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science322, 555–559 (2011).
[CrossRef]

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

Other (3)

J. Li, H. Lee, T. Chen, O. Painter, and K. Vahala, “Chip-based Brillouin lasers as spectral purifiers for photonic systems,” arXiv:1201.4212 (2011).

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation in monolithic microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, (CRC Press, 2009), Ch. 11.

G. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. (a) A schematic is shown for the sideband spectroscopy method used to measure dispersion. A phase modulator (PM) creates sidebands on a probe laser that are set to coincide approximately with the cavity FSR. Also, a Mach-Zehnder interferometer creates a reference spectrum to measure the offset frequency Δf. The laser is scanned so as to produce the spectrum shown in panel (b). (b) Schematic traces of the sideband spectroscopy are shown. When the phase modulation is “off” the red trace is observed showing that the laser is scanning through a single cavity resonance. With the phase modulation “on” and with its frequency set to be close in value to the cavity FSR, three spectral peaks appear as the two phase modulation sidebands scan through their respective cavity resonances (neighboring the resonance probed by the scan-laser, carrier wave). By using the green interferometer trace to measure the offset Δf and adding this offset to the phase modulation frequency, the cavity FSR can be measured.

Fig. 2
Fig. 2

Measurement of the FSR of the Mach Zehnder interferometer (MZI). (a) Measured power spectrum of the photocurrent output from a balanced photodetector whose inputs detect the complementary outputs of the MZI. For this measurement the laser frequency is close to a quadrature point of the MZI and the spectral measurement extends from 110–200 MHz. (b) FSR of the MZI extracted from each order in (a). The dashed line is the average.

Fig. 3
Fig. 3

Cavity transverse mode spectroscopy (a) Transmission spectrum for a 6 mm wedge resonator. Multiple transverse modes (labeled from A to J) are shown within the frequency sweep of one FSR (10.8 GHz). The lower green trace is the Mach-Zehnder reference inteferometer (MZI) (FSR of the MZI is 6.723 MHz, MZI fringes are resolved in panel (b)). By using the MZI fringes and the calibrated MZI FSR, the original horizontal axis (time span, as shown in Fig. 1(b)) can be converted to frequency span. (b) Zoom-in measurement of the peak G in panel (a). The Lorentzian fit shows a loaded cavity linewidth of 1.03 MHz. This is also the fundamental mode indicated in panels (c) and (d). (c) Mapping of the cavity transverse-order to each spectral peak by comparing the FSR measurement with FEM simulation. Three slightly different cavity geometries are used for FEM simulation, and the FSR of the simulated transverse modes maintains the sequence regardless of geometry. (d) Intensity profile of the 1st, 5th and 9th transverse-order modes calculated by FEM. The corresponding spectral peaks are given to the right of the profile.

Fig. 4
Fig. 4

Measurement of dispersion at two wavelengths for three cavity geometries. (a) Measured cavity FSR (wrt 32.9382 GHz) for 2 mm resonator (α ≈ 20°, oxide thickness, T ≈ 8μm) plotted versus relative azimuthal mode number M around the 1550 nm spectral region. The dashed, red line is a linear fit giving 12.2 kHz/FSR dispersion. (b) Measured (colored makers) and simulated cavity dispersion, ΔFSR, as a function of wavelength for 2 mm disk resonators with three wedge angles (α ≈ 10°, 20° and 30°, T ≈ 8μm). (c) Solid lines give the dispersion parameter, D, converted from the ΔFSR values in (b), using Δ F S R c 2 λ 2 D 4 π 2 n 3 R 2 [29]. The dashed line is the silica material dispersion from the Sellmeier equation. The three dotted lines are the geometric dispersion, obtained by subtracting the material dispersion from the total dispersion. The measurement data points are given as markers. (d) Intensity profile for 2 mm resonators with 10°, 20° and 30 ° wedge angles.

Equations (1)

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δ F S R = δ f m + T d T m δ F S R M + δ T d T m F S R M + T d δ T m T m 2 F S R M

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