Abstract

Frequency stabilization of a diode laser locked to a whispering gallery mode (WGM) reference resonator made of a MgF2 single crystal is demonstrated. The strong thermal dependence of the difference frequency between two orthogonally polarized TE an TM modes (dual-mode frequency) of the optically anisotropic crystal material allows sensitive measurement of the resonator’s temperature within the optical mode volume. This dual-mode signal was used as feedback for self-referenced temperature stabilization to nanokelvin precision, resulting in frequency stability of 0.3 MHz/h at 972 nm, which was measured by comparing with an independent ultrastable laser.

© 2012 OSA

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  1. V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun.158, 305–312 (1998).
    [CrossRef]
  2. T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J. Vahala, “Feedback control of ultra-high-Q microcavities: application to micro-Raman lasers and microparametric oscillators,” Opt. Express13, 3558–3566 (2005).
    [CrossRef] [PubMed]
  3. B. Sprenger, H. G. L. Schwefel, Z. H. Lu, S. Svitlov, and L. J. Wang, “CaF2 whispering-gallery-mode-resonator stabilized-narrow-linewidth laser,” Opt. Lett.35, 2870–2872 (2010).
    [CrossRef] [PubMed]
  4. 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]
  5. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, “Whispering-gallery-mode resonators as frequency references. II. Stabilization,” J. Opt. Soc. Am. B24, 2988–2997 (2007).
    [CrossRef]
  6. J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).
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    [CrossRef]
  8. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express15, 6768–6773 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B21, 697–705 (2004).
    [CrossRef]
  11. D. V. Strekalov, R. J. Thompson, L. M. Baumgartel, I. S. Grudinin, and N. Yu, “Temperature measurement and stabilization in a birefringent whispering gallery mode resonator,” Opt. Express19 (15), 14495–14501 (2011).
    [CrossRef] [PubMed]
  12. L. Baumgartel, R. Thompson, D. Strekalov, I. Grudinin, and N. Yu, “Dual Mode Frequency Stabilization of a Whispering Gallery Mode Optical Reference Cavity,” in CLEO: Science and Innovations, OSA Technical Digest (online), CTh3A.6. (2012).
  13. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Optical-RF frequency stability transformer,” Opt. Lett.36, 4527–4529 (2011).
    [CrossRef] [PubMed]
  14. J. R. Vig, “Dual-mode oscillators for clocks and sensors,” in Ultrasonics Symposium 1999 Proceedings 1999 IEEE, 2, 859–868 (2002).
  15. N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
    [CrossRef]
  16. M. E. Tobar, G. L. Hamilton, E. N. Ivanov, and J. G. Hartnett, “New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization,” IEEE Trans. on Ultrason. Ferro. Freq. Contr.50 (3), 214–219 (2003).
    [CrossRef]
  17. M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
    [CrossRef]
  18. A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical materials characterization final technical report,” Nat. Bur. Stand. (U.S.) Tech. Note993 (1978).
  19. J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A77, 053809 (2008).
    [CrossRef]
  20. G. Ghosh, “Handbook of Thermo-Optic Coefficients of Optical Materials with Applications,” (Academic, 1998).
  21. I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. V. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun.265 (1), 33–38 (2006).
    [CrossRef]
  22. 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]

2011 (4)

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A83, 21801 (2011).
[CrossRef]

D. V. Strekalov, R. J. Thompson, L. M. Baumgartel, I. S. Grudinin, and N. Yu, “Temperature measurement and stabilization in a birefringent whispering gallery mode resonator,” Opt. Express19 (15), 14495–14501 (2011).
[CrossRef] [PubMed]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Optical-RF frequency stability transformer,” Opt. Lett.36, 4527–4529 (2011).
[CrossRef] [PubMed]

2010 (2)

2008 (1)

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A77, 053809 (2008).
[CrossRef]

2007 (3)

2006 (1)

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. V. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun.265 (1), 33–38 (2006).
[CrossRef]

2005 (2)

N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
[CrossRef]

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J. Vahala, “Feedback control of ultra-high-Q microcavities: application to micro-Raman lasers and microparametric oscillators,” Opt. Express13, 3558–3566 (2005).
[CrossRef] [PubMed]

2004 (2)

M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B21, 697–705 (2004).
[CrossRef]

M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
[CrossRef]

2003 (1)

M. E. Tobar, G. L. Hamilton, E. N. Ivanov, and J. G. Hartnett, “New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization,” IEEE Trans. on Ultrason. Ferro. Freq. Contr.50 (3), 214–219 (2003).
[CrossRef]

2002 (1)

J. R. Vig, “Dual-mode oscillators for clocks and sensors,” in Ultrasonics Symposium 1999 Proceedings 1999 IEEE, 2, 859–868 (2002).

1998 (1)

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun.158, 305–312 (1998).
[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, 97–105 (1983).
[CrossRef]

1978 (1)

A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical materials characterization final technical report,” Nat. Bur. Stand. (U.S.) Tech. Note993 (1978).

Alnis, J.

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A77, 053809 (2008).
[CrossRef]

Baumgartel, L.

L. Baumgartel, R. Thompson, D. Strekalov, I. Grudinin, and N. Yu, “Dual Mode Frequency Stabilization of a Whispering Gallery Mode Optical Reference Cavity,” in CLEO: Science and Innovations, OSA Technical Digest (online), CTh3A.6. (2012).

Baumgartel, L. M.

Bazin, N.

N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
[CrossRef]

Boubekeur, N.

N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
[CrossRef]

Carmon, T.

Dodge, M. J.

A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical materials characterization final technical report,” Nat. Bur. Stand. (U.S.) Tech. Note993 (1978).

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]

Dros, D. C.

M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
[CrossRef]

Feldman, A.

A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical materials characterization final technical report,” Nat. Bur. Stand. (U.S.) Tech. Note993 (1978).

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]

Ghosh, G.

G. Ghosh, “Handbook of Thermo-Optic Coefficients of Optical Materials with Applications,” (Academic, 1998).

Giordano, V.

N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
[CrossRef]

Gorodetsky, M. L.

M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B21, 697–705 (2004).
[CrossRef]

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun.158, 305–312 (1998).
[CrossRef]

Grudinin, I.

L. Baumgartel, R. Thompson, D. Strekalov, I. Grudinin, and N. Yu, “Dual Mode Frequency Stabilization of a Whispering Gallery Mode Optical Reference Cavity,” in CLEO: Science and Innovations, OSA Technical Digest (online), CTh3A.6. (2012).

Grudinin, I. S.

Guillon, P.

M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
[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]

Hamilton, G. L.

M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
[CrossRef]

M. E. Tobar, G. L. Hamilton, E. N. Ivanov, and J. G. Hartnett, “New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization,” IEEE Trans. on Ultrason. Ferro. Freq. Contr.50 (3), 214–219 (2003).
[CrossRef]

Hänsch, T. W.

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A77, 053809 (2008).
[CrossRef]

Hartnett, J. G.

N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
[CrossRef]

M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
[CrossRef]

M. E. Tobar, G. L. Hamilton, E. N. Ivanov, and J. G. Hartnett, “New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization,” IEEE Trans. on Ultrason. Ferro. Freq. Contr.50 (3), 214–219 (2003).
[CrossRef]

Hofer, J.

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).

Hollberg, L.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun.158, 305–312 (1998).
[CrossRef]

Horowitz, D.

A. Feldman, D. Horowitz, R. M. Waxler, and M. J. Dodge, “Optical materials characterization final technical report,” Nat. Bur. Stand. (U.S.) Tech. Note993 (1978).

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]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Self-referenced stabilization of temperature of an optomechanical microresonator,” Phys. Rev. A83, 21801 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, “Optical-RF frequency stability transformer,” Opt. Lett.36, 4527–4529 (2011).
[CrossRef] [PubMed]

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, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, “Whispering-gallery-mode resonators as frequency references. II. Stabilization,” J. Opt. Soc. Am. B24, 2988–2997 (2007).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express15, 6768–6773 (2007).
[CrossRef] [PubMed]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. V. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun.265 (1), 33–38 (2006).
[CrossRef]

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun.158, 305–312 (1998).
[CrossRef]

Ivanov, E. N.

M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
[CrossRef]

M. E. Tobar, G. L. Hamilton, E. N. Ivanov, and J. G. Hartnett, “New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization,” IEEE Trans. on Ultrason. Ferro. Freq. Contr.50 (3), 214–219 (2003).
[CrossRef]

Kersale, Y.

N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
[CrossRef]

Kippenberg, T. J.

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J. Vahala, “Feedback control of ultra-high-Q microcavities: application to micro-Raman lasers and microparametric oscillators,” Opt. Express13, 3558–3566 (2005).
[CrossRef] [PubMed]

Kolachevsky, N.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A77, 053809 (2008).
[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]

Liang, W.

Lu, Z. H.

Maleki, L.

Matsko, A. B.

Matveev, A.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A77, 053809 (2008).
[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, 97–105 (1983).
[CrossRef]

Rokhsari, H.

Savchenkov, A. A.

Schliesser, A.

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).

Schwefel, H. G. L.

Seidel, D.

Spillane, S.

Sprenger, B.

Strekalov, D.

L. Baumgartel, R. Thompson, D. Strekalov, I. Grudinin, and N. Yu, “Dual Mode Frequency Stabilization of a Whispering Gallery Mode Optical Reference Cavity,” in CLEO: Science and Innovations, OSA Technical Digest (online), CTh3A.6. (2012).

Strekalov, D. V.

D. V. Strekalov, R. J. Thompson, L. M. Baumgartel, I. S. Grudinin, and N. Yu, “Temperature measurement and stabilization in a birefringent whispering gallery mode resonator,” Opt. Express19 (15), 14495–14501 (2011).
[CrossRef] [PubMed]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. V. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun.265 (1), 33–38 (2006).
[CrossRef]

Svitlov, S.

Thompson, R.

L. Baumgartel, R. Thompson, D. Strekalov, I. Grudinin, and N. Yu, “Dual Mode Frequency Stabilization of a Whispering Gallery Mode Optical Reference Cavity,” in CLEO: Science and Innovations, OSA Technical Digest (online), CTh3A.6. (2012).

Thompson, R. J.

Tobar, M. E.

N. Boubekeur, N. Bazin, Y. Kersale, V. Giordano, J. G. Hartnett, and M. E. Tobar, “Frequency stability of Ti3+-doped whispering gallery mode sapphire resonator oscillator at 34 K,” Electronics Letters41 (9), 534–535 (2005).
[CrossRef]

M. E. Tobar, G. L. Hamilton, J. G. Hartnett, E. N. Ivanov, D. C. Dros, and P. Guillon, “The dual-mode frequency-locked technique for the characterization of the temperature coefficient of permittivity of anisotropic materials,” Meas. Sci. Tech.15 (1), 29–34 (2004).
[CrossRef]

M. E. Tobar, G. L. Hamilton, E. N. Ivanov, and J. G. Hartnett, “New method to build a high stability sapphire oscillator from the temperature compensation of the difference frequency between modes of orthogonal polarization,” IEEE Trans. on Ultrason. Ferro. Freq. Contr.50 (3), 214–219 (2003).
[CrossRef]

Udem, Th.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A77, 053809 (2008).
[CrossRef]

Vahala, K. J.

Vassiliev, V. V.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun.158, 305–312 (1998).
[CrossRef]

Velichansky, V. L.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun.158, 305–312 (1998).
[CrossRef]

Vig, J. R.

J. R. Vig, “Dual-mode oscillators for clocks and sensors,” in Ultrasonics Symposium 1999 Proceedings 1999 IEEE, 2, 859–868 (2002).

Wang, C. Y.

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A846, 011804(R) (2011).

Wang, L. J.

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]

Waxler, R. M.

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Figures (5)

Fig. 1
Fig. 1

a) MgF2 resonator used for laser frequency stabilization. Ringing in the transmission signal observed in a fast laser frequency sweep across the resonance is shown by solid blue line. The envelope of the oscillations (dashed green line) indicates an exponential field decay from the WGM within 0.4 μs, corresponding to Q ≈ 3.9×108 and a linewidth of 800 kHz. Photograph of the resonator (with radius of 2 mm) on brass mount is shown in background. b) Temperature dependence of the thermorefractive deviation of the ordinary and extraordinary indexes of refraction of magnesium fluoride. The dependencies are obtained from measurement data [18] approximated for 972 nm.

Fig. 2
Fig. 2

The experimental setup for laser stabilization to a MgF2 resonator using the PDH method, the dual-mode temperature control and comparison to an ultrastable laser locked to a mirror-based cavity on another optical table. ECDL: external cavity diode laser; EOM: electro-optic modulator; λ/2: half-wavelength retardation plate; PBS: polarizing beam splitter; PD: photodiode; PI(D): proportional-integral-(differential) feedback controller; ULE: ultralow-expansion glass; VCO: voltage controlled oscillator. LED is a one watt light emitting diode shining onto the WGM resonator and used in feedback loop for stabilization of the dual-mode frequency.

Fig. 3
Fig. 3

a) Simultaneous measurement of the resonances of the ordinarily (blue) and extraordinarily (red) polarized WGM, probed with the laser carrier and a modulation sideband, respectively. Both linewidths are dominated by the unstabilized diode laser linewidth. b) Two error signals from these orthogonally polarized crystalline WGM modes are adjusted that signals overlap at time t1 and drift away at later times due to cooling of the WGM resonator.

Fig. 4
Fig. 4

a) Drift of the dual-mode frequency versus the simultaneously measured frequency of the beat note with an independently stabilized laser, while intentionally changing temperature of the vacuum chamber. Inset shows the same dependence measured during unstabilized temperature fluctuations. The ratio of the frequency drifts (inverse slope of the linear regression) is 17.2 ± 0.3. b) Absolute Allan deviations of the dual-mode frequency and the beat note frequency for the case of small temperature variations.

Fig. 5
Fig. 5

a) Long-term WGM absolute frequency (blue solid line) and dual-mode frequency (red solid line) drifts are shown as functions of the observation time when the temperature was free-running (t < 0 h) and stabilized (t > 0 h) by the dual-mode technique. Without temperature feedback the WGM frequency drift is typically up to 10 MHz/h and with the feedback 0.3 MHz/h. Inset magnifies fluctuations of the dual-mode frequency. b) Allan deviation of the stabilized temperature in the WGM resonator according to the in-loop (dual-mode) frequency drift. Inset shows Allan deviation of the optical beat note normalized to the optical carrier at 308 THz while the dual-mode stabilization is enabled.

Equations (7)

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d f d T = f ( α n ( o , e ) + α l ( o ) ) ,
α l ( o ) = 9.3 × 10 6 ,
α n ( o ) = 0.87 × 10 6 ,
α n ( e ) = 0.33 × 10 6 .
d f d T f α l ( o ) = 2.9 GHz / K .
d d T ( f o f e ) f o ( α n ( o ) α n ( e ) ) = 0.17 GHz / K .
d d T ( f i + 1 f i ) ( f i + 1 f i ) α l ( o ) c 2 π n R α l ( o ) = 160 kHz / K .

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