Abstract

Temperature measurement with nano-Kelvin resolution is demonstrated at room temperature, based on the thermal dependence of an optical crystal anisotropy in a high quality whispering gallery mode resonator. As the resonator’s TE and TM modes frequencies have different temperature coefficients, their differential shift provides a sensitive measurement of the temperature variation, which is used for active stabilization of the temperature.

© 2011 OSA

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  1. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express 15, 6768–6773 (2007).
    [CrossRef] [PubMed]
  2. 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]
  3. 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. Express 13, 3558–3566 (2005).
    [CrossRef] [PubMed]
  4. 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]
  5. 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]
  6. J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise limited laser stabilization to a crystalline whispering-gallery-mode resonator,” arXiv:1102.4227v1, (2011).
  7. 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. B 24, 2988–2997 (2007).
    [CrossRef]
  8. 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. A 83, 021801 (2011).
    [CrossRef]
  9. M. L. Gorodetsky and A. E. Fomin, “Geometrical Theory of Whispering-Gallery Modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006).
    [CrossRef]
  10. V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24, 723–725 (1999).
    [CrossRef]
  11. A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” Laser Resonators and Beam Control VII, ed. A.V. Kudryashov and A.H. Paxton, Proc. SPIE 5333, 231–239 (2004).
    [CrossRef]
  12. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal selfstability of microcavities,” Opt. Express 12, 4742–4750 (2004).
    [CrossRef] [PubMed]
  13. P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
    [CrossRef]
  14. I. Grudinin, H. Lee, T. Chen, and K. Vahala, “Compensation of thermal nonlinearity effect in optical resonators,” Opt. Express 19, 7365–7372 (2011).
    [CrossRef] [PubMed]
  15. J. Sanjuan, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, “Thermal diagnostics front-end electronics for LISA pathfinder,” Rev. Sci. Instrum. 78, 104904 (2007).
    [CrossRef] [PubMed]

2011 (2)

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. A 83, 021801 (2011).
[CrossRef]

I. Grudinin, H. Lee, T. Chen, and K. Vahala, “Compensation of thermal nonlinearity effect in optical resonators,” Opt. Express 19, 7365–7372 (2011).
[CrossRef] [PubMed]

2010 (2)

2008 (1)

P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef]

2007 (3)

2006 (1)

M. L. Gorodetsky and A. E. Fomin, “Geometrical Theory of Whispering-Gallery Modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006).
[CrossRef]

2005 (1)

2004 (2)

A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” Laser Resonators and Beam Control VII, ed. A.V. Kudryashov and A.H. Paxton, Proc. SPIE 5333, 231–239 (2004).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal selfstability of microcavities,” Opt. Express 12, 4742–4750 (2004).
[CrossRef] [PubMed]

1999 (1)

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]

Arcizet, O.

P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef]

Carmon, T.

Chen, T.

DelHaye, P.

P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef]

Fomin, A. E.

M. L. Gorodetsky and A. E. Fomin, “Geometrical Theory of Whispering-Gallery Modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006).
[CrossRef]

A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” Laser Resonators and Beam Control VII, ed. A.V. Kudryashov and A.H. Paxton, Proc. SPIE 5333, 231–239 (2004).
[CrossRef]

Gorodetsky, M. L.

M. L. Gorodetsky and A. E. Fomin, “Geometrical Theory of Whispering-Gallery Modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006).
[CrossRef]

A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” Laser Resonators and Beam Control VII, ed. A.V. Kudryashov and A.H. Paxton, Proc. SPIE 5333, 231–239 (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.

Grudinin, I. S.

A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” Laser Resonators and Beam Control VII, ed. A.V. Kudryashov and A.H. Paxton, Proc. SPIE 5333, 231–239 (2004).
[CrossRef]

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]

Holzwarth, R.

P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[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. A 83, 021801 (2011).
[CrossRef]

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, and L. Maleki, “Optical resonators with ten million finesse,” Opt. Express 15, 6768–6773 (2007).
[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. B 24, 2988–2997 (2007).
[CrossRef]

A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” Laser Resonators and Beam Control VII, ed. A.V. Kudryashov and A.H. Paxton, Proc. SPIE 5333, 231–239 (2004).
[CrossRef]

V. S. Ilchenko, X. S. Yao, and L. Maleki, “Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery modes,” Opt. Lett. 24, 723–725 (1999).
[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]

Kippenberg, T. J.

P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[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. Express 13, 3558–3566 (2005).
[CrossRef] [PubMed]

Lee, H.

Liang, W.

Lobo, A.

J. Sanjuan, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, “Thermal diagnostics front-end electronics for LISA pathfinder,” Rev. Sci. Instrum. 78, 104904 (2007).
[CrossRef] [PubMed]

Lu, Z. H.

Maleki, L.

Matsko, A. B.

Nofrarias, M.

J. Sanjuan, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, “Thermal diagnostics front-end electronics for LISA pathfinder,” Rev. Sci. Instrum. 78, 104904 (2007).
[CrossRef] [PubMed]

Ramos-Castro, J.

J. Sanjuan, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, “Thermal diagnostics front-end electronics for LISA pathfinder,” Rev. Sci. Instrum. 78, 104904 (2007).
[CrossRef] [PubMed]

Riu, P. J.

J. Sanjuan, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, “Thermal diagnostics front-end electronics for LISA pathfinder,” Rev. Sci. Instrum. 78, 104904 (2007).
[CrossRef] [PubMed]

Rokhsari, H.

Sanjuan, J.

J. Sanjuan, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, “Thermal diagnostics front-end electronics for LISA pathfinder,” Rev. Sci. Instrum. 78, 104904 (2007).
[CrossRef] [PubMed]

Savchenkov, A. A.

Schliesser, A.

P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef]

Schwefel, H. G. L.

Seidel, D.

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. A 83, 021801 (2011).
[CrossRef]

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]

Spillane, S.

Sprenger, B.

Svitlov, S.

Vahala, K.

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]

Wang, L. J.

Yang, L.

Yao, X. S.

Yarovitsky, A. 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]

Yu, N.

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

M. L. Gorodetsky and A. E. Fomin, “Geometrical Theory of Whispering-Gallery Modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (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]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (1)

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. A 83, 021801 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

P. DelHaye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett. 101, 053903 (2008).
[CrossRef]

Proc. SPIE (1)

A. E. Fomin, M. L. Gorodetsky, I. S. Grudinin, and V. S. Ilchenko, “Nonstationary nonlinear effects in optical microspheres,” Laser Resonators and Beam Control VII, ed. A.V. Kudryashov and A.H. Paxton, Proc. SPIE 5333, 231–239 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

J. Sanjuan, A. Lobo, M. Nofrarias, J. Ramos-Castro, and P. J. Riu, “Thermal diagnostics front-end electronics for LISA pathfinder,” Rev. Sci. Instrum. 78, 104904 (2007).
[CrossRef] [PubMed]

Other (1)

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise limited laser stabilization to a crystalline whispering-gallery-mode resonator,” arXiv:1102.4227v1, (2011).

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Figures (4)

Fig. 1
Fig. 1

The experimental setup. Temperature of the brass cube on the photo is set to 76 °C and stabilized to a few hundred nanodegrees using the dual-mode stabilization technique.

Fig. 2
Fig. 2

(a) A pair of TE and TM WGMs with a small frequency detuning Δf = fo fe . (b) Temperature dependence of Δf (T) is linear with a −89.8 MHz/K slope. The inset shows a small distortion around the set point Δf (Tset ) = 0 which is due to the WGMs cross-coupling.

Fig. 3
Fig. 3

(a) The WGMs shown in Fig. 2 are brought on-resonance by temperature control. These modes have weak nonlinear coupling. (b) Another pair of modes couples strongly and is not suitable for our application.

Fig. 4
Fig. 4

The Allan variance of the temperature fluctuations in the stabilized WGM resonator in nano-Kelvin and in terms of the expected fractional frequency stability. The straight line has a slope of 0.5 μK / s1/2. The error bars are based on the measurements statistics. On the inset: the spectral density of the temperature fluctuations measured in our system (below) and the noise-equivalent temperature spectral density in [15] (above).

Equations (5)

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f n 2 π c 1 R [ L + α q ( L / 2 ) 1 / 3 ] ,
1 f d f d T + 1 n d n d T + 1 R d R d T = 0.
α n ( o ) = ( 7.14 0.04062 T ) × 10 7 K 1 , α n ( e ) = ( 3.02 0.04071 T ) × 10 7 K 1 , α l ( o ) = 9 × 10 6 K 1 ,
d d T f o , e c λ α l ( o ) 1.73 GHz / K ,
d d T Δ f = c λ ( α n ( o ) α n ( e ) ) 79.1 MHz / K .

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