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

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).
7. 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]
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]
9. A. B. Matsko, A. A. Savchenkov, N. Yu, and L. Maleki, “Whispering-gallery-mode resonators as frequency references. I. Fundamental limitations,” J. Opt. Soc. Am. B24, 1324–1335 (2007). [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]

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]

Electronics Letters

• 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]

IEEE Trans. on Ultrason. Ferro. Freq. Contr.

• 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]

J. Opt. Soc. Am. B

• 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. B. Matsko, A. A. Savchenkov, N. Yu, and L. Maleki, “Whispering-gallery-mode resonators as frequency references. I. Fundamental limitations,” J. Opt. Soc. Am. B24, 1324–1335 (2007). [CrossRef]
• M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B21, 697–705 (2004). [CrossRef]

Meas. Sci. Tech.

• 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]

Nat. Bur. Stand. (U.S.) Tech. Note

• 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).

Opt. Commun.

• 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]
• 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]

Opt. Express

• 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]
• 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]
• 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]

Opt. Lett.

• 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]
• 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. 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]

Phys. Rev. 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).
• 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]
• 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]

Ultrasonics Symposium 1999 Proceedings 1999 IEEE

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

Other

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

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