Abstract

We report an investigation of laser frequency stabilization using a whispering gallery mode resonator that is temperature stabilized by a dual-mode technique. This dual-mode technique has yielded mode volume temperature instabilities at the nK level, suggesting that high frequency stability may also be reached. Here, we experimentally and theoretically investigate the dynamics of such a system and the important factors affecting the achievable frequency stability. We calculate that the dual-mode technique can reduce the effective fractional temperature coefficient of the reference system to 3.6×10−8 K−1 within the temperature feedback bandwidth. We demonstrate a 1560 nm laser stabilized to 1.3×10−12 at 1 s and 1.1×10−10 at 1000 s, corresponding to a long-term drift of 21 kHz/hr.

© 2012 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2012 (3)

2011 (2)

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, 14495–14501 (2011).
[CrossRef] [PubMed]

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. A84, 011804 (2011).
[CrossRef]

2010 (2)

2007 (2)

2006 (1)

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
[CrossRef]

2004 (2)

1999 (1)

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. B.31, 97–105 (1983).
[CrossRef]

Alnis, J.

I. Fescenko, J. Alnis, A. Schliesser, C. Y. Wang, T. J. Kippenberg, and T. W. Hänsch, “Dual-mode temperature compensation technique for laser stabilization to a crystalline whispering gallery mode resonator,” Opt. Express20, 19185–19193 (2012).
[CrossRef] [PubMed]

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. A84, 011804 (2011).
[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,” (Optical Society of America, 2012), p. CTh3A.6.

Baumgartel, L. M.

Carmon, T.

Chen, Q.-F.

A. Chijioke, Q.-F. Chen, A. Y. Nevsky, and S. Schiller, “Thermal noise of whispering-gallery resonators,” Phys. Rev. A85, 053814 (2012).
[CrossRef]

Chijioke, A.

A. Chijioke, Q.-F. Chen, A. Y. Nevsky, and S. Schiller, “Thermal noise of whispering-gallery resonators,” Phys. Rev. A85, 053814 (2012).
[CrossRef]

Del’Haye, P.

P. Del’Haye, S. Papp, and S. Diddams, “An all-optical resonator stabilization scheme with laser machined SiO2 microresonators,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh3A.7.

Diddams, S.

P. Del’Haye, S. Papp, and S. Diddams, “An all-optical resonator stabilization scheme with laser machined SiO2 microresonators,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh3A.7.

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. B.31, 97–105 (1983).
[CrossRef]

Fescenko, I.

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. B.31, 97–105 (1983).
[CrossRef]

Gorodetsky, M. L.

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,” (Optical Society of America, 2012), p. CTh3A.6.

Grudinin, I. S.

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. B.31, 97–105 (1983).
[CrossRef]

Hänsch, T. W.

I. Fescenko, J. Alnis, A. Schliesser, C. Y. Wang, T. J. Kippenberg, and T. W. Hänsch, “Dual-mode temperature compensation technique for laser stabilization to a crystalline whispering gallery mode resonator,” Opt. Express20, 19185–19193 (2012).
[CrossRef] [PubMed]

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. A84, 011804 (2011).
[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. A84, 011804 (2011).
[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. B.31, 97–105 (1983).
[CrossRef]

Ilchenko, V. S.

Kippenberg, T. J.

I. Fescenko, J. Alnis, A. Schliesser, C. Y. Wang, T. J. Kippenberg, and T. W. Hänsch, “Dual-mode temperature compensation technique for laser stabilization to a crystalline whispering gallery mode resonator,” Opt. Express20, 19185–19193 (2012).
[CrossRef] [PubMed]

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. A84, 011804 (2011).
[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. B.31, 97–105 (1983).
[CrossRef]

Liang, W.

Lu, Z. H.

Maleki, L.

Matsko, A. B.

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. B.31, 97–105 (1983).
[CrossRef]

Nevsky, A. Y.

A. Chijioke, Q.-F. Chen, A. Y. Nevsky, and S. Schiller, “Thermal noise of whispering-gallery resonators,” Phys. Rev. A85, 053814 (2012).
[CrossRef]

Papp, S.

P. Del’Haye, S. Papp, and S. Diddams, “An all-optical resonator stabilization scheme with laser machined SiO2 microresonators,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh3A.7.

Savchenkov, A. A.

Schiller, S.

A. Chijioke, Q.-F. Chen, A. Y. Nevsky, and S. Schiller, “Thermal noise of whispering-gallery resonators,” Phys. Rev. A85, 053814 (2012).
[CrossRef]

Schliesser, A.

I. Fescenko, J. Alnis, A. Schliesser, C. Y. Wang, T. J. Kippenberg, and T. W. Hänsch, “Dual-mode temperature compensation technique for laser stabilization to a crystalline whispering gallery mode resonator,” Opt. Express20, 19185–19193 (2012).
[CrossRef] [PubMed]

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. A84, 011804 (2011).
[CrossRef]

Schmidt, E.

E. Schmidt, Thermodynamics: Principles and Applications to Engineering (Dover Publications, 1966).

Schwefel, H. G. L.

Seidel, D.

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,” (Optical Society of America, 2012), p. CTh3A.6.

Strekalov, D. V.

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,” (Optical Society of America, 2012), p. CTh3A.6.

Thompson, R. J.

Vahala, K.

Wang, C. Y.

I. Fescenko, J. Alnis, A. Schliesser, C. Y. Wang, T. J. Kippenberg, and T. W. Hänsch, “Dual-mode temperature compensation technique for laser stabilization to a crystalline whispering gallery mode resonator,” Opt. Express20, 19185–19193 (2012).
[CrossRef] [PubMed]

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. A84, 011804 (2011).
[CrossRef]

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. B.31, 97–105 (1983).
[CrossRef]

Yang, L.

Yao, X. S.

Yu, N.

Appl. Phys. B. (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. B.31, 97–105 (1983).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (3)

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. A84, 011804 (2011).
[CrossRef]

A. Chijioke, Q.-F. Chen, A. Y. Nevsky, and S. Schiller, “Thermal noise of whispering-gallery resonators,” Phys. Rev. A85, 053814 (2012).
[CrossRef]

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A74, 063806 (2006).
[CrossRef]

Other (3)

P. Del’Haye, S. Papp, and S. Diddams, “An all-optical resonator stabilization scheme with laser machined SiO2 microresonators,” in “CLEO: Science and Innovations,” (Optical Society of America, 2012), p. CTh3A.7.

E. Schmidt, Thermodynamics: Principles and Applications to Engineering (Dover Publications, 1966).

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,” (Optical Society of America, 2012), p. CTh3A.6.

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Figures (4)

Fig. 1
Fig. 1

The experimental setup. (a) Schematic of the optical system and stabilization loops. Each proportional-integrator (PI) loop has both a slow and fast actuation branch. Polarization controller (PC) allows for control of excitation ratio between the two modes. (b) Photo of the resonator-TEM assembly. (c) Scope traces of the detector and PDH error signals as the laser is swept over the orthogonal mode pair; modulation frequency is 1 MHz.

Fig. 2
Fig. 2

FEM simulation. (a) Model setup showing the mesh, materials, a detail of the mode volume (pink region), and the line along which temperature and strain are plotted (dashed orange). BiTe: bismuth telluride. (b) Temperature map results showing how different gradients exist for different relative strengths of heat sources. Plots of temperature (c) and radial deformation (d) along the disc radius for T2 = T1 (solid red) and T2 = T1 + 50 mK (dashed blue), showing how the latter distribution is cooler in the center, contracting the disc radius by ≈6 pm.

Fig. 3
Fig. 3

Effect of environmental temperature: Time series (a) showing shift in optical frequency (Δfopt) and heat delivered to the resonator by the TEM as enclosure temperature changes in 12 mK steps. Inset shows mode volume temperature from the in-loop error signal; aside from spikes at the temperature steps, it remains extremely stable. The multidimensional relationship between parameters is shown in (b). T2T1 is the drift in enclosure temperature. Triangles are data from (a) averaged over 360 s bins. The isotherm is a fit to these data (solid blue line), while the slope of its projection onto the temperature-frequency axis (dashed red line) yields the effective frequency coefficient of 25.5 kHz/mK.

Fig. 4
Fig. 4

Overlapping Allan deviation of a laser locked to the WGMR cavity, as compared to the frequency comb, under nominally identical conditions except that the dual-mode loop is closed (blue triangles) or open (red circles). Significant improvement is observed for time scales > 100 ms. Inset: Time sequences of the data run showing frequency excursions for the dual-mode (blue, left scale) and free-running (red, right scale) resonator, showing periodic oscillation from the enclosure’s analog temperature controller.

Equations (2)

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q rad = σ 1 / ε 1 + A 1 / A 2 ( 1 / ε 2 1 ) ( T 1 4 T 2 4 ) ,
q laser = I η Q Q abs

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