Abstract

As stability and continuous operation are important for almost any use of a microcavity, we demonstrate here experimentally and theoretically a self-stable equilibrium solution for a pump-microcavity system. In this stable equilibrium, intensity- and wavelength-perturbations cause a small thermal resonant-drift that is enough to compensate for the perturbation (noises); consequently the cavity stays warm and loaded as perturbations are self compensated. We also compare here, our theoretical prediction for the thermal line broadening (and for the wavelength hysteretic response) to experimental results.

© 2004 Optical Society of America

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  1. V. B. Braginsky, M. L. Gordetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393 (1989)
    [CrossRef]
  2. V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt Lett 26, 256, (2001).
    [CrossRef]
  3. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, ““Ultra-high-Q toroid microcavity on a chip”,” Nature 421, 925 (2003).
    [CrossRef] [PubMed]
  4. M.L. Gorodetsky and V.S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B. 16, 147 (1999).
    [CrossRef]
  5. B.E. Little, J. P. Laine, and H.A. Haus. “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17, 704 (1999).
    [CrossRef]
  6. V. B. Braginsky, Y.I. Vorontsov, and K.S. Thorne, “Quantum non-demolition measurements,” Science,  209, 47 (1980).
  7. V. B. Braginskii and V. S. Il’chenko, Dokl. Akad. Nauk SSSR,  293, 1358 (1987).
  8. D. F. Walls and G. Milburn, Quantum Optics, (Springer, New York, 1994).
  9. M. Scully and M. Zubairy, Quantum Optics, (Cambridge,1996).
  10. Bouwmeester, A. Ekert, and A. Zeilinger, “The Physics of Quantum Information,” (Heidelberg, 2000).
  11. S. M. Spillance, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature,  415, 621 (2002).
    [CrossRef]
  12. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
    [CrossRef]
  13. F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
    [CrossRef] [PubMed]
  14. Lan Yang, D. K. Armani, and K. J. Vahalab, “Fiber-coupled Erbium Microlasers on a chip,” Appl. Phys. Lett,  83, 825 (2003).
    [CrossRef]
  15. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity induced optical parametric oscillation in a ultra-high-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
    [CrossRef] [PubMed]
  16. V. Lefevre-Seguin and S. Haroche, “Towards cavity-QED experiments with silica microspheres,” Mater. Sci. Eng. B 48, 53–58 (1997).
    [CrossRef]
  17. D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
    [CrossRef]
  18. F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
    [CrossRef]
  19. A. Serpenguzel, S. Arnold, and G. Griffel, “Excitation of resonances of microspheres on an optical fiber,” Opt. Lett. 20, 654–656 (1995).
    [CrossRef] [PubMed]
  20. R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, (World Scientific, Singapore, 1996).
  21. V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004 (1992).
  22. F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).
  23. To be precise, while heat convection is proportional to the surface area (l2), heat conduction is proportional to the area divided by the pass length (l2/l=l). Since both convection and conduction contribute here, the precise scaling is ΔT ∝ l ÷ l2. Being very precise, one should also consider the fact that light wavelength is usually not scaled down and hence the mode volume scaling is actually slightly smaller than l3.
  24. David N. Nikogosyan, Properties of Optical and Laser Related Materials A Handbook, (John Wiley & Son, 1997).
  25. M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B 21, 697, (2004).
    [CrossRef]
  26. In this case one should use:Cp1ΔT˙1(t)=Ih1(λp−λ0(1+a(ΔT1(t)+ΔT2(t)))Δλ2)2+1−K1ΔT1(t)Cp2ΔT˙2(t)=K1ΔT1(t)−K2ΔT2(t),where the first equation describes heat dissipation from the mode volume to the cavity structure and the second equation describes heat dissipation from the cavity structure to the surrounding. Here Cp1 is the thermal capacity of the mode volume, Cp2 is the thermal capacity of the cavity structure, K1 is the thermal conductivity between the mode volume and the rest of the cavity, K2 is the thermal conductivity between the cavity and the surrounding, ΔT1 is the temperature difference between the mode volume and the rest of the cavity and ΔT2 is the temperature difference between the cavity and the surrounding.
  27. T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

2004 (2)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity induced optical parametric oscillation in a ultra-high-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B 21, 697, (2004).
[CrossRef]

2003 (2)

Lan Yang, D. K. Armani, and K. J. Vahalab, “Fiber-coupled Erbium Microlasers on a chip,” Appl. Phys. Lett,  83, 825 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, ““Ultra-high-Q toroid microcavity on a chip”,” Nature 421, 925 (2003).
[CrossRef] [PubMed]

2002 (2)

S. M. Spillance, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature,  415, 621 (2002).
[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

2001 (1)

V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt Lett 26, 256, (2001).
[CrossRef]

1999 (2)

M.L. Gorodetsky and V.S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B. 16, 147 (1999).
[CrossRef]

B.E. Little, J. P. Laine, and H.A. Haus. “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17, 704 (1999).
[CrossRef]

1998 (2)

D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

1997 (1)

V. Lefevre-Seguin and S. Haroche, “Towards cavity-QED experiments with silica microspheres,” Mater. Sci. Eng. B 48, 53–58 (1997).
[CrossRef]

1996 (1)

F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

1995 (1)

1992 (2)

V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004 (1992).

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

1989 (1)

V. B. Braginsky, M. L. Gordetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393 (1989)
[CrossRef]

1987 (1)

V. B. Braginskii and V. S. Il’chenko, Dokl. Akad. Nauk SSSR,  293, 1358 (1987).

1980 (1)

V. B. Braginsky, Y.I. Vorontsov, and K.S. Thorne, “Quantum non-demolition measurements,” Science,  209, 47 (1980).

Armani, D. K.

Lan Yang, D. K. Armani, and K. J. Vahalab, “Fiber-coupled Erbium Microlasers on a chip,” Appl. Phys. Lett,  83, 825 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, ““Ultra-high-Q toroid microcavity on a chip”,” Nature 421, 925 (2003).
[CrossRef] [PubMed]

Arnold, S.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

A. Serpenguzel, S. Arnold, and G. Griffel, “Excitation of resonances of microspheres on an optical fiber,” Opt. Lett. 20, 654–656 (1995).
[CrossRef] [PubMed]

Bouwmeester,

Bouwmeester, A. Ekert, and A. Zeilinger, “The Physics of Quantum Information,” (Heidelberg, 2000).

Braginskii, V. B.

V. B. Braginskii and V. S. Il’chenko, Dokl. Akad. Nauk SSSR,  293, 1358 (1987).

Braginsky, V. B.

V. B. Braginsky, M. L. Gordetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393 (1989)
[CrossRef]

V. B. Braginsky, Y.I. Vorontsov, and K.S. Thorne, “Quantum non-demolition measurements,” Science,  209, 47 (1980).

Braun, D.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

Campillo, A. J.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, (World Scientific, Singapore, 1996).

Carmon, T.

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

Chang, R. K.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, (World Scientific, Singapore, 1996).

Ekert, A.

Bouwmeester, A. Ekert, and A. Zeilinger, “The Physics of Quantum Information,” (Heidelberg, 2000).

Furusawa, A.

D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Georgiades, N. P.

D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Gordetsky, M. L.

V. B. Braginsky, M. L. Gordetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393 (1989)
[CrossRef]

Gorodetskii, M. L.

V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004 (1992).

Gorodetsky, M. L.

Gorodetsky, M.L.

V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt Lett 26, 256, (2001).
[CrossRef]

M.L. Gorodetsky and V.S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B. 16, 147 (1999).
[CrossRef]

Griffel, G.

Grudinin, I. S.

Hare, J.

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Haroche, - S.

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

Haroche, S.

V. Lefevre-Seguin and S. Haroche, “Towards cavity-QED experiments with silica microspheres,” Mater. Sci. Eng. B 48, 53–58 (1997).
[CrossRef]

F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Haus, H.A.

Il’chenko, V. S.

V. B. Braginskii and V. S. Il’chenko, Dokl. Akad. Nauk SSSR,  293, 1358 (1987).

Ilchenko, V. S.

D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

V. S. Ilchenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004 (1992).

V. B. Braginsky, M. L. Gordetsky, and V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393 (1989)
[CrossRef]

Ilchenko, V.S.

V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt Lett 26, 256, (2001).
[CrossRef]

M.L. Gorodetsky and V.S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B. 16, 147 (1999).
[CrossRef]

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

Khoshsima, M.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

Kimble, H. J.

D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity induced optical parametric oscillation in a ultra-high-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, ““Ultra-high-Q toroid microcavity on a chip”,” Nature 421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillance, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature,  415, 621 (2002).
[CrossRef]

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

Laine, J. P.

Lefevre-Seguin, V.

V. Lefevre-Seguin and S. Haroche, “Towards cavity-QED experiments with silica microspheres,” Mater. Sci. Eng. B 48, 53–58 (1997).
[CrossRef]

Lefèvre-Seguin, V.

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Libchaber, A.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

Little, B.E.

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Maleki, L.

V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt Lett 26, 256, (2001).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Milburn, G.

D. F. Walls and G. Milburn, Quantum Optics, (Springer, New York, 1994).

Nikogosyan, David N.

David N. Nikogosyan, Properties of Optical and Laser Related Materials A Handbook, (John Wiley & Son, 1997).

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Raimond, J.-M.

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

Raimond,, J. -M.

F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Roch, J.-F.

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

Rokhsari, H.

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

Scully, M.

M. Scully and M. Zubairy, Quantum Optics, (Cambridge,1996).

Serpenguzel, A.

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Spillance, S. M.

S. M. Spillance, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature,  415, 621 (2002).
[CrossRef]

Spillane, S.

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity induced optical parametric oscillation in a ultra-high-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, ““Ultra-high-Q toroid microcavity on a chip”,” Nature 421, 925 (2003).
[CrossRef] [PubMed]

Teraoka, I.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

Thorne, K.S.

V. B. Braginsky, Y.I. Vorontsov, and K.S. Thorne, “Quantum non-demolition measurements,” Science,  209, 47 (1980).

Treussart, F.

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Vahala, K. J,

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity induced optical parametric oscillation in a ultra-high-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, ““Ultra-high-Q toroid microcavity on a chip”,” Nature 421, 925 (2003).
[CrossRef] [PubMed]

S. M. Spillance, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature,  415, 621 (2002).
[CrossRef]

Vahalab, K. J.

Lan Yang, D. K. Armani, and K. J. Vahalab, “Fiber-coupled Erbium Microlasers on a chip,” Appl. Phys. Lett,  83, 825 (2003).
[CrossRef]

Vernooy, D.W.

D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Vollmer, F.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

Vorontsov, Y.I.

V. B. Braginsky, Y.I. Vorontsov, and K.S. Thorne, “Quantum non-demolition measurements,” Science,  209, 47 (1980).

Walls, D. F.

D. F. Walls and G. Milburn, Quantum Optics, (Springer, New York, 1994).

Yang, L.

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

Yang, Lan

Lan Yang, D. K. Armani, and K. J. Vahalab, “Fiber-coupled Erbium Microlasers on a chip,” Appl. Phys. Lett,  83, 825 (2003).
[CrossRef]

Yao, X.S.

V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt Lett 26, 256, (2001).
[CrossRef]

Zeilinger, A.

Bouwmeester, A. Ekert, and A. Zeilinger, “The Physics of Quantum Information,” (Heidelberg, 2000).

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M. Scully and M. Zubairy, Quantum Optics, (Cambridge,1996).

Appl. Phys. Lett (1)

Lan Yang, D. K. Armani, and K. J. Vahalab, “Fiber-coupled Erbium Microlasers on a chip,” Appl. Phys. Lett,  83, 825 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

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[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold. “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057–4059 (2002).
[CrossRef]

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V. B. Braginskii and V. S. Il’chenko, Dokl. Akad. Nauk SSSR,  293, 1358 (1987).

Eur. Phys. J. D. (1)

F. Treussart, V.S. Ilchenko, J.-F. Roch, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and - S. Haroche. “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D. 1, 235–238 (1998).

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

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

M.L. Gorodetsky and V.S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B. 16, 147 (1999).
[CrossRef]

Laser Phys. (1)

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Nature (2)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, ““Ultra-high-Q toroid microcavity on a chip”,” Nature 421, 925 (2003).
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[CrossRef]

Opt Lett (1)

V.S. Ilchenko, M.L. Gorodetsky, X.S. Yao, and L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt Lett 26, 256, (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

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D.W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

F. Treussart, J. Hare, V. Lefèvre-Seguin, J. -M. Raimond,, and S. Haroche. “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
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T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity induced optical parametric oscillation in a ultra-high-Q toroid microcavity,” Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef] [PubMed]

Science (1)

V. B. Braginsky, Y.I. Vorontsov, and K.S. Thorne, “Quantum non-demolition measurements,” Science,  209, 47 (1980).

Other (8)

D. F. Walls and G. Milburn, Quantum Optics, (Springer, New York, 1994).

M. Scully and M. Zubairy, Quantum Optics, (Cambridge,1996).

Bouwmeester, A. Ekert, and A. Zeilinger, “The Physics of Quantum Information,” (Heidelberg, 2000).

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities, (World Scientific, Singapore, 1996).

In this case one should use:Cp1ΔT˙1(t)=Ih1(λp−λ0(1+a(ΔT1(t)+ΔT2(t)))Δλ2)2+1−K1ΔT1(t)Cp2ΔT˙2(t)=K1ΔT1(t)−K2ΔT2(t),where the first equation describes heat dissipation from the mode volume to the cavity structure and the second equation describes heat dissipation from the cavity structure to the surrounding. Here Cp1 is the thermal capacity of the mode volume, Cp2 is the thermal capacity of the cavity structure, K1 is the thermal conductivity between the mode volume and the rest of the cavity, K2 is the thermal conductivity between the cavity and the surrounding, ΔT1 is the temperature difference between the mode volume and the rest of the cavity and ΔT2 is the temperature difference between the cavity and the surrounding.

T. Carmon, T. J. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. J, Vahala, “Power locked and wavelength locked ultra-high-Q optical microcavities,” Submitted to Appl. Phys. Lett. (Aug, 2004).

To be precise, while heat convection is proportional to the surface area (l2), heat conduction is proportional to the area divided by the pass length (l2/l=l). Since both convection and conduction contribute here, the precise scaling is ΔT ∝ l ÷ l2. Being very precise, one should also consider the fact that light wavelength is usually not scaled down and hence the mode volume scaling is actually slightly smaller than l3.

David N. Nikogosyan, Properties of Optical and Laser Related Materials A Handbook, (John Wiley & Son, 1997).

Supplementary Material (2)

» Media 1: MOV (2352 KB)     
» Media 2: MOV (6463 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Dynamical thermal behavior of a toroidal microcavity (a) As the pump makes a 46 Å/s wavelength scan (upper red) it approaches the cavity resonance (upper blue) and cause a thermal drift of the resonance line. In the upper plot, the right ordinate describes the temperature of the mode volume relative to the ambient temperature and the left ordinate gives the pump wavelength and cavity resonance wavelength (relative to the cold resonance). The pump-cavity transmission is presented as a function of time (middle) and as a function of the pump wavelength (bottom). Here blue dots represent experimentally measured data and lines stand for calculations. The parameters used for the fit are Ih /K=7.16°C and Ih /Cp =18000 °C/s. The cold resonance wavelength of the microcavity is λ 0 =1545nm and its quality factor is Q = 2×107, the pump power was 1.8 mW. (b) To emphasize fine details, we repeat the same calculation but using a reduced Q (Q = 5×105), For convenience, the cavity FWHM is marked on the cavity resonance wavelength (top blue).

Fig. 2.
Fig. 2.

(2.4 MB) Movie of the cavity wavelength response (6.6 MB version). The scanning-pump (red) induces thermal drift of the resonant lineshape (blue). The intersection point between the pump line and the cavity Lorentzian draws the hysteretic absorption (black). Parameters here are identical to the parameters in Fig. 1(b). The movie is in slow motion as each scan cycle truly takes 80 ms

Fig. 3
Fig. 3

Equilibrium solutions: (a) Presented are the resonant thermal wavelength-drift (left ordinate) and the cavity temperature (right ordinate, relative to the ambient temperature) at equilibrium for various values of pump wavelength (horizontal axis). The 3 distinct equilibrium regimes are color coded. On the right (b, c, and d), we illustrate a solution-triplet for the pump position shown in the left panel. (Parameters are as in Fig. 1(b))

Fig. 4.
Fig. 4.

Numerical calculation of dynamical noise response at equilibrium. (a) Warm stable-equilibrium: The stable warm equilibrium is reached by an upward wavelength scan, stopping at a pump wavelength of 0.56 angstrom above the cold resonance. In this equilibrium, the system overcomes Gaussian noise in the pump wavelength (with amplitude of one cavity width). The noise spectra is of random amplitude and spread Gaussianly in the Fourier space having FWHM of 100 KHz around the DC. (b) Unstable warm equilibrium: Starting in the unstable warm equilibrium (pump wavelength 0.56 angstrom and cavity thermal-drifted resonance 0.52 angstrom above the cold resonance), the smallest positive noise will take the system to the warm stable-equilibrium; while the smallest negative noise will take the system to the cold stable-equilibrium. Noise here is smaller than 1/1010 of the cavity FWHM. In this figure all parameters are as in Fig 1(b) (except for the pump wavelength), Figs. 2 and 3. All temperatures are relative to the ambient temperature and all wavelengths are relative to the cold cavity resonance.

Fig. 5.
Fig. 5.

The wavelength response for a slow scan (0.002 Å/s) possesses a stable, warm equilibrium during the upward wavelength scan. A fast pass through resonance occurs during the downward wavelength scan (note that we zoom in here and show only a fraction of the wavelength scan). When in the warm stable equilibrium (in a region near 20 s in the scan), the system can recover from a perturbation as shown in the inset. We used a spherical cavity with a diameter of 0.26mm and Q = 2×106.

Equations (7)

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N = 2 πr c 1 ( 1 + ε Δ T ) λ r ( n 0 + dn dT Δ T )
λ r ( Δ T ) λ 0 [ 1 + ( ε + dn dT n 0 ) Δ T ]
λ 0 ( 1 + a Δ T ) .
q ˙ in = I η Q Q abs 1 ( λ p λ r Δ λ 2 ) 2 + 1 I h 1 ( λ p λ 0 ( 1 + a Δ T ) Δ λ 2 ) 2 + 1
Cp Δ T ˙ ( t ) = q ˙ in q ˙ out
= I h 1 ( λ p λ 0 ( 1 + a Δ T ) Δ λ 2 ) 2 + 1 K Δ T ( t ) .
0 = I h 1 ( λ p λ 0 ( 1 + a Δ T ) Δ λ 2 ) 2 + 1 K Δ T .

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