Abstract

Regenerative pulsation from whispering gallery modes excited by a continuous-wave laser beam is observed in silica microspheres that feature a diminishing thermal nonlinearity near 20K. The regenerative pulsation arises from the competition between Kerr nonlinearity and the much reduced thermal nonlinearity, when the two nonlinearities with very different timescales are comparable in magnitude but opposite in sign.

© 2007 Optical Society of America

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References

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  1. R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, 1996).
    [CrossRef]
  2. For a recent review, see for example, K. J. Vahala, Nature 424, 839 (2003).
    [CrossRef] [PubMed]
  3. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
    [CrossRef] [PubMed]
  4. A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
    [CrossRef]
  5. S. Lacey and H. Wang, Opt. Lett. 26, 1943 (2001).
    [CrossRef]
  6. S. Lacey, H. Wang, D. Foster, and J. Noeckel, Phys. Rev. Lett. 91, 033902 (2003).
    [CrossRef] [PubMed]
  7. Y. S. Park, A. Cook, and H. Wang, Nano Lett. 6, 2075 (2006).
    [CrossRef] [PubMed]
  8. S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
    [CrossRef]
  9. H. Rokhsari, T. Kippenberg, T. Carmon, and K. J. Vahala, Opt. Express 13, 5293 (2005).
    [CrossRef] [PubMed]
  10. M. B. Reid and M. Ozcan, Opt. Eng. 37, 237 (1998).
    [CrossRef]
  11. G. K. White, Phys. Rev. Lett. 34, 204 (1975).
    [CrossRef]
  12. G. K. White, J. Phys. D 6, 2070 (1973).
    [CrossRef]
  13. J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
    [CrossRef]
  14. T. Carmon, L. Yang, and K. J. Vahala, Opt. Express 12, 4742 (2004).
    [CrossRef] [PubMed]
  15. R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971).
    [CrossRef]
  16. We assume that optical absorption in silica is considerably smaller at low temperature than that at room temperature.

2006 (2)

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Y. S. Park, A. Cook, and H. Wang, Nano Lett. 6, 2075 (2006).
[CrossRef] [PubMed]

2005 (2)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. Kippenberg, T. Carmon, and K. J. Vahala, Opt. Express 13, 5293 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (3)

S. Lacey, H. Wang, D. Foster, and J. Noeckel, Phys. Rev. Lett. 91, 033902 (2003).
[CrossRef] [PubMed]

S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
[CrossRef]

For a recent review, see for example, K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

2001 (1)

1998 (1)

M. B. Reid and M. Ozcan, Opt. Eng. 37, 237 (1998).
[CrossRef]

1996 (1)

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

1982 (1)

J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
[CrossRef]

1975 (1)

G. K. White, Phys. Rev. Lett. 34, 204 (1975).
[CrossRef]

1973 (1)

G. K. White, J. Phys. D 6, 2070 (1973).
[CrossRef]

1971 (1)

R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971).
[CrossRef]

Bateman, R.

S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
[CrossRef]

Campillo, A. J.

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

Carmon, T.

Chang, R. K.

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

Cook, A.

Y. S. Park, A. Cook, and H. Wang, Nano Lett. 6, 2075 (2006).
[CrossRef] [PubMed]

Del'Haye, P.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Foster, D.

S. Lacey, H. Wang, D. Foster, and J. Noeckel, Phys. Rev. Lett. 91, 033902 (2003).
[CrossRef] [PubMed]

Gibbs, H. M.

J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
[CrossRef]

Gossard, A. C.

J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
[CrossRef]

James, S. W.

S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
[CrossRef]

Jewell, J. L.

J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
[CrossRef]

Kippenberg, T.

Kippenberg, T. J.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Lacey, S.

S. Lacey, H. Wang, D. Foster, and J. Noeckel, Phys. Rev. Lett. 91, 033902 (2003).
[CrossRef] [PubMed]

S. Lacey and H. Wang, Opt. Lett. 26, 1943 (2001).
[CrossRef]

Noeckel, J.

S. Lacey, H. Wang, D. Foster, and J. Noeckel, Phys. Rev. Lett. 91, 033902 (2003).
[CrossRef] [PubMed]

Noonan, P.

S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
[CrossRef]

Nooshi, N.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Ozcan, M.

M. B. Reid and M. Ozcan, Opt. Eng. 37, 237 (1998).
[CrossRef]

Park, Y. S.

Y. S. Park, A. Cook, and H. Wang, Nano Lett. 6, 2075 (2006).
[CrossRef] [PubMed]

Pohl, R. O.

R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971).
[CrossRef]

Reid, M. B.

M. B. Reid and M. Ozcan, Opt. Eng. 37, 237 (1998).
[CrossRef]

Rokhsari, H.

H. Rokhsari, T. Kippenberg, T. Carmon, and K. J. Vahala, Opt. Express 13, 5293 (2005).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Schliesser, A.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Tarng, S. S.

J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
[CrossRef]

Tatam, R. P.

S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
[CrossRef]

Twin, A.

S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
[CrossRef]

Vahala, K. J.

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. Kippenberg, T. Carmon, and K. J. Vahala, Opt. Express 13, 5293 (2005).
[CrossRef] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, Opt. Express 12, 4742 (2004).
[CrossRef] [PubMed]

For a recent review, see for example, K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Wang, H.

Y. S. Park, A. Cook, and H. Wang, Nano Lett. 6, 2075 (2006).
[CrossRef] [PubMed]

S. Lacey, H. Wang, D. Foster, and J. Noeckel, Phys. Rev. Lett. 91, 033902 (2003).
[CrossRef] [PubMed]

S. Lacey and H. Wang, Opt. Lett. 26, 1943 (2001).
[CrossRef]

White, G. K.

G. K. White, Phys. Rev. Lett. 34, 204 (1975).
[CrossRef]

G. K. White, J. Phys. D 6, 2070 (1973).
[CrossRef]

Wiegmann, W.

J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
[CrossRef]

Yang, L.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, Opt. Express 12, 4742 (2004).
[CrossRef] [PubMed]

Zeller, R. C.

R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971).
[CrossRef]

Appl. Phys. Lett. (1)

J. L. Jewell, H. M. Gibbs, S. S. Tarng, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 40, 291 (1982).
[CrossRef]

J. Phys. D (1)

G. K. White, J. Phys. D 6, 2070 (1973).
[CrossRef]

Meas. Sci. Technol. (1)

S. W. James, R. P. Tatam, A. Twin, R. Bateman, and P. Noonan, Meas. Sci. Technol. 14, 1409 (2003).
[CrossRef]

Nano Lett. (1)

Y. S. Park, A. Cook, and H. Wang, Nano Lett. 6, 2075 (2006).
[CrossRef] [PubMed]

Nature (1)

For a recent review, see for example, K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

Opt. Eng. (1)

M. B. Reid and M. Ozcan, Opt. Eng. 37, 237 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971).
[CrossRef]

Phys. Rev. Lett. (4)

G. K. White, Phys. Rev. Lett. 34, 204 (1975).
[CrossRef]

S. Lacey, H. Wang, D. Foster, and J. Noeckel, Phys. Rev. Lett. 91, 033902 (2003).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

Other (2)

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

We assume that optical absorption in silica is considerably smaller at low temperature than that at room temperature.

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Figures (3)

Fig. 1
Fig. 1

(a) WGM spectrum near λ 632 nm for a deformed silica microsphere with a diameter of 35 μ m . The WGMs were excited near the equator with the free-space evanescent excitation technique. (b) Solid squares show the relative frequency of a WGM resonance ( λ 632 nm ) as a function of temperature. The solid line is a guide to the eye. Zero crossing of the slope of the temperature dependence occurs near 20 K .

Fig. 2
Fig. 2

Optical transmission as a function of time at T = 18.5 K when a WGM is excited by a continuous-wave laser beam. Square dots, experimental data; solid lines, theoretical calculation. The excitation power used is 2 mW for (a) and 4.5 mW for (b). For both (a) and (b), the top and bottom curves were obtained with Δ ω 0 = 0.7 γ C and Δ ω 0 = 0.3 γ C , respectively. For the theoretical calculation, the thermal relaxation rate is used as an adjustable parameter with γ T = 7.72 kHz , γ T = 7.36 kHz , γ T = 6.62 kHz , and γ T = 6.78 kHz from the top to bottom curves, respectively.

Fig. 3
Fig. 3

Schematic illustrates the shift of the cavity resonance with respect to the laser frequency through the four dynamic stages of regenerated pulsation. See text for detailed discussions.

Equations (3)

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ω ( t ) = ω 0 [ 1 ( α + 1 n 0 d n d T ) Δ T ( t ) n 2 n 0 P C ( t ) S ] ,
d Δ T ( t ) d t = γ T Δ T ( t ) + α abs C p ρ S P C ( t ) ,
d E C ( t ) d t = [ γ C 2 + i Δ ω ( t ) ] E C ( t ) + i η τ C E in ,

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