Abstract

We report experimental observations of power-dependent, nonexponential decay of light stored in whispering gallery modes caused by stimulated Raman scattering in the resonator host material. Specifically, we show that the instantaneous decay rate of whispering gallery modes of a calcium fluoride resonator increases as the amount of light stored in the resonator decreases.

© 2007 Optical Society of America

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References

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  1. R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
    [CrossRef]
  2. S.-X. Qian, J. B. Snow, and R. K. Chang, Opt. Lett. 10, 499 (1985).
    [CrossRef] [PubMed]
  3. H. B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
    [CrossRef] [PubMed]
  4. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
    [CrossRef] [PubMed]
  5. T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 10, 1219 (2004).
    [CrossRef]
  6. A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Commun. 260, 662 (2006).
    [CrossRef]
  7. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
    [CrossRef]
  8. J. P. Russel, Proc. Phys. Soc. London 85, 194 (1965).
    [CrossRef]
  9. A. R. Gee, D. C. O'Shea, and H. Z. Cummins, Solid State Commun. 4, 43 (1965).
    [CrossRef]
  10. V. G. Keramidas and W. B. White, J. Chem. Phys. 59, 1561 (1973).
    [CrossRef]

2006

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Commun. 260, 662 (2006).
[CrossRef]

2004

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 10, 1219 (2004).
[CrossRef]

2002

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

1994

H. B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
[CrossRef] [PubMed]

1985

1980

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

1973

V. G. Keramidas and W. B. White, J. Chem. Phys. 59, 1561 (1973).
[CrossRef]

1965

J. P. Russel, Proc. Phys. Soc. London 85, 194 (1965).
[CrossRef]

A. R. Gee, D. C. O'Shea, and H. Z. Cummins, Solid State Commun. 4, 43 (1965).
[CrossRef]

Barber, P. W.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Campillo, A. J.

H. B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
[CrossRef] [PubMed]

Chang, R. K.

S.-X. Qian, J. B. Snow, and R. K. Chang, Opt. Lett. 10, 499 (1985).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Cummins, H. Z.

A. R. Gee, D. C. O'Shea, and H. Z. Cummins, Solid State Commun. 4, 43 (1965).
[CrossRef]

Gee, A. R.

A. R. Gee, D. C. O'Shea, and H. Z. Cummins, Solid State Commun. 4, 43 (1965).
[CrossRef]

Ilchenko, V. S.

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Keramidas, V. G.

V. G. Keramidas and W. B. White, J. Chem. Phys. 59, 1561 (1973).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 10, 1219 (2004).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

Lin, H. B.

H. B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
[CrossRef] [PubMed]

Maleki, L.

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Commun. 260, 662 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Commun. 260, 662 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Min, B.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 10, 1219 (2004).
[CrossRef]

O'Shea, D. C.

A. R. Gee, D. C. O'Shea, and H. Z. Cummins, Solid State Commun. 4, 43 (1965).
[CrossRef]

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Qian, S.-X.

Russel, J. P.

J. P. Russel, Proc. Phys. Soc. London 85, 194 (1965).
[CrossRef]

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Commun. 260, 662 (2006).
[CrossRef]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Snow, J. B.

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 10, 1219 (2004).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

Vahala, K. J.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 10, 1219 (2004).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

White, W. B.

V. G. Keramidas and W. B. White, J. Chem. Phys. 59, 1561 (1973).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, IEEE J. Sel. Top. Quantum Electron. 10, 1219 (2004).
[CrossRef]

J. Chem. Phys.

V. G. Keramidas and W. B. White, J. Chem. Phys. 59, 1561 (1973).
[CrossRef]

Nature

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

Opt. Commun.

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Commun. 260, 662 (2006).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Phys. Rev. Lett.

H. B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
[CrossRef] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Proc. Phys. Soc. London

J. P. Russel, Proc. Phys. Soc. London 85, 194 (1965).
[CrossRef]

Solid State Commun.

A. R. Gee, D. C. O'Shea, and H. Z. Cummins, Solid State Commun. 4, 43 (1965).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Scheme of the experimental setup. (A) The frequency of a continuous-wave Nd:YAG laser was slowly swept across the free spectral range of the resonator. When coupling of the light to a WGM exceeded 30%, the light was abruptly switched off with an electro-optic modulator triggered by an oscilloscope. In this configuration critical coupling (all light is entering the resonator) corresponds to zero signal on the photodiode, while zero coupling corresponds to the maximum signal on the photodiode. (B) The light exiting the resonator was collimated and geometrically separated from the Stokes light.

Fig. 2
Fig. 2

Typical ringdown characteristics of the fluorite WGM resonator. Solid curve, experimental observation; dotted curve, simulation based on the theoretical analysis developed in Ref. [6]. To find the initial as well as final Q factor, we have approximated a selected section of the ringdown curve with an exponent. Using the decay time inferred from the exponent ( T 1 and T 2 are the initial and final instantaneous decay times, respectively), we have derived the initial and final instantaneous Q factors ( Q = 2 π c T λ ) .

Fig. 3
Fig. 3

Decrease of the light power emitted by the resonator mode with time. The curves were taken by finding the beat note (see inset) maxima and minima. Inset, typical ringdown characteristic of the fluorite WGM resonator when the frequency of the pump laser is scanned through a selected WGM. The solid red line shows the exponential decay fit of the start and end of the ringdown signal. Rates T 1 and T 2 describe the corresponding power decay rates of the resonator.

Fig. 4
Fig. 4

Spectrum of light exiting the Raman-active WGM resonator. Inset, structure of the Stokes line. The wavelength difference between the peaks shown in the inset corresponds to the free spectral range of the resonator.

Equations (1)

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P ( t ) P th = P out ( t ) P th + ξ P S out ( t ) P th = P in P th e 2 γ t ( 1 ξ ) 1 + ( P in P th 1 ) exp [ P in P th ( 1 e 2 γ t ) ] + ξ P in P th e 2 γ t ,

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