Abstract

Measurements of the quality factor Q8×109 are reported for the whispering-gallery modes (WGM's) of quartz microspheres for the wavelengths 670, 780, and 850  nm; these results correspond to finesse F2.2×106. The observed independence of Q from wavelength indicates that losses for the WGM's are dominated by a mechanism other than bulk absorption in fused silica in the near infrared. Data obtained by atomic force microscopy combined with a simple model for surface scattering suggest that Q can be limited by residual surface inhomogeneities. Absorption by absorbed water can also explain why the material limit is not reached at longer wavelengths in the near infrared.

© 1998 Optical Society of America

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References

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    [Crossref] [PubMed]
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1996 (2)

H. Mabuchi, Q. A. Turchette, M. S. Chapman, and H. J. Kimble, Opt. Lett. 21, 1393 (1996).
[Crossref] [PubMed]

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Maroche, Phys. Rev. A 54, R1777 (1996).
[Crossref]

1995 (3)

1994 (3)

1993 (1)

L. Collot, V. Lefèvre-Seguin, M. Brune, J.-M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[Crossref]

1992 (3)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1992).
[Crossref]

G. Rempe, R. J. Thompson, H. J. Kimble, and R. Lalezari, Opt. Lett. 17, 363 (1992).
[Crossref] [PubMed]

M. L. Gorodetsky and V. S. Ilchenko, Laser Phys. 2, 1004 (1992).

1987 (1)

V. B. Braginsky and V. S. Ilchenko, Sov. Phys. Dokl. 32, 307 (1987).

1973 (1)

Arnold, S.

A. Serpengüzel, S. Arnold, and G. Griffel, Opt. Lett. 20, 654 (1995).
[Crossref]

G. Griffel, A. Serpengüzel, and S. Arnold, 1995 IEEE Symposium on Frequency Control (Institute of Electrical and Electronics Engineers, New York, 1995).

Benner, R. E.

S. C. Hill and R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1992).
[Crossref]

V. B. Braginsky and V. S. Ilchenko, Sov. Phys. Dokl. 32, 307 (1987).

Brune, M.

L. Collot, V. Lefèvre-Seguin, M. Brune, J.-M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[Crossref]

Chapman, M. S.

Collot, L.

Gorodetsky, M. L.

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, Opt. Lett. 21, 453 (1995).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, Opt. Commun. 113, 133 (1994).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, Laser Phys. 2, 1004 (1992).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1992).
[Crossref]

Griffel, G.

A. Serpengüzel, S. Arnold, and G. Griffel, Opt. Lett. 20, 654 (1995).
[Crossref]

G. Griffel, A. Serpengüzel, and S. Arnold, 1995 IEEE Symposium on Frequency Control (Institute of Electrical and Electronics Engineers, New York, 1995).

Hale, G. M.

Hare, J.

Haroche, S.

Hill, S. C.

S. C. Hill and R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

Ilchenko, V. S.

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, Opt. Lett. 21, 453 (1995).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, Opt. Commun. 113, 133 (1994).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, Laser Phys. 2, 1004 (1992).

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1992).
[Crossref]

V. B. Braginsky and V. S. Ilchenko, Sov. Phys. Dokl. 32, 307 (1987).

Kimble, H. J.

Lalezari, R.

Lefèvre, V.

Lefèvre-Seguin, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Maroche, Phys. Rev. A 54, R1777 (1996).
[Crossref]

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, Opt. Lett. 20, 1835 (1995).
[Crossref] [PubMed]

L. Collot, V. Lefèvre-Seguin, M. Brune, J.-M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[Crossref]

Lin, C.

C. Lin, in Handbook of Microwave and Optical Components, K. Chang, ed. (Wiley, New York, 1991), p. 11.

Mabuchi, H.

Maroche, S.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Maroche, Phys. Rev. A 54, R1777 (1996).
[Crossref]

Querry, M. R.

Raimond, J. M.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Maroche, Phys. Rev. A 54, R1777 (1996).
[Crossref]

F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. Sandoghdar, J. M. Raimond, and S. Haroche, Opt. Lett. 19, 1651 (1994).
[Crossref] [PubMed]

Raimond, J.-M.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, Opt. Lett. 20, 1835 (1995).
[Crossref] [PubMed]

L. Collot, V. Lefèvre-Seguin, M. Brune, J.-M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[Crossref]

Rempe, G.

Sandoghdar, V.

Savchenkov, A. A.

Serpengüzel, A.

A. Serpengüzel, S. Arnold, and G. Griffel, Opt. Lett. 20, 654 (1995).
[Crossref]

G. Griffel, A. Serpengüzel, and S. Arnold, 1995 IEEE Symposium on Frequency Control (Institute of Electrical and Electronics Engineers, New York, 1995).

Thompson, R. J.

Treussart, F.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Maroche, Phys. Rev. A 54, R1777 (1996).
[Crossref]

F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. Sandoghdar, J. M. Raimond, and S. Haroche, Opt. Lett. 19, 1651 (1994).
[Crossref] [PubMed]

Turchette, Q. A.

Unger, H. G.

H. G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), p. 130.

Weiss, D. S.

Appl. Opt. (1)

Europhys. Lett. (1)

L. Collot, V. Lefèvre-Seguin, M. Brune, J.-M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[Crossref]

Laser Phys. (1)

M. L. Gorodetsky and V. S. Ilchenko, Laser Phys. 2, 1004 (1992).

Opt. Commun. (1)

M. L. Gorodetsky and V. S. Ilchenko, Opt. Commun. 113, 133 (1994).
[Crossref]

Opt. Lett. (7)

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, Phys. Lett. A 137, 393 (1992).
[Crossref]

Phys. Rev. A (1)

V. Sandoghdar, F. Treussart, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Maroche, Phys. Rev. A 54, R1777 (1996).
[Crossref]

Sov. Phys. Dokl. (1)

V. B. Braginsky and V. S. Ilchenko, Sov. Phys. Dokl. 32, 307 (1987).

Other (5)

H. J. Kimble, in Cavity Quantum Electrodynamics, P. R. Berman, ed., Supplement 2 of Advances in Atomic, Molecular and Optical Physics (Academic, San Diego, Calif., 1994), pp. 203–266.

G. Griffel, A. Serpengüzel, and S. Arnold, 1995 IEEE Symposium on Frequency Control (Institute of Electrical and Electronics Engineers, New York, 1995).

S. C. Hill and R. E. Benner, in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

C. Lin, in Handbook of Microwave and Optical Components, K. Chang, ed. (Wiley, New York, 1991), p. 11.

H. G. Unger, Planar Optical Waveguides and Fibres (Clarendon, Oxford, 1977), p. 130.

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Figures (4)

Fig. 1
Fig. 1

The highest Q values measured at 670, 780, and 850  nm are shown, along with the wavelength dependencies for Qmat limited by intrinsic material absorption (solid curve), Qss for surface scattering (the shaded region shows a bound with AFM surface data), and Qw for an adsorbed layer of water (dashed curve). The point at 633  nm is from Ref.  11.

Fig. 2
Fig. 2

Surface data obtained by AFM on a 20-nm square grid of 256×256 points show a rms roughness σ2 nm.

Fig. 3
Fig. 3

(a) Correlation function Ru and (b) estimate of its Fourier transform, the power spectral density Pk, shown after averaging over 256 scans on a 20-nm square grid, as explained in the text. Both support the identification of the correlation length B5 nm.

Fig. 4
Fig. 4

The highest Q values measured in spheres of diameter D at 670  nm. The dependence QssD1/2 (solid curve) is suggested by relation  (1).

Equations (2)

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Qss3ϵϵ+224π3ϵ-15/2λ7/2D1/2σ2B2.
Qwπ8n3D1/2δλ1/2βwλ,

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