Abstract

We have observed that very high-Q Mie resonances in silica microspheres are split into doublets. This splitting is attributed to internal backscattering that couples the two degenerate whispering-gallery modes propagating in opposite directions along the sphere equator. We have studied this doublet structure by high-resolution spectroscopy. Time-decay measurements have also been performed and show a beat note corresponding to the coupling rate between the clockwise and counterclockwise modes. A simple model of coupled oscillators describes our data well, and the backscattering efficiency that we measure is consistent with what is observed in optical fibers.

© 1995 Optical Society of America

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References

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    [CrossRef]
  3. S. Haroche, in Fundamental Systems in Quantum Optics, Les Houches Summer School, Session LII1, 1990, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 769–940.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1995 (1)

1994 (2)

1993 (2)

G. Chen, M. M. Mazumder, Y. R. Chemla, A. Serpengüzel, R. K. Chang, S. C. Hill, Opt. Lett. 18, 1993 (1993).
[CrossRef] [PubMed]

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

1992 (1)

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

1991 (1)

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

1988 (1)

R. J. C. Spreeuw, J. P. Woerdman, D. Lenstra, Phys. Rev. Lett. 61, 318 (1988).
[CrossRef] [PubMed]

1980 (1)

1979 (1)

1977 (1)

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Benner, R. E.

S. C. Hill, R. E. Benner, in Optical Effects Associated With Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988).

Bjorklund, G. C.

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Brune, M.

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

Chang, R. K.

Chemla, Y. R.

Chen, G.

Collot, L.

Dubreuil, N.

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Giallorenzi, T. G.

Gorodetsky, M. L.

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

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Hare, J.

Haroche, S.

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

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

S. Haroche, in Fundamental Systems in Quantum Optics, Les Houches Summer School, Session LII1, 1990, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 769–940.

Hill, S. C.

G. Chen, M. M. Mazumder, Y. R. Chemla, A. Serpengüzel, R. K. Chang, S. C. Hill, Opt. Lett. 18, 1993 (1993).
[CrossRef] [PubMed]

S. C. Hill, R. E. Benner, in Optical Effects Associated With Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988).

Ilchenko, V. S.

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

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Knight, J. C.

Lai, H. M.

Lam, C. C.

Lefèvre, V.

Lefèvre-Seguin, V.

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

Lenstra, D.

R. J. C. Spreeuw, J. P. Woerdman, D. Lenstra, Phys. Rev. Lett. 61, 318 (1988).
[CrossRef] [PubMed]

Leung, P. T.

Leventhal, D. K.

Li, Y.

B. Lü, Y. Wang, Y. Li, Y. Liu, Opt. Commun. 108, 13 (1994).
[CrossRef]

Lin, S.-C.

Liu, Y.

B. Lü, Y. Wang, Y. Li, Y. Liu, Opt. Commun. 108, 13 (1994).
[CrossRef]

Lü, B.

B. Lü, Y. Wang, Y. Li, Y. Liu, Opt. Commun. 108, 13 (1994).
[CrossRef]

Mazumder, M. M.

Raimond, J. M.

Sandoghdar, V.

Serpengüzel, A.

Spreeuw, R. J. C.

R. J. C. Spreeuw, J. P. Woerdman, D. Lenstra, Phys. Rev. Lett. 61, 318 (1988).
[CrossRef] [PubMed]

Treussart, F.

Wang, Y.

B. Lü, Y. Wang, Y. Li, Y. Liu, Opt. Commun. 108, 13 (1994).
[CrossRef]

Weiss, D. S.

Woerdman, J. P.

R. J. C. Spreeuw, J. P. Woerdman, D. Lenstra, Phys. Rev. Lett. 61, 318 (1988).
[CrossRef] [PubMed]

Young, K.

Appl. Opt. (1)

Europhys. Lett. (1)

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

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

Laser Phys. (1)

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

Opt. Commun. (1)

B. Lü, Y. Wang, Y. Li, Y. Liu, Opt. Commun. 108, 13 (1994).
[CrossRef]

Opt. Lett. (4)

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, Phys. Lett. A 137, 393 (1989).
[CrossRef]

Phys. Rev. Lett. (2)

R. J. C. Spreeuw, J. P. Woerdman, D. Lenstra, Phys. Rev. Lett. 61, 318 (1988).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Other (2)

S. Haroche, in Fundamental Systems in Quantum Optics, Les Houches Summer School, Session LII1, 1990, J. Dalibard, J. M. Raimond, J. Zinn-Justin, eds. (North-Holland, Amsterdam, 1992), pp. 769–940.

S. C. Hill, R. E. Benner, in Optical Effects Associated With Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experiment: PZT, piezoelectric transducer; BS, beam splitter; PMT, photomultiplier tube.

Fig. 2
Fig. 2

Doublet resonances recorded at the same time (a) in the forward direction, by the phase-modulation technique, and (b) in the backward direction. They lie at the same frequencies and show the same splitting Δν = 1 MHz and the same width w = 270 kHz. The forward signal is proportional to the field amplitude, whereas the backward signal is proportional to the CCW field intensity. Fits calculated with our coupled-oscillators model are superimposed onto the signals. The small amount of backward light, reflected from the prism output face and coupled into the sphere (approximately 1%), explains the imbalance of the two peaks.

Fig. 3
Fig. 3

Time-decay signal with the laser sideband locked at the center of the doublet shown in the inset. The two eigenmodes are then equally excited and give rise to a beat note of period T = 0.92 μs according to the fit shown by the smooth solid curve. To get enough signal, we decreased the prism–sphere gap, and the decay time was only 2τ = 0.51 μs. The measured beat-note period and the decay time agree well with the data obtained by continuous spectroscopy. This is clearly seen in the inset, where the Fourier transform of the temporal signal (dashed curve) is superimposed onto the experimental doublet.

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