Abstract

Oscillations that are superimposed on the smooth, exponential decay of light from microcavity modes are observed, and they are characteristic of the temporal beating of adjacent, degeneracy-split azimuthal modes in distorted spheres. The perturbation theory result for the frequency splitting of azimuthal modes in distorted spheres is used to determine the distortion amplitude from the temporal oscillations associated with mode beating. The beating period can be used to determine whether the spectrally measured resonance linewidth Δωl,n is broadened by closely spaced, degeneracy-split azimuthal modes of slightly nonspherical droplets.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. W. Barber, R. K. Chang, eds., Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).
  2. V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
    [CrossRef]
  3. L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
    [CrossRef]
  4. S. Arnold, C. T. Liu, W. B. Witten, J. M. Ramsey, “Room-temperature microparticle-based persistent spectral hole burning memory,” Opt. Lett. 16, 420–422 (1991).
    [CrossRef] [PubMed]
  5. G. Griffel, S. Arnold, D. Taskent, A. Serpengüzel, J. Connolly, N. Morris, “Morphology-dependent resonances of a microsphere–optical fiber system,” Opt. Lett. 21, 695–697 (1996).
    [CrossRef] [PubMed]
  6. H. Mabuchi, H. J. Kimble, “Atom galleries for whispering atoms: binding atoms in stable orbits around an optical resonator,” Opt. Lett. 19, 749–751 (1994).
    [CrossRef] [PubMed]
  7. F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. Sandoghdar, J. M. Raimond, S. Haroche, “Quantized atom–field force at the surface of a microsphere,” Opt. Lett. 19, 1651–1653 (1994).
    [CrossRef] [PubMed]
  8. A. J. Campillo, J. D. Eversole, H-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
    [CrossRef] [PubMed]
  9. J. C. Knight, N. Dubreuil, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, S. Haroche, “Mapping whisperinggallery modes in microspheres with a near-field probe,” Opt. Lett. 20, 1515–1517 (1995).
    [CrossRef] [PubMed]
  10. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5189 (1990).
    [CrossRef] [PubMed]
  11. G. Chen, R. K. Chang, S. C. Hill, P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1269–1271 (1991).
    [CrossRef] [PubMed]
  12. S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
    [CrossRef] [PubMed]
  13. J. C. Swindal, D. H. Leach, R. K. Chang, K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
    [CrossRef] [PubMed]
  14. J.-Z. Zhang, D. H. Leach, R. K. Chang, “Photon lifetime within a droplet: temporal determination of elastic and stimulated Raman scattering,” Opt. Lett. 13, 270–272 (1988).
    [CrossRef] [PubMed]
  15. A. Serpengüzel, G. Chen, R. K. Chang, W.-F. Hsieh, “Heuristic model for the growth and coupling of nonlinear proceses in droplets,” J. Opt. Soc. Am. 9, 871–883 (1992).
    [CrossRef]
  16. H. Lamb, Hydronamics (Dover, New York, 1945), pp. 475 and 639.
  17. T. D. Taylor, A. Acrivos, “On the deformation and drag of a falling viscous drop at low Reynolds number,” J. Fluid Mech. 18, 466–476 (1964).
    [CrossRef]
  18. J. C. Swindal, G. Chen, K. Schaschek, R. K. Chang, “Measurement of the evaporation rates of closely spaced flowing droplets by optical cavity resonances,” Atom. Sprays 6, 331–351 (1996).
  19. G. Chen, M. Mazumder, Y. R. Chemla, A. Serpengüzel, R. K. Chang, S. C. Hill, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).

1996 (2)

G. Griffel, S. Arnold, D. Taskent, A. Serpengüzel, J. Connolly, N. Morris, “Morphology-dependent resonances of a microsphere–optical fiber system,” Opt. Lett. 21, 695–697 (1996).
[CrossRef] [PubMed]

J. C. Swindal, G. Chen, K. Schaschek, R. K. Chang, “Measurement of the evaporation rates of closely spaced flowing droplets by optical cavity resonances,” Atom. Sprays 6, 331–351 (1996).

1995 (1)

1994 (2)

1993 (3)

1992 (1)

A. Serpengüzel, G. Chen, R. K. Chang, W.-F. Hsieh, “Heuristic model for the growth and coupling of nonlinear proceses in droplets,” J. Opt. Soc. Am. 9, 871–883 (1992).
[CrossRef]

1991 (3)

1990 (2)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5189 (1990).
[CrossRef] [PubMed]

S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
[CrossRef] [PubMed]

1989 (1)

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

1988 (1)

1964 (1)

T. D. Taylor, A. Acrivos, “On the deformation and drag of a falling viscous drop at low Reynolds number,” J. Fluid Mech. 18, 466–476 (1964).
[CrossRef]

Acrivos, A.

T. D. Taylor, A. Acrivos, “On the deformation and drag of a falling viscous drop at low Reynolds number,” J. Fluid Mech. 18, 466–476 (1964).
[CrossRef]

Arnold, S.

Barber, P. W.

G. Chen, R. K. Chang, S. C. Hill, P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1269–1271 (1991).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5189 (1990).
[CrossRef] [PubMed]

Braginski, V. B.

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Brune, M.

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Campillo, A. J.

A. J. Campillo, J. D. Eversole, H-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Chang, R. K.

Chemla, Y. R.

Chen, G.

J. C. Swindal, G. Chen, K. Schaschek, R. K. Chang, “Measurement of the evaporation rates of closely spaced flowing droplets by optical cavity resonances,” Atom. Sprays 6, 331–351 (1996).

G. Chen, M. Mazumder, Y. R. Chemla, A. Serpengüzel, R. K. Chang, S. C. Hill, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).

A. Serpengüzel, G. Chen, R. K. Chang, W.-F. Hsieh, “Heuristic model for the growth and coupling of nonlinear proceses in droplets,” J. Opt. Soc. Am. 9, 871–883 (1992).
[CrossRef]

G. Chen, R. K. Chang, S. C. Hill, P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1269–1271 (1991).
[CrossRef] [PubMed]

Collot, L.

F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. Sandoghdar, J. M. Raimond, S. Haroche, “Quantized atom–field force at the surface of a microsphere,” Opt. Lett. 19, 1651–1653 (1994).
[CrossRef] [PubMed]

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Connolly, J.

Dubreuil, N.

Eversole, J. D.

A. J. Campillo, J. D. Eversole, H-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Folan, L. M.

Gorodetsky, M. L.

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Griffel, G.

Hare, J.

Haroche, S.

Hill, S. C.

Hsieh, W.-F.

A. Serpengüzel, G. Chen, R. K. Chang, W.-F. Hsieh, “Heuristic model for the growth and coupling of nonlinear proceses in droplets,” J. Opt. Soc. Am. 9, 871–883 (1992).
[CrossRef]

Ilchenko, V. S.

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Kimble, H. J.

Knight, J. C.

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5189 (1990).
[CrossRef] [PubMed]

Lamb, H.

H. Lamb, Hydronamics (Dover, New York, 1945), pp. 475 and 639.

Leach, D. H.

Lefèvre, V.

Lefèvre-Seguin, V.

J. C. Knight, N. Dubreuil, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, S. Haroche, “Mapping whisperinggallery modes in microspheres with a near-field probe,” Opt. Lett. 20, 1515–1517 (1995).
[CrossRef] [PubMed]

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Leung, P. T.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5189 (1990).
[CrossRef] [PubMed]

Lin, H-B.

A. J. Campillo, J. D. Eversole, H-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Liu, C. T.

Mabuchi, H.

Mazumder, M.

Morris, N.

Raimond, J. M.

Ramsey, J. M.

Sandoghdar, V.

Schaschek, K.

J. C. Swindal, G. Chen, K. Schaschek, R. K. Chang, “Measurement of the evaporation rates of closely spaced flowing droplets by optical cavity resonances,” Atom. Sprays 6, 331–351 (1996).

Serpengüzel, A.

Spock, D. E.

Swindal, J. C.

J. C. Swindal, G. Chen, K. Schaschek, R. K. Chang, “Measurement of the evaporation rates of closely spaced flowing droplets by optical cavity resonances,” Atom. Sprays 6, 331–351 (1996).

J. C. Swindal, D. H. Leach, R. K. Chang, K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[CrossRef] [PubMed]

Taskent, D.

Taylor, T. D.

T. D. Taylor, A. Acrivos, “On the deformation and drag of a falling viscous drop at low Reynolds number,” J. Fluid Mech. 18, 466–476 (1964).
[CrossRef]

Treussart, F.

Weiss, D. S.

Witten, W. B.

Young, K.

J. C. Swindal, D. H. Leach, R. K. Chang, K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5189 (1990).
[CrossRef] [PubMed]

Zhang, J.-Z.

Atom. Sprays (1)

J. C. Swindal, G. Chen, K. Schaschek, R. K. Chang, “Measurement of the evaporation rates of closely spaced flowing droplets by optical cavity resonances,” Atom. Sprays 6, 331–351 (1996).

Europhys. Lett. (1)

L. Collot, V. Lefèvre-Seguin, M. Brune, J. M. Raimond, S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

J. Fluid Mech. (1)

T. D. Taylor, A. Acrivos, “On the deformation and drag of a falling viscous drop at low Reynolds number,” J. Fluid Mech. 18, 466–476 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

A. Serpengüzel, G. Chen, R. K. Chang, W.-F. Hsieh, “Heuristic model for the growth and coupling of nonlinear proceses in droplets,” J. Opt. Soc. Am. 9, 871–883 (1992).
[CrossRef]

Opt. Lett. (10)

G. Chen, M. Mazumder, Y. R. Chemla, A. Serpengüzel, R. K. Chang, S. C. Hill, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).

G. Chen, R. K. Chang, S. C. Hill, P. W. Barber, “Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets,” Opt. Lett. 16, 1269–1271 (1991).
[CrossRef] [PubMed]

S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
[CrossRef] [PubMed]

J. C. Swindal, D. H. Leach, R. K. Chang, K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993).
[CrossRef] [PubMed]

J.-Z. Zhang, D. H. Leach, R. K. Chang, “Photon lifetime within a droplet: temporal determination of elastic and stimulated Raman scattering,” Opt. Lett. 13, 270–272 (1988).
[CrossRef] [PubMed]

S. Arnold, C. T. Liu, W. B. Witten, J. M. Ramsey, “Room-temperature microparticle-based persistent spectral hole burning memory,” Opt. Lett. 16, 420–422 (1991).
[CrossRef] [PubMed]

G. Griffel, S. Arnold, D. Taskent, A. Serpengüzel, J. Connolly, N. Morris, “Morphology-dependent resonances of a microsphere–optical fiber system,” Opt. Lett. 21, 695–697 (1996).
[CrossRef] [PubMed]

H. Mabuchi, H. J. Kimble, “Atom galleries for whispering atoms: binding atoms in stable orbits around an optical resonator,” Opt. Lett. 19, 749–751 (1994).
[CrossRef] [PubMed]

F. Treussart, J. Hare, L. Collot, V. Lefèvre, D. S. Weiss, V. Sandoghdar, J. M. Raimond, S. Haroche, “Quantized atom–field force at the surface of a microsphere,” Opt. Lett. 19, 1651–1653 (1994).
[CrossRef] [PubMed]

J. C. Knight, N. Dubreuil, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, S. Haroche, “Mapping whisperinggallery modes in microspheres with a near-field probe,” Opt. Lett. 20, 1515–1517 (1995).
[CrossRef] [PubMed]

Phys. Lett. A (1)

V. B. Braginski, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Phys. Rev. A (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5189 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. J. Campillo, J. D. Eversole, H-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Other (2)

P. W. Barber, R. K. Chang, eds., Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).

H. Lamb, Hydronamics (Dover, New York, 1945), pp. 475 and 639.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Schematic of an ethanol droplet that is illuminated at the equator by a focused input beam. (b) Droplets were investigated at various distances d between 0.7 and 2.5 cm below the vibrating orifice of the droplet generator. (c) Time profile of the last five of the ten 100-ps, green (λ = 532 nm), input laser separated by 13.2 ns. (d) Time profile of the SRS leaking from B observed at ϕ = 180° for a droplet at d = 1.5 cm. (e) Same as (d) except for a droplet at d = 1.0 cm.

Fig. 2
Fig. 2

Period of the beating (T beat) of equatorial m modes for droplets of various distances from the orifice of the droplet generator.

Fig. 3
Fig. 3

Droplet distortion amplitude |e| (left axis) deduced from the beat period [see Eq. (2)] and the total extent of the frequency splitting (in inverse centimeters) of the m modes, ω(n) - ω(0) (right axis) deduced from |e| [see Eq. (3)], as a function of droplet distance from the orifice of the droplet generator.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ω m = ω 0 1 - e 6 1 - 3 m 2 n n + 1 ,
2 π / T beat = Ω beat = Δ ω m = ω m - ω m - 1 .
| e | = 4 π n n + 1 ω 0 T beat 2 m - 1 ,
ω n - ω 0 = ω 0 | e | 2 n n + 1 .

Metrics