Abstract

The intensity of elastic scattered light from a single water droplet levitated by the 514.5-nm radiation of an argon-ion laser was recorded as the droplet was slowly evaporating. Abrupt changes in the scattered-light intensity were observed at the positions of morphology-dependent resonances with order numbers less than or equal to 3 and mode numbers between 129 and 165. The corresponding mode numbers and order numbers have been identified. Features attributable to the deformations of the droplet because of the sudden increase of the levitation force near the narrow morphology-dependent resonances were observed.

© 1995 Optical Society of America

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References

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  1. P. W. Barber and R. K. Chang, Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988), and references therein.
  2. A. Ashkin, J. M. Dziedzic, and R. H. Stolen, "Outer diameter measurement of low birefringence optical fibers by a new resonant backscatter technique," Appl. Opt. 20, 2299–2303 (1981).
    [CrossRef] [PubMed]
  3. P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
    [CrossRef]
  4. J. D. Eversole, H.-B. Lin, A. L. Huston, and A. J. Campillo, "Spherical-cavity-mode assignments of optical resonances in microdroplets using elastic scattering," J. Opt. Soc. Am. A 7, 2159–2168 (1990).
    [CrossRef]
  5. T. R. Lettieri, W. D. Jenkins, and D. A. Swyt, "Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio," Appl. Opt. 20, 2799–2805 (1981).
    [CrossRef] [PubMed]
  6. P. Chýlek, V. Ramaswamy, A. Ashkin, and J. M. Dziedzic, "Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data," Appl. Opt. 22, 2302–2307 (1983).
    [CrossRef] [PubMed]
  7. A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, "Precision of light scattering techniques for measuring optical parameters of microdroplets," Appl. Opt. 27, 3974–3983 (1991).
    [CrossRef]
  8. G. Schweiger, "Observation of input and output structural resonances in the Raman spectrum of a single spheroidal dielectric microparticle," Opt. Lett. 15, 156–158 (1990).
    [CrossRef] [PubMed]
  9. G. Schweiger, "Radiation pressure effect on light scattering from optically levitated microparticles" J. Opt. Soc. Am. B 8, 174–176 (1991).
    [CrossRef]
  10. S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, "Lasing droplets: highlighting the liquid–air interface by laser emission," Science 231, 486–488 (1986).
    [CrossRef] [PubMed]
  11. T. K. Fahlen and H. C. Bryant, "Optical back scattering from single water droplets," J. Opt. Soc. Am. 58, 304–310 (1968).
    [CrossRef]
  12. S. Arnold, M. Neuman, and A. B. Pluchino, "Molecular spectroscopy of a single aerosol particle," Opt. Lett. 9, 4–6 (1984).
    [CrossRef] [PubMed]
  13. S. Arnold, K. M. Leung, and A. Pluchino, "Optical bistability of an aerosol particle," Opt. Lett. 11, 800–802 (1986).
    [CrossRef] [PubMed]
  14. S. Arnold and A. B. Pluchino, "Infrared spectrum of a single aerosol particle by photothermal modulation of structural resonances," Appl. Opt. 21, 4194–4196 (1982).
    [CrossRef]
  15. K. H. Fung, I. N. Tang, and H. R. Munkelwitz, "Study of condensational growth of water droplets by Mie resonance spectroscopy," Appl. Opt. 26, 1282–1287 (1987).
    [CrossRef] [PubMed]
  16. C. B. Richardson, R. L. Hightower, and A. L. Pigg, "Optical measurement of the evaporation of sulfuric acid droplets," Appl. Opt. 25, 1226–1229 (1986).
    [CrossRef] [PubMed]
  17. J. H. Eickmans, W.-F. Hsieh, and R. K. Chang, "Laserinduced explosion of H2O droplets: spatially resolved spectra" Opt. Lett. 11, 22–24 (1987).
    [CrossRef]
  18. A. Ashkin and J. M. Dziedzic, "Optical levitation of liquid drops by radiation pressure," Science 187, 1073–1075 (1975).
    [CrossRef] [PubMed]
  19. J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594–4601 (1989).
    [CrossRef]
  20. A. Ashkin and J. M. Dziedzic, "Stability of optical levitation by radiation pressure," Appl. Phys. Lett. 24, 586–588 (1974).
    [CrossRef]
  21. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  22. H. Eisenberg, "Equation for the refractive index of water," J. Chem. Phys. 43, 3887–3892 (1965).
    [CrossRef]
  23. G. M. Hale and M. R. Querry, "Imaginary part of water refractive index a function of λ at 25 °C," Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]
  24. For the sampling rate used, the bl 5 resonances are broad enough to be well resolved and narrow enough to permit accurate determination of the times at which they occur.
  25. C. C. Lam, P. T. Leung, and K. Young, "Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering," J. Opt. Soc. Am. B 9, 1585–1592 (1992).
    [CrossRef]
  26. H. M. Lai, C. C. Lam, P. T. Leung, and K. Young, "Effect of perturbations on the widths of narrow morphology-dependent resonances in Mie scattering," J. Opt. Soc. Am. B 8, 1962–1973 (1991).
    [CrossRef]
  27. For a droplet of 10 μm in radius in air whose viscosity is 180 μP, the resonance-induced deformation becomes significant when the rise time of the levitation force, because of narrow resonance, is ˜ 1 ms or faster.
  28. H.-M. Tzeng, M. M. Long, R. K. Chang, and P. W. Barber, "Laser-induced shape distortions of flowing droplets deduced from morphology-dependent resonances in fluorescence spectra," Opt. Lett. 5, 209–211 (1985).
    [CrossRef]
  29. The results of Ref. 28 were obtained with ethanol. We believe that the relaxation time of water is of the same order as that of ethanol.
  30. S. Arnold, K. M. Leung, and A. Pluchino, "Optical bistability of an aerosol particle," Opt. Lett. 11, 800–802 (1986).
    [CrossRef] [PubMed]
  31. The argon-ion laser was in multimode operation. The theoretical Q values of these fourth-order modes are ˜106 and thus are not high enough to resolve the laser modes.
  32. The angle of 2.5° spanned by the length of the slit cannot explain the large observed values of ΔI either.

1992 (1)

1991 (3)

1990 (2)

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

1987 (2)

J. H. Eickmans, W.-F. Hsieh, and R. K. Chang, "Laserinduced explosion of H2O droplets: spatially resolved spectra" Opt. Lett. 11, 22–24 (1987).
[CrossRef]

K. H. Fung, I. N. Tang, and H. R. Munkelwitz, "Study of condensational growth of water droplets by Mie resonance spectroscopy," Appl. Opt. 26, 1282–1287 (1987).
[CrossRef] [PubMed]

1986 (4)

1985 (1)

H.-M. Tzeng, M. M. Long, R. K. Chang, and P. W. Barber, "Laser-induced shape distortions of flowing droplets deduced from morphology-dependent resonances in fluorescence spectra," Opt. Lett. 5, 209–211 (1985).
[CrossRef]

1984 (1)

1983 (1)

1982 (2)

S. Arnold and A. B. Pluchino, "Infrared spectrum of a single aerosol particle by photothermal modulation of structural resonances," Appl. Opt. 21, 4194–4196 (1982).
[CrossRef]

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

1981 (2)

1975 (1)

A. Ashkin and J. M. Dziedzic, "Optical levitation of liquid drops by radiation pressure," Science 187, 1073–1075 (1975).
[CrossRef] [PubMed]

1974 (1)

A. Ashkin and J. M. Dziedzic, "Stability of optical levitation by radiation pressure," Appl. Phys. Lett. 24, 586–588 (1974).
[CrossRef]

1973 (1)

1968 (1)

1965 (1)

H. Eisenberg, "Equation for the refractive index of water," J. Chem. Phys. 43, 3887–3892 (1965).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

Allen, T. M.

A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, "Precision of light scattering techniques for measuring optical parameters of microdroplets," Appl. Opt. 27, 3974–3983 (1991).
[CrossRef]

Arnold, S.

Ashkin, A.

Barber, P. W.

H.-M. Tzeng, M. M. Long, R. K. Chang, and P. W. Barber, "Laser-induced shape distortions of flowing droplets deduced from morphology-dependent resonances in fluorescence spectra," Opt. Lett. 5, 209–211 (1985).
[CrossRef]

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

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

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

Bryant, H. C.

Campillo, A. J.

Chang, R. K.

J. H. Eickmans, W.-F. Hsieh, and R. K. Chang, "Laserinduced explosion of H2O droplets: spatially resolved spectra" Opt. Lett. 11, 22–24 (1987).
[CrossRef]

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, "Lasing droplets: highlighting the liquid–air interface by laser emission," Science 231, 486–488 (1986).
[CrossRef] [PubMed]

H.-M. Tzeng, M. M. Long, R. K. Chang, and P. W. Barber, "Laser-induced shape distortions of flowing droplets deduced from morphology-dependent resonances in fluorescence spectra," Opt. Lett. 5, 209–211 (1985).
[CrossRef]

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

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

Chýlek, P.

Davis, E. J.

A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, "Precision of light scattering techniques for measuring optical parameters of microdroplets," Appl. Opt. 27, 3974–3983 (1991).
[CrossRef]

Dziedzic, J. M.

Eickmans, J. H.

J. H. Eickmans, W.-F. Hsieh, and R. K. Chang, "Laserinduced explosion of H2O droplets: spatially resolved spectra" Opt. Lett. 11, 22–24 (1987).
[CrossRef]

Eisenberg, H.

H. Eisenberg, "Equation for the refractive index of water," J. Chem. Phys. 43, 3887–3892 (1965).
[CrossRef]

Eversole, J. D.

Fahlen, T. K.

Fung, K. H.

Hale, G. M.

Hightower, R. L.

Hill, S. C.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Hsieh, W.-F.

J. H. Eickmans, W.-F. Hsieh, and R. K. Chang, "Laserinduced explosion of H2O droplets: spatially resolved spectra" Opt. Lett. 11, 22–24 (1987).
[CrossRef]

Huston, A. L.

Jenkins, W. D.

Lai, H. M.

Lam, C. C.

Lettieri, T. R.

Leung, K. M.

Leung, P. T.

Lin, H.-B.

Long, M. M.

H.-M. Tzeng, M. M. Long, R. K. Chang, and P. W. Barber, "Laser-induced shape distortions of flowing droplets deduced from morphology-dependent resonances in fluorescence spectra," Opt. Lett. 5, 209–211 (1985).
[CrossRef]

Munkelwitz, H. R.

Neuman, M.

Owen, J. F.

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

Pigg, A. L.

Pluchino, A.

Pluchino, A. B.

Qian, S.-X.

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, "Lasing droplets: highlighting the liquid–air interface by laser emission," Science 231, 486–488 (1986).
[CrossRef] [PubMed]

Querry, M. R.

Ramaswamy, V.

Ray, A. K.

A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, "Precision of light scattering techniques for measuring optical parameters of microdroplets," Appl. Opt. 27, 3974–3983 (1991).
[CrossRef]

Richardson, C. B.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

Schweiger, G.

Snow, J. B.

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, "Lasing droplets: highlighting the liquid–air interface by laser emission," Science 231, 486–488 (1986).
[CrossRef] [PubMed]

Souyri, A.

A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, "Precision of light scattering techniques for measuring optical parameters of microdroplets," Appl. Opt. 27, 3974–3983 (1991).
[CrossRef]

Stolen, R. H.

Swyt, D. A.

Tang, I. N.

Tzeng, H.-M.

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, "Lasing droplets: highlighting the liquid–air interface by laser emission," Science 231, 486–488 (1986).
[CrossRef] [PubMed]

H.-M. Tzeng, M. M. Long, R. K. Chang, and P. W. Barber, "Laser-induced shape distortions of flowing droplets deduced from morphology-dependent resonances in fluorescence spectra," Opt. Lett. 5, 209–211 (1985).
[CrossRef]

Young, K.

Appl. Opt. (8)

A. K. Ray, A. Souyri, E. J. Davis, and T. M. Allen, "Precision of light scattering techniques for measuring optical parameters of microdroplets," Appl. Opt. 27, 3974–3983 (1991).
[CrossRef]

G. M. Hale and M. R. Querry, "Imaginary part of water refractive index a function of λ at 25 °C," Appl. Opt. 12, 555–563 (1973).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, and R. H. Stolen, "Outer diameter measurement of low birefringence optical fibers by a new resonant backscatter technique," Appl. Opt. 20, 2299–2303 (1981).
[CrossRef] [PubMed]

T. R. Lettieri, W. D. Jenkins, and D. A. Swyt, "Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio," Appl. Opt. 20, 2799–2805 (1981).
[CrossRef] [PubMed]

S. Arnold and A. B. Pluchino, "Infrared spectrum of a single aerosol particle by photothermal modulation of structural resonances," Appl. Opt. 21, 4194–4196 (1982).
[CrossRef]

C. B. Richardson, R. L. Hightower, and A. L. Pigg, "Optical measurement of the evaporation of sulfuric acid droplets," Appl. Opt. 25, 1226–1229 (1986).
[CrossRef] [PubMed]

K. H. Fung, I. N. Tang, and H. R. Munkelwitz, "Study of condensational growth of water droplets by Mie resonance spectroscopy," Appl. Opt. 26, 1282–1287 (1987).
[CrossRef] [PubMed]

P. Chýlek, V. Ramaswamy, A. Ashkin, and J. M. Dziedzic, "Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data," Appl. Opt. 22, 2302–2307 (1983).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

A. Ashkin and J. M. Dziedzic, "Stability of optical levitation by radiation pressure," Appl. Phys. Lett. 24, 586–588 (1974).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

P. W. Barber, J. F. Owen, and R. K. Chang, "Resonant scattering for characterization of axisymmetric dielectric objects," IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, "Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam," J. Appl. Phys. 66, 4594–4601 (1989).
[CrossRef]

J. Chem. Phys. (1)

H. Eisenberg, "Equation for the refractive index of water," J. Chem. Phys. 43, 3887–3892 (1965).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (3)

Opt. Lett. (6)

Science (2)

A. Ashkin and J. M. Dziedzic, "Optical levitation of liquid drops by radiation pressure," Science 187, 1073–1075 (1975).
[CrossRef] [PubMed]

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, "Lasing droplets: highlighting the liquid–air interface by laser emission," Science 231, 486–488 (1986).
[CrossRef] [PubMed]

Other (7)

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

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

The results of Ref. 28 were obtained with ethanol. We believe that the relaxation time of water is of the same order as that of ethanol.

For the sampling rate used, the bl 5 resonances are broad enough to be well resolved and narrow enough to permit accurate determination of the times at which they occur.

The argon-ion laser was in multimode operation. The theoretical Q values of these fourth-order modes are ˜106 and thus are not high enough to resolve the laser modes.

The angle of 2.5° spanned by the length of the slit cannot explain the large observed values of ΔI either.

For a droplet of 10 μm in radius in air whose viscosity is 180 μP, the resonance-induced deformation becomes significant when the rise time of the levitation force, because of narrow resonance, is ˜ 1 ms or faster.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup: M, aluminum mirror; FL1, FL2, convex lenses. The z axis is along the vertical. The laser beam is polarized in the yz plane. Data were collected only when a single water droplet was levitated.

Fig. 2
Fig. 2

Portion of I versus x recorded in Run No. 1 (upper curve) and the theoretical match (lower curve). The arrows indicate the successive fifth-order TE mode resonances.

Fig. 3
Fig. 3

Scattered-light intensity I versus x. Curves with noise: experimental data; the sudden jumps of I are indicated by the short arrows. Smooth solid curves: numerical calculation with n1 = 1.336. Dotted curves: numerical calculation with n1 = 1.334. The calculated narrow resonance features that cannot be resolved in the figure are represented by vertical straight lines. They are labeled and indicated by the long solid arrows for n1 = 1.336 and the dotted arrows for n1 = 1.334. The resonance features that are due to the TM modes obtained by theory are very weak and barely seen. The broad peaks shown in (a), (b), and (c) are due to the b1336, b1296, and b1335 resonances, respectively. For clarity, the dotted curve in (a) has been shifted downward by 200. For an explanation of the horizontal bar in (c), see text.

Fig. 4
Fig. 4

Effect of changing the scattering angle θ. The solid curve is the same as the smooth solid curve shown in Fig. 3(a). Dotted curve: θ = 92.8°, x downshifted by 0.812; dashed–dotted curve: θ = 94.1°, x upshifted by 0.812.

Fig. 5
Fig. 5

The essentially flat region of I before a sudden jump in Run No. 2 (indicated by the horizontal bar). The jump is attributable to the b1571 resonance.

Fig. 6
Fig. 6

Splitting of the b1374 mode recorded in Run No. 1. The smooth curve represents the result of numerical calculation.

Tables (2)

Tables Icon

Table 1 Values of the Fitting Parameters in Eq. (1)

Tables Icon

Table 2 Summary of Scattered-Light Intensity Narrow Features and the Associated Parameters

Equations (4)

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

x ( t ) = x l , 5 - c l ( t - t l ) - e l ( t - t l ) 2 ,
x ( t l - 1 ) = x l - 1 , 5 , x ( t l - 2 ) = x l - 2 , 5 .
θ ( x ) = θ 0 + 0.0065° ( 133 - x ) + 0.0001° ( 133 - x ) 2 ,
x l , i + ( ξ a ) ( 5 4 π ) ( 1 - 3 m 2 l ( l + 1 ) ) x l , i ,             m = - l , - l + 1 , , l .

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